Video-Based Assessment and Learning of Exponential and Logarithmic Functions Across Instructional Modalities

Video-Based Assessment and Learning of Exponential and Logarithmic Functions Across Instructional Modalities | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Video-Based Assessment and Learning of Exponential and Logarithmic Functions Across Instructional Modalities Eunmi Joung, Miran Byun This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8634003/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This mixed-methods study examined video-based assessments across online ( n = 29) and face-to-face (F2F, n = 70) undergraduate mathematics courses. Students created videos explaining exponential and logarithmic functions and their inverse relationship. Data included video project scores (conceptual and procedural knowledge), unit test performance, and open-ended surveys. Conceptual knowledge was comparable across modalities (F2F: M = 27.59; online: M = 26.29, p = .141), but F2F students demonstrated higher procedural knowledge ( M = 39.75 vs. M = 38.02, p = .046, d = 0.54). Despite similar unit test performance, only F2F students’ procedural knowledge correlated with test scores ( r = .34, p = .004), while online students’ video performance showed no relationship to test outcomes ( r = .01, p = .964). Qualitative analysis revealed online students engaged in more extensive preparation through scripting (75% vs. 55%), self-assessment (20% identified weaknesses vs. 3% F2F), and time investment (50% spent 3 + hours vs. 20% F2F). F2F students emphasized retention benefits without elaboration. Findings indicate video-based assessments support conceptual learning across modalities while revealing modality-based differences in procedural knowledge development and transfer. video-based assessment online learning face-to-face instruction procedural knowledge conceptual knowledge exponential functions logarithmic functions Figures Figure 1 Introduction Video-based assessments have resulted in innovative, more applicable methods to analyze teachers’ formative assessment interactions with students (Gotwals et al., 2015 ). Building on this, in this study, video-based assessment refers to the use of student-generated or instructor-provided video recordings as the primary assessment tool for evaluating students’ knowledge, skills, and performance, often coupled with opportunities for feedback and reflection (Blomberg et al., 2013 ; Gaudin & Chaliès, 2015 ; Kaiser et al., 2015 ; Sherin & Dyer, 2017 ). Studies point out that video-based assessments enhance students’ ability to observe and interpret classroom situations, foster the development of pedagogical content knowledge, reflection skills, and professional growth, and contribute to the improvement of their mathematics content knowledge using student video presentations (Kaiser et al., 2015 ; Sherin & Dyer, 2017 ). One mathematical domain where video-based assessment shows particular promise is exponential and logarithmic functions. These functions are important tools in STEM education for modeling growth and decay phenomena. However, undergraduate students experience persistent difficulties with these functions, and no broadly accepted instructional approach has emerged to address these challenges (Kenney, 2005 ; Kuper & Carlson, 2020 ). Research on understanding the inverse relationship between exponential and logarithmic functions is particularly limited. This study examines a video-based assessment designed to support students' understanding of this inverse relationship with a focus on graphing. Purpose of the Study This study explores whether and how video-based assessments affect learning of the inverse relationship between exponential and logarithmic functions across online and face-to-face (F2F) modalities. Video recordings serve as tools to assess students’ procedural and conceptual knowledge in intermediate algebra courses, a prerequisite for students pursuing STEM careers. By comparing these modalities, this research addresses how video-based assessments function in diverse learning environments as institutions increasingly offer mathematics courses in multiple formats. Four research questions guide this investigation: RQ1: How does students’ conceptual knowledge of the inverse relationship between exponential and logarithmic functions, as demonstrated through video projects, differ between online and F2F courses? RQ2: How does students’ procedural knowledge of the inverse relationship between exponential and logarithmic functions, as demonstrated through video projects, differ between online and F2F courses? RQ3: How does unit test performance on exponential and logarithmic functions differ between online and F2F courses, and how do video project scores relate to unit test performance within each modality? RQ4: How do students in online versus F2F courses perceive the effectiveness of video-based assessment for learning exponential and logarithmic functions? Theoretical Framework This study examines how video-based assessment supports learning of exponential and logarithmic functions across online and face-to-face instructional modalities. We integrate four theoretical perspectives that together explain how, why, and under what conditions video-based assessment supports mathematical learning across modalities. First, video creation engages students in self-explanation, the process of articulating understanding in their own words. Self-explanation is a constructive learning activity that promotes deeper understanding than passive or active engagement (Chi & Wylie, 2014 ). This constructive process should operate similarly regardless of modality, as the cognitive demand remains constant. This generates our first prediction: conceptual knowledge should develop comparably across modalities. Second, mathematical proficiency encompasses conceptual knowledge (understanding principles) and procedural knowledge (facility with procedures), which develop iteratively (National Research Council, 2001 ; Rittle-Johnson & Alibali, 1999 ). However, procedural knowledge takes different forms. Instrumental understanding means executing procedures without understanding why they work, while relational understanding means procedural fluency grounded in conceptual comprehension (Skemp, 1976 , 2006 ). These forms have different transfer properties: instrumental knowledge remains situation-bound, while relational knowledge transfers across situations (Greeno, 1998 ). Video projects allow resource access, enabling success through either form. The distinction emerges on timed tests without resources. This generates our second prediction: procedural knowledge development may differ across modalities, and transfer patterns will reveal whether students developed instrumental or relational understanding. Third, online and face-to-face environments provide different regulatory supports (Zimmerman, 2002 ). Face-to-face instruction offers immediate feedback and gestural grounding that may foster relational understanding through iterative practice with correction. Online instruction requires greater self-regulation; students must independently monitor understanding and identify gaps, which may support conceptual understanding but not necessarily procedural fluency. This generates our third prediction: face-to-face students' access to immediate feedback may support relational procedural knowledge that transfers to tests, while online students may develop instrumental procedural knowledge that succeeds on video projects but not tests. To operationalize this framework, three key constructs require explicit definition. Conceptual knowledge encompasses understanding of principles and relationships governing mathematical domains (Rittle-Johnson & Alibali, 1999 ). For exponential and logarithmic functions, this includes understanding why functions are inverses, what properties represent mathematically, and how inverse relationships appear graphically. Procedural knowledge involves facility with procedures and algorithms (National Research Council, 2001 ), but Skemp’s ( 1976 , 2006 ) framework distinguishes instrumental (executing without understanding) from relational (grounded in concepts) procedural knowledge. Because both types can produce correct performance when resources are available, we distinguished them through transfer examination. Transfer refers to applying knowledge across situations (Greeno, 1998 ). We operationalized this as correlations between video project procedural scores and unit test performance within each modality. Significant correlations indicate relational knowledge that transfers; non-significant correlations suggest instrumental knowledge that fails to transfer when supports are removed. Video-Based Assessment: Supporting Knowledge Construction Empirical research demonstrates that video-based assessments support mathematical learning across multiple contexts. Studies examining video-based assessment in mathematics education show that these assessments enable both formative and summative evaluation (Bennett, 2011 ; Borowczak & Burrows, 2016 ; Kippers et al., 2018 ). When implemented formatively, video-based assessments provide opportunities for students to receive feedback on their explanations and revise their understanding (Bennett, 2011 ). Summatively, they evaluate students’ ability to articulate mathematical concepts at the conclusion of instruction (Kippers et al., 2018 ). Studies found that video-based assessment enables educators to identify student misconceptions and analyze mathematical thinking from multiple perspectives (Kaiser et al.,2015; Sherin & Dyer, 2017 ). Gotwals et al. ( 2015 ) demonstrated that reviewing student-created videos helps instructors recognize patterns in student reasoning that might not be visible through traditional assessments. Empirical and meta-analytic research on self-explanation, learning-by-teaching, and formative assessment indicates that video-based assessment supports learning by prompting students to articulate and reflect on their understanding (Chi et al., 2001 ; Fiorella & Mayer, 2013 ; Black & Wiliam, 2010 ). Chi et al. ( 2001 ) found that students who explain content to others demonstrate deeper understanding than those who passively review material. Similarly, Fiorella and Mayer’s ( 2013 ) meta-analysis of learning-by-teaching studies showed that explanation enhances both understanding and retention, with effect sizes ranging from moderate to large across content domains. Black and Wiliam ( 2010 ) further demonstrated that assessment approaches requiring explanation and reflection produce stronger learning gains than traditional testing formats. However, research on video-based assessment has focused predominantly on preservice teacher education programs. Kaiser et al. ( 2015 ) examined preservice teachers’ use of video to analyze classroom instruction, while Sherin and Dyer ( 2017 ) studied how video analysis supports the development of pedagogical knowledge in teacher candidates. To date, there appears to be limited research on video-based assessment in undergraduate mathematics courses outside teacher preparation programs. More critically, there appears to be a lack of systematic research examining whether video-based assessment functions similarly across online and face-to-face instructional modalities. This gap is significant because the instructional conditions under which students prepare and complete video-based assessments vary across modalities, even when the cognitive demand of self-explanation remains consistent. This evidence establishes that video creation engages self-explanation processes, but whether these processes operate similarly across different instructional modalities remains unexplored. Conceptual and Procedural Knowledge: Development and Challenges Studies document how conceptual and procedural knowledge develop in mathematics learning (Rittle-Johnson & Alibali, 1999 ; Rittle-Johnson & Schneider, 2015 ; Dorner et al., 2025 ; Hiebert & Lefevre, 1986 ; Kilpatrick et al., 2001). Rittle-Johnson and Alibali’s ( 1999 ) longitudinal study of elementary students found that conceptual understanding and procedural skill develop iteratively, with gains in one domain predicting subsequent gains in the other. Extending this work, Rittle-Johnson and Schneider ( 2015 ) synthesized evidence across mathematical domains and age groups and concluded that relations between conceptual and procedural knowledge are often bidirectional and iterative, but that the strength and symmetry of these relations depend on instructional conditions and task design. Importantly, this synthesis also documents that conceptual and procedural knowledge can develop independently when instruction emphasizes procedural execution without explicit conceptual connections. Hiebert and Lefevre ( 1986 ) found that students often acquire procedural skills through rote memorization without developing corresponding conceptual understanding, resulting in fragile knowledge that does not transfer to novel problems. The distinction between instrumental and relational procedural understanding has substantial empirical support. Skemp’s ( 1976 , 2006 ) original work documented students who could execute algebraic procedures correctly but could not explain why those procedures worked or when to apply them. Subsequent research has repeatedly confirmed this distinction. Star ( 2005 ) found that students with relational understanding of equation solving could flexibly adapt procedures to different problem types, while students with instrumental understanding could only apply memorized procedures to familiar problem formats. Rittle-Johnson et al. (2001) demonstrated that students taught procedures with conceptual explanations showed better transfer to novel problems than students taught procedures alone. Transfer of Mathematical Knowledge Research on transfer demonstrates that instrumental and relational knowledge differ in how they apply across different situations and assessment formats. Greeno ( 1998 ) demonstrated that knowledge acquired in specific situations often fails to transfer when contextual supports change. Students may succeed on familiar problems but struggle when problem features or available resources differ, even when the underlying mathematics remains identical. This situation-dependence characterizes instrumental knowledge, where students rely on memorized procedures tied to specific formats without understanding underlying principles. In contrast, transfer occurs when students develop understanding of general principles that can be applied flexibly across different problem types and formats. Singley and Anderson ( 1989 ) found that when students understand underlying principles rather than memorizing surface-level procedures, they successfully transfer knowledge to problems with different features. Rittle-Johnson et al. (2017) provided empirical support through classroom experiments, showing that comparing multiple solution methods for the same problem fostered procedural flexibility and transfer to new equation types, whereas focusing on comparing different problem types resulted in more rigid, format-specific knowledge. Instructional design influences transfer outcomes. Renkl et al. (2002) demonstrated that gradually reducing support from complete worked examples to independent problem solving promoted transfer by helping students develop abstract understanding without cognitive overload. Similarly, research on analogical problem solving shows that students who develop abstract schemas transfer solution procedures more successfully than students who focus on superficial problem similarities (Gentner et al., 2003 ). These transfer patterns are particularly relevant for understanding how students apply procedural knowledge across different assessment formats. Video projects that allow resource access and rehearsal provide contextual supports that may enable success through either instrumental or relational knowledge. In contrast, timed tests without resources require independent retrieval and flexible application, revealing whether students developed transferable understanding or situation-bound procedures. Students’ Understanding of Exponential and Logarithmic Functions Research on exponential and logarithmic functions documents persistent student difficulties with both conceptual understanding and procedural facility (Confrey & Smith, 1995 ; Weber, 2016 ; Kuper & Carlson, 2020 ; Makgakga & Sepeng, 2013 ; Campo-Meneses & García-García, 2023 ). Kuper and Carlson ( 2020 ) interviewed 12 undergraduate students and found sustained difficulty reasoning about covariation in exponential functions. Students were unable to explain how changes in the base influence function behavior. Makgakga and Sepeng ( 2013 ) studied 64 South African students and found that only 23% correctly identified the inverse relationship between exponential and logarithmic functions when translating between representations. Campo-Meneses and García-García ( 2023 ) reported that students frequently failed to connect algebraic, graphical, and numerical representations, instead treating each representation as an isolated topic rather than as expressions of a single mathematical relationship. Additional evidence highlights weaknesses in students’ understanding of logarithmic functions. Confrey and Smith ( 1995 ) examined calculus students’ knowledge and found substantial gaps in foundational understanding. On a placement examination, only 48% of students correctly identified the graph of a logarithmic function. Many students confused exponential and logarithmic graphs, could not explain domain and range constraints, and did not recognize that logarithms represent exponents. Weber ( 2016 ) observed that common instructional approaches emphasize procedural tasks such as converting between exponential and logarithmic forms and applying logarithmic rules, with limited attention to conceptual meaning. As a result, students often acquire procedural competence without developing an understanding of what logarithms represent or why the procedures are valid, which restricts their ability to transfer logarithmic reasoning across different representations and problem types. The persistent difficulties students experience with exponential and logarithmic functions, particularly the tendency to develop procedural fluency without conceptual understanding (Weber, 2016 ), make this domain especially appropriate for examining how video-based assessments support different types of knowledge development across instructional modalities. Learning Across Instructional Modalities: Self-Regulation and Support Research comparing online and face-to-face mathematics learning has produced inconsistent findings, indicating that learning outcomes vary according to instructional conditions rather than instructional modality alone (Eggert, 2009 ; Jones, 2013 ; Lynch-Newberg, 2010 ; Ryan, 2001 ; Wiggers et al., 2023 ; Xu & Jaggars, 2011 ). Early studies reported no significant differences in achievement. Ryan ( 2001 ) compared web-based, video-based telecourse, and classroom-based statistics instruction and found no differences in final course grades. Eggert ( 2009 ) similarly reported no significant differences in completion rates between online and classroom-based developmental mathematics courses. In contrast, later studies identified modality-related differences. Lynch-Newberg ( 2010 ) found higher success rates for developmental mathematics students enrolled in online courses than for students in traditional lecture formats. However, Xu and Jaggars ( 2011 ), analyzing data from more than 40,000 community college students, found that enrollment in online mathematics courses was associated with lower grades and reduced course completion. Jones ( 2013 ) found that face-to-face students achieved higher mean grades than online students, although this difference decreased over time. Wiggers et al. ( 2023 ) concluded that well-designed online mathematics instruction can yield outcomes comparable to face-to-face instruction, while noting that average achievement in online courses remains slightly lower. These mixed findings suggest that direct comparisons of instructional modality obscure important differences in learning conditions. Face-to-face instruction provides immediate instructor feedback during problem solving, which supports learning by identifying errors early and reducing repeated practice of incorrect procedures (Francis et al., 2019 ). Alibali and Nathan ( 2012 ) found that mathematics instructors frequently use gestures to connect symbolic notation to physical actions, supporting conceptual understanding and procedural execution. These gestures include pointing gestures that link related information, representational gestures that model mathematical actions, and metaphoric gestures that convey abstract processes. This immediate feedback and gestural support may promote procedural knowledge that is grounded in conceptual understanding and therefore more likely to transfer. Online mathematics instruction creates different learning conditions. Ward et al. ( 2020 ) found that online students must regulate their learning more independently, monitoring understanding and progress without immediate instructor observation. Broadbent and Poon ( 2015 ) reported that successful online learners demonstrate strong metacognitive monitoring and strategic planning skills, while students with weaker self-regulation skills experience greater difficulty in online environments. Research also indicates that online mathematics students spend more time on coursework than face-to-face students. Artino and Stephens ( 2009 , as cited in Al-Zohbi & Pilotti, 2022) and Park ( 2024 ) found that online learners spent substantially more time on learning activities, reflecting the increased planning and monitoring required in the absence of real-time instructional guidance. Increased time investment alone, however, does not guarantee improved learning outcomes. Differences in mathematical communication further distinguish instructional modalities. Jaggars ( 2014 ) found that communication in online mathematics courses occurs primarily through written text, with limited opportunities for synchronous verbal interaction. In contrast, face-to-face courses provide frequent verbal exchanges between students and instructors. This difference is relevant for assessments requiring spoken explanation. Research found that verbal explanation supports deeper learning than written explanation alone, suggesting that students’ prior opportunities for oral mathematical communication may influence performance on explanation-based assessments (Chi et al., 2001 ; Roscoe & Chi, 2007 ). Despite extensive research comparing online and face-to-face mathematics learning, assessment practices requiring explanation remain largely unexamined across modalities. Most comparative studies focus on traditional assessments such as exams, quizzes, and homework. Video-based assessments in online courses may face additional challenges. The literature reveals three well-established findings: video-based assessment supports mathematical learning through self-explanation; conceptual and procedural knowledge are distinct constructs with different development pathways and transfer properties; and online and face-to-face mathematics learning differ in regulatory supports and communication opportunities. However, these three lines of research have not been integrated: prior research has examined video-based assessment and modality differences independently, with little is known about how video-based assessments across modalities for mathematically demanding topics requiring both conceptual understanding and procedural fluency. This gap has important implications. Mathematics courses are increasingly offered across instructional modalities, often using common assessments without evidence that they function equivalently. Although video-based assessment may support conceptual understanding through self-explanation, its effects on procedural knowledge development and transfer may depend on modality-specific regulatory supports and communication practices. This study addresses this gap by examining how video-based assessments of exponential and logarithmic functions operate in online versus face-to-face intermediate algebra courses. Drawing on the integrated theoretical framework, this research investigates four questions. First, does video-based assessment support conceptual knowledge development similarly across modalities, as predicted by theories of self-explanation and constructive learning? Second, does procedural knowledge development differ across modalities, as self-regulated learning theory suggests? Third, do different modalities foster different types of procedural knowledge (instrumental versus relational) as evidenced by transfer patterns from video projects to unit tests? Fourth, how do students in each modality experience and approach video project creation, and do these experiences reflect predicted differences in self-regulatory demands between modalities? By examining both performance outcomes and student experiences, this research provides empirical evidence on how video-based assessment supports mathematical learning across instructional modalities. Methods A mixed-methods comparative design was used to investigate students’ understanding of the inverse relationship between exponential and logarithmic functions across online and F2F instructional modalities. Quantitative data included video project scores (conceptual and procedural knowledge) and unit test performance. Qualitative data were collected through open-ended survey questions examining student perceptions of the video project. Participants Participants were recruited from intermediate algebra courses at a 4-year university in the Western United States during Fall 2023, Spring 2024, and Summer 2024. All students provided informed consent before participating in the study. The final sample consisted of 99 students enrolled in either online ( n = 29) or F2F ( n = 70) sections of the course. Among the participants, 56 (56.6%) identified as male and 43 (43.4%) identified as female. Gender distribution differed notably across modalities: the online group included 10 males (34.5%) and 19 females (65.5%), while the F2F group included 46 males (65.7%) and 24 females (34.3%). The smaller online sample size ( n = 29) reflected fewer online course sections offered rather than differential consent rates. Across the three semesters, two online sections enrolled approximately 58 students, with 29 (50%) providing consent. In comparison, four F2F sections enrolled approximately 120 students, with 70 (58%) providing consent. The similar consent rates across modalities (50% vs. 58%) suggest that selection bias due to nonresponse is unlikely to differentially affect the two groups. Chi-square analysis confirmed no significant difference in consent rates between modalities ( χ² = 1.01, p = .31), indicating that selection bias due to differential nonresponse is unlikely. Intermediate Algebra is an undergraduate mathematics course and a prerequisite for higher-level mathematics courses for students pursuing careers in STEM fields. Topics covered include linear, polynomial, quadratic, exponential, logarithmic, and rational functions from algebraic and graphical perspectives. The course used Lumen Online Homework Manager (OHM), a digital course platform, rather than a traditional textbook. Procedure Students in both online and F2F sections completed a video project assignment involving exponential and logarithmic functions. Students received a problem set of nine problems requiring them to find key properties of given functions (domain, range, asymptotes, inverse function using algebraic methods, and x- and y-intercepts) and sketch graphs to visualize the inverse relationship between exponential and logarithmic functions. While recording themselves on video, students solved these problems and explained their mathematical reasoning. Videos were limited to approximately 5 minutes and submitted through Canvas. Following the video project, students took a Unit Test covering exponential and logarithmic functions. The test used the same problem types as the video project but with different numerical values and was worth 15 points total. Students were then invited to complete an optional follow-up survey exploring their experiences with the video project. Of the 99 participants, 80 students (20 online, 60 F2F) completed the survey, which included five open-ended questions addressing preparation strategies, engagement, challenges, confidence, and time investment. All students provided informed consent for their video project scores, unit test scores, and survey responses to be used for research purposes. Obtaining informed consent from online students presented additional logistical challenges, as consent forms were distributed and collected electronically rather than in person. Instruments Three instruments were used to examine students’ understanding of the inverse relationship between exponential and logarithmic functions: (a) a problem set with rubric for the video project, (b) an open-ended survey questionnaire assessing students’ experiences with the video project, and (c) a unit exam assessing retention of mathematical knowledge. Students completed a problem set requiring them to find properties of exponential and logarithmic functions (domain, range, asymptotes, x- and y-intercepts, and inverse functions) and sketch graphs of these functions while recording themselves using tools such as Kaltura, Windows Media Player, or QuickTime Player. Rubric . Videos were assessed using a 100-point rubric with two components. Video skills (20 points) evaluated presentation quality, including structure (introductions, conclusions, transitions) and delivery (pacing, editing). Content knowledge (80 points; see Fig. 1) assessed conceptual understanding (36 points) and procedural knowledge (44 points). Conceptual knowledge measured students’ ability to explain the meaning of domains, ranges, asymptotes, and intercepts; describe relationships between functions and their inverses; and interpret graphical representations. Procedural knowledge evaluated students’ ability to correctly calculate these same elements using appropriate mathematical notation, find inverse functions algebraically, and produce accurate graphs showing all key features. The rubric also provided personalized feedback to clarify concepts and direct students to additional resources. Follow-up Survey . An open-ended follow-up survey was used to collect students’ perceptions of their experience with the video project. The following questions were included in the survey: How did you prepare to complete this video project assignment to solve the problem set, and what resources did you use in your problem-solving process? Did you find the video project more engaging than traditional assignments? Why or why not? Was there anything you found particularly challenging about creating a video presentation? How confident do you feel about the material learned after completing this video project compared to traditional assignments? How much time did you spend on preparing and creating the video presentation? Retention Measure . After completing the video project, students took a unit exam with problems on the inverse relationship between exponential and logarithmic functions. The exam used the same problem types as the video project but with different numerical values. Data Analysis These analytical choices directly operationalize the theoretical constructs and predictions outlined in our framework. To address RQ1 regarding conceptual knowledge, descriptive statistics were calculated for video project conceptual knowledge scores (36 points possible) for both online and F2F groups. An independent samples t -test examined differences between groups. Effect sizes (Cohen’s d ) were calculated to assess the practical significance of any difference. Prior to conducting the t -test, assumptions of normality and homogeneity of variance were tested using Shapiro-Wilk and Levene’s tests, respectively, and were satisfied. To address RQ2 regarding procedural knowledge, parallel analyses were conducted using the procedural knowledge scores from the video project rubric (44 points possible). Descriptive statistics and an independent samples t-test for group comparisons were performed for both online and F2F sections. Effect sizes (Cohen’s d ) were calculated to assess practical significance. To address RQ3 regarding unit test performance and relationships among variables, an independent samples t-test was conducted to examine the difference in mean unit test scores between online and F2F groups. Effect sizes (Cohen’s d ) were calculated to assess practical significance. Additionally, Pearson correlation analyses were conducted separately for each instructional group to examine the relationships among video project conceptual knowledge scores, procedural knowledge scores, and unit test performance. Correlation matrices were generated to identify patterns of association within each learning modality. To address RQ4 regarding student perceptions, responses from open-ended follow-up survey questionnaires were analyzed using six-phase framework for thematic analysis (Braun & Clarke, 2006): (a) familiarization with data, (b) generating initial codes, (c) searching for themes, (d) reviewing themes, (e) defining and naming themes, and (f) producing the report. To identify potential differences in perceptions across instructional modalities, responses from online and F2F students were analyzed separately, allowing for both within-group theme identification and between-group comparison of emerging patterns. The analysis proceeded iteratively, with constant comparison used to identify themes common to both groups as well as modality-specific themes. To establish coding reliability, two researchers independently coded a preliminary subset of responses and met to discuss emergent themes, resolve discrepancies, and develop a unified coding scheme. Following codebook refinement, both researchers independently coded all responses to assess inter-rater reliability. Cohen’s kappa coefficients ranged from moderate to almost perfect agreement across both modalities (see Table 1 ). Any remaining discrepancies were resolved through consensus discussion between the two researchers. Table 1 Inter-Rater Reliability Coefficients by Question and Course Modality Question Online Course F2F Course Q1 0.886 0.687 Q2 0.505 0.452 Q3 0.860 0.953 Q4 0.640 0.783 Q5 0.855 0.910 M 0.749 0.757 Note. All values represent Cohen’s kappa coefficients. Interpretation based on Landis and Koch (1977): κ < 0.00 = poor, 0.00–0.20 = slight, 0.21–0.40 = fair, 0.41–0.60 = moderate, 0.61–0.80 = substantial, 0.81–1.00 = almost perfect. Results RQ1: Conceptual Knowledge An independent samples t -test was conducted to compare conceptual knowledge scores between online and F2F groups. Descriptive statistics are presented in Table 2 . The F2F group ( M = 27.59, SD = 3.52) scored slightly higher than the online group ( M = 26.29, SD = 4.78), but this difference was not statistically significant, t( 97) = 1.484, p = .141, d = 0.33. The small-to-medium effect size suggests a minor practical difference favoring F2F instruction. Table 2 Descriptive Statistics for Video Project Conceptual Knowledge Scores by Instructional Group Group n M SD df t p d F2F 70 27.59 3.52 97 1.484 .141 .33 Online 29 26.29 4.78 Note. F2F = face-to-face. Cohen’s d calculated using pooled standard deviation. RQ2: Procedural Knowledge An independent samples t -test was conducted to compare procedural knowledge scores between online and F2F groups. Descriptive statistics are presented in Table 3 . The F2F group ( M = 39.75, SD = 3.80) scored significantly higher than the online group ( M = 38.02, SD = 3.91), t (97) = 2.02, p = .046, d = 0.54. This medium effect size indicates a meaningful practical difference, suggesting that video projects may be more effective for developing procedural knowledge in F2F courses compared to online courses. Table 3 Descriptive Statistics for Video Project Procedural Knowledge Scores by Instructional Group Group n M SD df t p d F2F 70 39.75 3.80 97 2.02 .046 .54 Online 29 38.02 3.91 RQ3: Unit Test Performance and Relationships Among Variables An independent samples t -test was conducted to compare unit test performance on exponential and logarithmic functions between online and F2F groups after completing video projects. Descriptive statistics are presented in Table 4 . Table 4 Descriptive Statistics for Unit Test Performance by Instructional Group Group n M SD df t p d F2F 70 10.35 3.61 97 \(\:-\) 1.85 .068 −0.44 Online 29 11.74 2.98 Note. Cohen’s d calculated using pooled standard deviation. Maximum possible score = 15 points. The online group ( M = 11.74, SD = 2.98) scored slightly higher than the F2F group ( M = 10.35, SD = 3.61), but this difference was not statistically significant, t (97) = \(\:-\) 1.85, p = .068, d = − 0.44. The small effect size suggests a minor practical difference favoring online instruction, though the groups performed similarly overall on the unit test. To examine the relationships among video project performance and unit test outcomes, Pearson correlation analyses were conducted separately for each group. Correlation matrices are presented in Tables 5 and 6 . For the online group ( see Table 5 ), conceptual knowledge and procedural knowledge were moderately positively correlated ( r = .45, p = .017), suggesting that students who performed well on conceptual tasks also tended to perform well on procedural tasks. However, neither conceptual knowledge ( r = .17, p = .379) nor procedural knowledge ( r = .01, p = .964) showed significant correlations with unit test performance. These findings indicate that video project performance in online courses was not predictive of subsequent unit test scores. Table 5 Intercorrelations Among Video Project Scores and Unit Test Performance for Online Group Online 1 2 3 1. Conceptual Knowledge — 2. Procedural Knowledge .45* — 3. Unit Test Performance .17 .01 — Note. n = 29. * p < .05. For the F2F group (see Table 6 ), conceptual knowledge and procedural knowledge were also moderately positively correlated ( r = .45, p < .001), demonstrating a similar pattern to the online group. Notably, procedural knowledge showed a significant moderate positive correlation with unit test performance ( r = .34, p = .004), indicating that students who demonstrated stronger procedural skills on video projects tended to perform better on the unit test. However, conceptual knowledge was not significantly correlated with unit test performance ( r = .06, p = .628). Table 6 Intercorrelations Among Video Project Scores and Unit Test Performance for F2F Group F2F 1 2 3 1. Conceptual Knowledge — 2. Procedural Knowledge .45*** — 3. Unit Test Performance .06 .34** — Note. n = 70. ** p < .01. *** p < .001. RQ4: Student Perceptions of Video-Based Assessment Effectiveness by Course Modality To address RQ4, we analyzed student responses to five open-ended questions about their experiences with the video project. Table 7 presents themes related to student preparation strategies and resource use for the video project. Table 7 Open-Ended Question 1: Themes in Student Preparation and Resource Use Themes Description Online F2F Example from Student Response 1–1: Review of Instructional Materials Students reviewed their notebooks, textbooks, class notes, or course materials to prepare for their video project 70% 65% Online : “To prepare to complete this video project assignment I read through all of my notes that had to do with the assigned questions and solved for those questions. I used the textbook, past homework assignments and my notes as resources” F2F : “For this project, I utilized the notes I'd taken in class and the examples I'd completed in the Canvas assignments. Therefore, I used the course materials and resources available in Canvas.” 1–2: External Resources Students used resources outside the course materials, such as Photomath, ChatGPT, YouTube videos, or other online tools. 55% 58% Online : “Math is always a struggle for me, I did find this difficult. I asked my coworkers to teach me the concepts. I also relooked at the assignments and the chapter reading/practices/ I watched YouTube videos for clarity” F2F : “I used chat ChatGPT to come up with problems for me to solve” 1–3: Preparing to Explain Students prepared the video presentation by writing scripts, rehearsing explanations, organizing steps for clarity, or practicing their verbal delivery. 75% 55% Online : “I prepared by writing out step by step for each question being asked and then reviewing my steps to simplify them when explaining. I used Desmos to help with graphing both the original equation and the inverse equation.” F2F : “I practiced problems from our class worksheets to make sure I didn’t mess up the steps in the video and had good point to talk about.” 1–4: Interact with others Students worked with classmates or tutors in the Math Lab. 0% 15% Online : None F2F : “I prepared by going to the math lab and working with classmates to study and learn the material.” Note. Students often mentioned multiple preparation and resource use strategies in their responses (e.g., reviewing notes while also using YouTube videos and practicing their explanation). Therefore, percentages exceed 100% as codes are not mutually exclusive. Online N = 20; F2F N = 60. Both online and F2F students reported similar patterns of preparation, with the majority reviewing instructional materials (online: 70%; F2F: 65%) and approximately half using external resources such as ChatGPT, YouTube, or Photomath (online: 55%; F2F: 58%). The primary difference between modalities emerged in the Preparing to Explain theme (1–3), which was substantially more prevalent among online students (75%) compared to F2F students (55%). Online students frequently reported writing scripts, rehearsing explanations, and organizing their presentation strategies before recording. A notable finding was the Interact with Others theme (1–4), which appeared exclusively among F2F students (15%), who reported working with classmates or tutors in the Math Lab to prepare their videos. This resource was not mentioned by any online students. Table 8 presents themes related to student engagement with the video project. The majority of students in both modalities found the video project more engaging than traditional assignments, though patterns of engagement differed by modality. The most prevalent theme was Deeper Understanding Required (1-a), reported by 70% online and 58% F2F students, respectively. Notable differences emerged in several themes. Creative Engagement (1-b) was more common among F2F students (23%) than online students (10%), with F2F students appreciating the different form of assignment. Reflection on Weaknesses (1-e) was substantially higher among online students (20%) compared to F2F students (3%), suggesting online students used the video project to identify areas needing improvement. Better Retention (1-g) appeared exclusively among F2F students (10%), with no online students mentioning this benefit. Among students who did not find the video more engaging, the primary concern was Time-Consuming Technical Issues (2-b), reported by 2% of F2F students but absent among online student responses. Table 8 Open-Ended Question 2: Comparison of Student Engagement Themes Themes Description Online F2F Example from student responses YES: MORE ENGAGING 1-a: Deeper understanding required Video required deeper understanding to explain concepts 70% 58% Online : “I found it more engaging because I had to know the information well enough to teach it, so I had to redo the questions multiple times.” F2F :” I think it was pretty engaging and made sure that we could explain and understand these concepts.” 1-b: Creative engagement Video project allowed different ways to present content 10% 23% Online : “I would prefer to do something like this rather than traditional assignments, It is interactive, and traditional assignments feel overdone and repetitive.” F2F : “It was engaging in a different way; I wouldn't say it was more engaging...” 1-c: Showing work clearly Students showed their problem-solving written work clearly while explaining 5% 5% Onlin e: “…it allowed us to visually show what we know rather than just from work written on a paper. It allows our teachers to actually hear us when we are going step by step and see how we process what is being taught to us” F2F : “The project was very engaging sense I had to write out all of the equations and film myself explaining it all.” 1-d: Confidence/ comfortable Completing this project increased students’ confidence and comfort with the content 10% 2% Online : “I did because I wanted to make it perfect so I made sure I understood what I was solving so I could present it professionally and it makes me proud when I know what I am talking about” F2F : “...What most compelled me to do was to show off my skills and what I learned in the unit. Of course, it wasn’t perfect, but I felt good...” 1-e: Reflection on weaknesses Video project helped them identify area needed improvement 20% 3% Online : “…it did help me to identify what I need improvement on…” F2F: “... explaining them allowed me to pay closer attention to the mistakes and errors I made during the process.” 1-f: Enjoyable and fun Students found this project enjoyable and fun 20% 17% Online : “Yes, I thoroughly enjoyed creating the video and watching it back over to see my thought process on things and to see how much sense I made” F2F :” It was more engaging, I found it pretty fun.” 1-g: Better retention Explaining improved content retention 0% 10% Online : None F2F : “...This helps improve the memorization of formulas and solution methods...” 1-h: Challenging Video project was challenging but engaging 15% 15% Online : “Yes, it was more engaging, but there was an added level of difficulty to match the rubric” F2F : “I found it much more engaging, and a little bit more frustrating because I had to create a video for this assignment where I show I my work....” 1-i: No further explanation Students provided no reason why engaging 0% 2% Online : None F2F: “ I liked the video project.” NO: NOT MORE ENGAGING 2-a: Just change from routine Student found it different but not significantly more engaging 5% 0% Online : “ …Just change from routine” F2F : None 2-b Time consuming because of tech issue or difficulties Technical or preparing difficulties reduced engagement 0% 2% Online : None F2F : “It definitely took a lot more out of me to complete this assignment I wasn't the biggest fan of having to do a lot of research for something that doesn't involve learning math, like spending an hour trying to figure out how I can record and things of that nature.” 2-c: Speaking replaces written work Video simply substituted verbal for written explanation 5% 0% Online : “I found the project to be about the same engagement as compared to traditional assignments. I think if we were to have more problems to explain, then I think it would make it more engaging and encouraging to do more work to present” F2F : none Note. Percentages exceed 100% because students could mention multiple preparation strategies (codes are not mutually exclusive). Online N = 20; F2F N = 60. Table 9 presents challenges students encountered when creating their video presentations. Table 9 Open-Ended Question 3: Challenges in Creating Video Presentation Themes Description Online F2F Example from Student Responses 3-a: Time constraint Students struggled to fit content within 5-minute time limit 45% 43% Online : “…It was hard to show all of my work with every step in just a 5 min time frame.” F2F :“The most challenging part of the video project for me was trying to keep the video within that 3–5 minute mark...” 3-b: Technical difficulties Students encountered technology or recording issues 25% 37% Online : “I found making the video the hardest part, even though the math was hard I just couldn't get my video to look good” F2F : “I wasn’t sure how it should have been filmed so I had to refill and submit it.” 3-c: Remembering rubric requirement Students found it difficult to remember all rubric points while recording 5% 8% Online : “The only thing I found really challenging was trying to remember all the points I wanted to hit on the rubric because it is hard to remember it all when I was talking” F2F : “The thing I found challenging was remembering everything, like remembering how to solve each problem.” 3-d: Explaining content clearly Students struggled to explain concepts clearly and concisely 40% 13% Online : “Creating the content was difficult, trying to figure out. My explanation tends to be long, and I can work on my presentation skills to make it more concise.” F2F : “The most challenging thing about the video presentation was smoothly explaining everything in the allotted amount of time.” 3-e: Anxiety Students felt anxious or nervous about recording themselves. 20% 15% Online : “I just get anxious when it comes to presenting and math isn't my strong suit so I second guess myself.” F2F : “I get anxious when doing videos for assignments, presentations, and just things that other people will see so doing the video what challenging in general,” 3-f: Time-consuming Students spent more time than expected on this project. 0% 13% Online : None F2F : “...Another obstacle was the time it took to record and re-record sections to make them clearer.” 3-g: No challenges Students did not find anything challenging. 5% 8% Online : “I do not think I found anything too challenging about creating this video presentation” F2F : “No i felt like the assignment wasn't difficult and rather fun” Note. Students often mentioned multiple challenges in their responses. Percentages may exceed 100% because codes are not mutually exclusive. Online N = 20; F2F N = 60. The most commonly reported challenge across both modalities was Time Constraint (3-a), with online students (45%) and F2F students (43%) struggling to fit content within the 5-minute time limit. The second most prevalent challenge was Explaining Content Clearly (3-d), with online students reporting this substantially more frequently (40% vs. 13%). Online students found it more difficult to articulate explanations concisely and clearly on camera. Notably, Technical Difficulties (3-b) were more common among F2F students (37% vs. 25%), with F2F students reporting challenges with technology and recording issues. Anxiety (3-e) was somewhat higher among online students (20% vs. 15%), with students expressing nervousness about recording themselves. Time-Consuming (3-f) was reported exclusively by F2F students (13% vs. 0%). Interestingly, a small percentage of students in both groups reported No Challenges (3-g: online 5%, F2F 8%). Table 10 presents themes related to student confidence in solving similar problems after completing the video project. Most students in both modalities reported feeling very confident, though online students demonstrated substantially higher confidence levels. Understanding Both Conceptually and in Depth (4-1-a) was the most prevalent theme among online students (70%) and F2F students (50%). Online students expressed strong confidence in their ability to solve similar problems, attributing this to the deep understanding gained through teaching the material. Helped Knowledge Retention (4-1-d) appeared more frequently among online students (20%) than F2F students (7%). Notably, the theme No Further Explanation (4-1-e) appeared exclusively among F2F students (23%), who expressed confidence without elaborating on the reasons. Within the “Somewhat Confident” category, small percentages of F2F students indicated they Still Need Practice (8%) or felt confident Only for Similar Problems in the Project (3%). Among students who were “Not More Confident,” small percentages indicated the project had Same as a Standard Assignment (4-3-a) (online 0% vs. F2F 7%) or that they Still Cannot Solve Without Class Resources (4-3-b) (online 0% vs. F2F 2%). Table 11 presents the time students spent preparing and creating their video presentations. The most common time range for both modalities was Between 1 and 3 Hours (5-b: online 45%, F2F 52%). The second most prevalent range was More Than 6 Hours (5-d), with online students reporting this substantially more frequently (25% vs. 5%). Notable differences emerged across time categories. Online students were more likely to spend extended time: 25% spent 3–6 Hours (5-c) versus 15% of F2F students, and 25% spent More Than 6 Hours (5-d) versus 5% of F2F students. Conversely, F2F students more frequently completed assignments in Less Than 1 Hour (5-a: 13% vs. 5%). Overall, online students invested considerably more time in the video project than F2F students, with 50% of online students spending more than 3 hours compared to 20% of F2F students spending comparable time. Table 10 Open-Ended Question 4: Student Confidence in Solving Similar Problems Themes Description Online F2F Example from Student Responses Very Confident 4-1-a: Understanding both conceptually and in depth Students gained deep conceptual understanding through teaching. 70% 50% Online : “I feel very confident that I know the material because I was able to teach it.” F2F : “I feel much more confident than I did previously. It makes me feel better about taking the exam.” 4-1-b: Requiring a lot of practice The project required a lot of practice, which helped build confidence in learning. 0% 7% Online : None F2F : “I feel pretty confident and this helped me practice a lot.” 4-1-c: identify areas for improvement Identifying areas for improvement from the video gave students the opportunity to correct themselves. 0% 2% Online : None F2F : “I feel more confident with the material after completing the video project. ...helped me consolidate my understanding and identify areas where I needed to clarify my knowledge.” 4-1-d: Helped knowledge retention Video project helped retain knowledge 20% 7% Online : “I feel more confident, which allowed me to dive deeper into the set, and explaining helped me retain the information better.” F2F : “I am pretty confident with what i know and my knowledge retention” 4-1-e: No further explanation Students provided no explanation 0% 23% Online : None F2F : “A lot more confident that before!” Somewhat Confident 4-2-a: Still need practice Students gained confidence while recognizing the need for further practice. 0% 8% Online : None F2F : “I feel a little bit more prepared, but I still need to study.” 4-2-b: Only for similar questions in the project Confidence limited to similar problems 0% 3% Online : None F2F : “I feel a little more confident about the material I learned after completing this project. I also believe I can answer another question that is similar to the one that was provided for this project.” 4-2-c: Remember better Students built confidence by improving their memory 0% 2% Online : None F2F: “... I do think it'll help me remember for the test, though.” Not More Confident 4-3-a: Same as a standard assignment The project has the same effect as a standard assignment. 0% 7% Online : None F2F : “I feel the same, maybe a little more refreshed on the topic but that is all.” 4-3-b: Still cannot solve without class resources Students still need class resources to solve 0% 2% Online : None F2F : “I still feel like unless I look at my notes I'm not sure how to solve for it.” Note. Students within each confidence level could mention multiple reasons. Percentages within sub-themes may exceed the total for that confidence level because codes are not mutually exclusive. Table 11 Open-Ended Question 5: Time Spent on Video Presentation Themes Description Online F2F Example from Student Responses 5-a: Less than 1 hour Students spent less than 1 hour 5% 13% Online : “I spent about an hour preparing for the assignment, mostly just polishing up on my ability to solve” F2F : “I spent around 30 minutes.” 5-b: Between 1 and 3 hours Students spent 1–3 hours 45% 52% Online : “I would say I spent about 2 hours overall preparing, explaining, and editing the video to make sure it fit the time frame and that everything was explained to the best of my abilities.” F2F : “In total I probably spent about an hour and a half on this assignment.” 5-c: 3–6 hours Students spent 3–6 hours 25% 15% Online : “For preparation, it took me about 45 minutes to do the worksheet, and all the work. It took about 3 hours for me to put the presentation together, and it took me about 30 minutes to film, as I needed a couple of takes!” F2F : “I spent about 4 hours learning the material and explaining it to my classmates to be able to take the video.” 5-d: More than 6 hours Students spent more than 6 hours 25% 5% Online : “It took me about a day to prepare for this video project. I worked out the 9 questions for a few hours and then it took about two hours to record. I kept messing up the videos so it took me a while since I had to start over numerous times.” F2F : “I think I spent between 8 hours, about 4 hours solving the exercise, organizing, and planning, 1 hour recording, and about 3 practicing my speech.” Discussion This study examines how video-based assessments function in undergraduate mathematics courses across online and F2F modalities, integrating four theoretical perspectives: self-explanation, iterative knowledge development, instrumental versus relational understanding, and self-regulation. Three key findings emerged that illuminate these theoretical predictions. First, video-based assessments supported conceptual understanding equally well in both modalities, consistent with self-explanation theory predicting that constructive learning processes operate similarly regardless of instructional format. Second, F2F students demonstrated stronger procedural knowledge development, consistent with predictions about differential regulatory supports across modalities. Third, transfer patterns revealed modality-based differences in the type of procedural knowledge developed. F2F students showed significant correlations between video and test performance, suggesting relational procedural understanding, while online students showed non-significant correlations, suggesting instrumental procedural knowledge that succeeded when resources were available but did not transfer to timed assessments. These patterns reveal that video-based assessment operates differently across instructional modalities in theoretically predictable ways. No statistically significant difference emerged in conceptual knowledge scores between F2F and online students who completed video projects, though a small-to-medium effect size favored F2F instruction ( d = 0.33). This equivalence indicates that video projects supported conceptual learning similarly across modalities, consistent with research demonstrating that appropriately designed online and F2F mathematics instruction can yield comparable outcomes (Edwards et al., 2013 ; Russell et al., 2009 ). The similarity in conceptual knowledge may reflect the self-explaining demands inherent in video creation, which require students to articulate mathematical ideas in their own words regardless of modality (Niess & Walker, 2010 ). Within the ICAP framework, self-explaining constitutes a constructive learning activity that promotes deeper conceptual understanding than passive or active engagement (Chi & Wylie, 2014 ). Both groups demonstrated comparable gains (F2F: M = 27.59; online: M = 26.29, p = .141, d = 0.33), though the effect size suggests F2F interaction may confer modest benefits. In contrast, F2F students demonstrated significantly higher procedural knowledge ( M = 39.75 vs. M = 38.02, p = .046, d = 0.54). This difference may reflect instructional supports more readily available in F2F settings, where mathematics instruction often incorporates gestures that ground procedures in physical action and make abstract ideas concrete (Alibali & Nathan, 2012 ). Additionally, procedural development is supported by iterative practice with immediate feedback (Rittle-Johnson & Alibali, 1999 ) and hands-on manipulation (Moyer et al., 2002 ), both more consistently available when instructors can observe students’ work in real time. These findings align with self-regulated learning theory (Zimmerman, 2002 ), which predicts that different instructional modalities provide different regulatory supports. F2F instruction offers external regulation through instructor observation and correction, while online instruction requires students to self-regulate more independently. The relationship between video project performance and unit test outcomes provides critical evidence about the type of procedural knowledge students developed in each modality. Skemp ( 1976 , 2006 ) distinguished two forms of procedural understanding: instrumental understanding, which involves performing procedures without understanding why they work, and relational understanding, which involves procedural fluency grounded in conceptual comprehension. These two forms have different transfer properties. Instrumental knowledge remains situation-bound and does not transfer when supports change, while relational knowledge transfers across different assessment formats (Greeno, 1998 ). Our findings support this theoretical distinction. For F2F students, procedural knowledge scores on video projects correlated significantly with unit test performance ( r = .34, p = .004). This indicates that students who demonstrated procedural fluency on video projects also succeeded on timed tests. This pattern suggests relational procedural understanding that transferred even when supports such as resources and extra time were removed. In contrast, online students showed no significant correlation between video procedural scores and test performance ( r = .01, p = .964). This pattern suggests instrumental procedural knowledge. Online students could perform procedures successfully when resources were available during video creation, but this knowledge did not transfer to the resource-restricted test environment. Notably, these differential transfer patterns emerged despite comparable unit test scores between groups (online: M = 11.74; F2F: M = 10.35, p = .068, d = − 0.44). This indicates that both groups achieved similar test outcomes but through different knowledge development pathways. These knowledge transfer differences were reflected in how students experienced the video project. Open-ended survey responses revealed substantial modality-based differences. Online students more frequently reported scripting and rehearsing (75% vs. 55%), identifying weaknesses (20% vs. 3%), struggling with clear explanation (40% vs. 13%), attributing confidence to conceptual understanding (70% vs. 50%), and investing over three hours (50% vs. 20%). F2F students more often cited retention benefits (10% vs. 0%), experienced technical difficulties (37% vs. 25%), and expressed confidence without elaboration (23% vs. 0%). Online students’ emphasis on scripting and rehearsing (75% vs. 55%) indicates they recognized the need to transform mathematical understanding into teachable explanations, a process that requires verbalization and supports deeper conceptual understanding (Roscoe & Chi, 2007 ). Explaining content engages learners in constructive activities (Chi et al., 2001 ) and enhances learning outcomes (Fiorella & Mayer, 2013 ). Moreover, preparing to explain made knowledge gaps more visible, prompting online students to identify areas needing improvement at substantially higher rates (20% vs. 3%). This pattern of planning explanations through scripting, monitoring understanding, and reflecting on gaps represents self-regulated learning. In such processes, metacognitive activities promote deeper understanding (Zimmerman, 2002 ). This extensive metacognitive engagement may help explain why online students achieved similar conceptual knowledge scores despite different learning environments ( M = 26.29 vs. M = 27.59, p = .141). In contrast, F2F students’ emphasis on retention benefits (10% vs. 0%) suggests they used video projects as study tools rather than diagnostic opportunities. Challenges differed by modality: 40% of online students reported difficulty explaining content clearly compared to 13% of F2F students, consistent with their greater preparation through scripting. F2F students experienced technical difficulties more frequently (37% vs. 25%) despite investing less time overall. Despite online students’ extensive preparation, F2F students achieved higher procedural knowledge scores ( M = 39.75 vs. M = 38.02, p = .046), indicating that time investment and metacognitive reflection, while supporting conceptual understanding, did not automatically translate to procedural fluency. Conceptual understanding and procedural fluency are distinct yet related strands of mathematical proficiency that develop through different instructional pathways (Jbeili, 2012 ; National Research Council, 2001 ), with F2F students’ access to immediate instructor feedback potentially supporting greater procedural fluency (Francis et al., 2019 ). Online students more frequently attributed confidence to conceptual understanding gained through teaching (70% vs. 50%) and to improved retention (20% vs. 7%), consistent with research showing that explaining to others enhances both (Fiorella & Mayer, 2013 ). F2F students more often expressed confidence without elaboration (23% vs. 0%). These differing approaches were reflected in time investment: 50% of online students spent over 3 hours compared to 20% of F2F students, with online students more likely to invest substantial time (25% spent 3–6 hours; 25% over 6 hours) than F2F students (15% spent 3–6 hours; 5% over 6 hours). These patterns directly support our theoretical prediction that online students demand greater self-regulatory effort (Zimmerman, 2002 ), while F2F students benefited from external regulatory supports through instructor presence and peer interaction. Research indicates that online environments demand greater self-regulation, leading students to devote more time to planning, monitoring, and evaluating (Artino & Stephens, 2009 , as cited in Al-Zohbi & Pilotti, 2022; Cardinale & Johnson, 2017 ; Park, 2024 ). Research indicates that online environments demand greater self-regulation, leading students to devote more time to planning, monitoring, and evaluating (Artino & Stephens, 2009 , as cited in Al- Zohbi & Pilotti, 2022; Cardinale & Johnson, 2017 ; Park, 2024 ). That F2F students spent less time despite higher technical difficulties (37% vs. 25%) suggests technical challenges do not fully explain the difference; rather, online learners chose extended engagement (Al-Zohbi & Pilotti, 2022; Park, 2024 ), with both groups relying on self-regulation enacted differently across modalities (Glenn, 2014 ). The relationship between video performance and unit test scores differed by modality. In F2F courses, procedural knowledge correlated significantly with test performance ( r = .34, p = .004), whereas online students' video scores showed no such relationship ( r = .01, p = .964). Although online students developed strong metacognitive awareness through scripting and self-assessment, this preparation did not translate to improved test performance, possibly because extended preparation reinforced deliberate problem solving rather than the procedural fluency required under time pressure. In contrast, F2F students’ regular verbal mathematical explanations during class may have supported both conceptual understanding and efficient problem solving. These patterns align with evidence that online video assignments promote metacognitive awareness and self-regulated learning through planning, explanation, and reflection (Cardinale & Johnson, 2017 ; Cardace et al., 2024 ), whereas F2F instruction provides immediate feedback that supports procedural fluency (Al-Zohbi & Pilotti, 2022; Park, 2024 ). Taken together, these findings demonstrate that video-based assessment operates differently across instructional modalities in theoretically predictable ways. Self-explanation through video creation supported conceptual knowledge development equally across modalities, as predicted by constructivist learning theory. However, procedural knowledge development and transfer varied by modality in ways consistent with self-regulated learning theory and Skemp's instrumental-relational framework. Online students engaged in extensive metacognitive planning and developed conceptual understanding but often developed instrumental procedural knowledge. F2F students benefited from immediate feedback and iterative correction that supported relational procedural understanding with stronger transfer. These findings reveal that video-based assessment effectiveness depends not only on self-explanation demands but also on how instructional modality shapes regulatory supports available during knowledge construction. Limitations and Future Research Several limitations should be considered. The study was conducted at a single institution with undergraduate mathematics students, limiting generalizability. The smaller online sample ( n = 29) relative to the F2F group ( n = 70) reflected fewer online sections offered rather than differential consent rates. Because students were not randomly assigned to instructional modality, observed differences may reflect both instructional context and pre-existing characteristics; accordingly, the study emphasizes patterns of performance and knowledge transfer rather than causal comparisons. Despite reduced power for some analyses, the study detected medium-to-large effects, including a significant difference in procedural knowledge ( d = 0.54). Additionally, the study examined video projects focused on a single topic, limiting generalizability to other content areas. Future research should investigate video-based assessments across diverse mathematical topics and student populations and explore instructional scaffolds that support procedural knowledge transfer in online environments. Despite these limitations, the findings indicate that video projects support conceptual learning comparably across modalities while revealing modality-based differences in procedural knowledge development and transfer. Conclusion This study demonstrates that video projects effectively support conceptual understanding of exponential and logarithmic functions in both F2F and online mathematics courses. However, the type of procedural knowledge developed differed by modality. F2F students appeared to develop relational procedural knowledge that transferred to timed assessments, while online students appeared to develop instrumental procedural knowledge alongside strong metacognitive awareness but with limited transfer to unsupported testing contexts. By revealing how video-based assessments function differently across modalities, this study contributes to the understanding how innovative assessment approaches can support mathematics learning in diverse instructional environments. Declarations Competing Interests: The authors have no relevant financial or non-financial interests to disclose. Ethics Approval: This study was approved by the Utah Valley University Institutional Review Board. Informed Consent: Informed consent was obtained from all participants included in the study. Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. 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(1986). In Hiebert, J. Conceptual and procedural knowledge in mathematics: An introductory analysis. Jaggars, S. S. (2014). Choosing between online and face-to-face courses: Community college student voices. American Journal of Distance Education , 28 (1), 27–38. https://doi.org/10.1080/08923647.2014.867697 Jbeili, I. (2012). The effect of cooperative learning with metacognitive scaffolding on mathematics conceptual understanding and procedural fluency. International Journal for Research in Education (IJRE) , 32 , 45–71. Jones, S. J. (2013). Learning equity between online and on-site mathematics courses. Journal of Online Learning and Teaching , 9 (1), 54–72. Kaiser, G., Busse, A., Hoth, J., König, J., & Blömeke, S. (2015). About the complexities of video-based assessments: Theoretical and methodological approaches to overcoming shortcomings of research on teachers’ competence. International Journal of Science and Mathematics Education , 13 , 369–387. https://doi.org/10.1007/S10763-015-9616-7 Kilpatrick, J. (2001). Understanding mathematical literacy: The contribution of research. Educational studies in mathematics , 47 (1), 101–116. https://doi.org/10.1023/A:1017973827514 Kippers, W. B., Wolterinck, C. H. D., Schildkamp, K., Poortman, C. L., & Visscher, A. J. (2018). Teachers’ views on the use of assessment for learning and data-based decision making in classroom practice. Teaching and Teacher Education , 75 , 199–213. Kenney, R. H. (2005). Students’ understanding of logarithmic function notation . In G. M. Lloyd, M. Wilson, J. L. M. Wilkins, & S. L. Behm (Eds.), Proceedings of the 27th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 871–878). PME-NA. Kuper, E., & Carlson, M. (2020). Foundational ways of thinking for understanding the idea of logarithm. Journal of Mathematical Behavior, 57 . https://doi.org/10.1016/j.jmathb.2019.100740 Lynch-Newberg, S. A. (2010). The retention, success, and progress rates of rural females in traditional lecture and online developmental mathematics courses (Publication No. 3452860) [Doctoral dissertation, University of Kentucky]. ProQuest Dissertations & Theses Global.​. Makgakga, T., & Sepeng, P. (2013). Teaching and learning the mathematical exponential and logarithmic functions: A transformation approach. Mediterranean Journal of Social Sciences , 4 (13), 77–85. Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics , 8 (6), 372–377. https://doi.org/10.5951/TCM.8.6.0372 National Research Council. (2001). Adding it up: Helping children learn mathematics . National Academy. https://doi.org/10.17226/9822 Niess, M. L., & Walker, J. M. (2010). Guest editorial: Digital videos as tools for learning mathematics. Contemporary Issues in Technology and Teacher Education , 10 (1). https://citejournal.org/volume-10/issue-1-10/mathematics/guest-editorial-digital-videos- as-tools-for-learning-mathematics Park, E. H. (2024). Exploring the differences in learning strategy use between online and offline classes. Journal of English Teaching through Movies and Media , 25 (1), 54–65. https://doi.org/10.16875/stem.2024.25.1.54 Rittle-Johnson, B., & Alibali, M. W. (1999). Conceptual and procedural knowledge of mathematics: Does one lead to the other? Journal of Educational Psychology , 91 (1), 175–189. Rittle-Johnson, B., & Schneider, M. (2015). Developing conceptual and procedural knowledge in mathematics. In R. Cohen, Kadosh, & A. Dowker (Eds.), Oxford handbook of numerical cognition (pp. 1102–1118). Oxford University Press. https://doi.org/10.1093/oxfordhb/9780199642342.013.014 Roscoe, R. D., & Chi, M. T. H. (2007). Understanding tutor learning: Knowledge-building and knowledge-telling in peer tutors’ explanations and questions. Review of Educational Research , 77 (4), 534–574. https://doi.org/10.3102/0034654307309920 Russell, M., Carey, R., Kleiman, G., & Venable, J. D. (2009). Face-to-face and online professional development for mathematics teachers: A comparative study. Journal of Asynchronous Learning Networks , 13 (2), 71–87. Ryan, S. G. (2001). Is online learning right for you? [Paper presentation]. American Institute of Higher Education Conference. Sherin, M. G., & Dyer, E. B. (2017). Mathematics teachers’ self-captured video and opportunities for learning. Journal of Mathematics Teacher Education , 20 (5), 477–495. https://doi.org/10.1007/s10857-017-9383-1 Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics teaching , 77 (1), 20–26. Skemp, R. R. (2006). Relational understanding and instrumental understanding. Mathematics Teaching in the Middle School , 12 (2), 88–95. https://doi.org/10.5951/MTMS.12.2.0088 Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for research in mathematics education , 36 (5), 404–411. https://doi.org/10.2307/30034943 Ward, B., Motz, B., & Quick, J. (2020). How to support and lead the urgent transition to quality online learning in intro math: A resource guide. Ithaka S + R . https://doi.org/10.18665/sr.314227 Weber, C. (2016). Making logarithms accessible–Operational and structural basic models for logarithms. Journal für Mathematik-Didaktik , 37 (Suppl. 1), 69–98. https://doi.org/10.1007/s13138-016-0104-6 Wiggers, G., Buhl, M., & Ryberg, T. (2023). A scoping review of experimental evidence on face-to-face components of blended learning in higher education. Studies in Higher Education , 48 (10), 1541–1558. https://doi.org/10.1080/03075079.2022.2123911 Xu, D., & Jaggars, S. S. (2011). The effectiveness of distance education across Virginia’s community colleges: Evidence from introductory college-level math and English courses. Educational Evaluation and Policy Analysis , 33 (3), 360–377. https://doi.org/10.3102/0162373711413871 Zimmerman, B. J. (2002). Becoming a self-regulated learner: An overview. Theory Into Practice , 41 (2), 64–70. https://doi.org/10.1207/s15430421tip4102_2 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8634003","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":581355395,"identity":"29917c14-5f6b-44e8-b9dd-b4917dd4ee26","order_by":0,"name":"Eunmi Joung","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAsklEQVRIiWNgGAWjYFCCAyDCBsLmIUFLGklawOAwCVr4GQ8fky74dT5xw40Exgdv24jQItlwLE16Zt9tkBZmw7nEaDE4cMZMmrfnduLMGQls0rzEaLGHaDkH0sL+mygtBgxALTw/DiT2SySwMROlReLAsWRr3oZk436eh82Sc84RoYV/xuGDt3n+2Mm2sScf/PCmjAgtQGsYGBjB7mFsIEY9yBqQwj9EKh4Fo2AUjIKRCQDvvjgUQTeSowAAAABJRU5ErkJggg==","orcid":"","institution":"Utah Valley University","correspondingAuthor":true,"prefix":"","firstName":"Eunmi","middleName":"","lastName":"Joung","suffix":""},{"id":581355396,"identity":"42c3a7d3-a791-47fd-936e-6d9523ee874e","order_by":1,"name":"Miran Byun","email":"","orcid":"","institution":"John A. Logan College","correspondingAuthor":false,"prefix":"","firstName":"Miran","middleName":"","lastName":"Byun","suffix":""}],"badges":[],"createdAt":"2026-01-19 01:08:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8634003/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8634003/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101442913,"identity":"c8e9fdac-7085-4ec6-8656-fcf15215d799","added_by":"auto","created_at":"2026-01-29 17:34:03","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":85869,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eRubric for Students’ Content Knowledge\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8634003/v1/31fc367134c0fd77486de6e7.png"},{"id":105728864,"identity":"8e83e411-3a7b-496d-b605-0dcd62a96f64","added_by":"auto","created_at":"2026-03-30 11:12:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1573862,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8634003/v1/21c23238-75e9-46ef-837b-c9086623953e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Video-Based Assessment and Learning of Exponential and Logarithmic Functions Across Instructional Modalities","fulltext":[{"header":"Introduction","content":"\u003cp\u003eVideo-based assessments have resulted in innovative, more applicable methods to analyze teachers’ formative assessment interactions with students (Gotwals et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Building on this, in this study, video-based assessment refers to the use of student-generated or instructor-provided video recordings as the primary assessment tool for evaluating students’ knowledge, skills, and performance, often coupled with opportunities for feedback and reflection (Blomberg et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Gaudin \u0026amp; Chaliès, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Kaiser et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Sherin \u0026amp; Dyer, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Studies point out that video-based assessments enhance students’ ability to observe and interpret classroom situations, foster the development of pedagogical content knowledge, reflection skills, and professional growth, and contribute to the improvement of their mathematics content knowledge using student video presentations (Kaiser et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Sherin \u0026amp; Dyer, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOne mathematical domain where video-based assessment shows particular promise is exponential and logarithmic functions. These functions are important tools in STEM education for modeling growth and decay phenomena. However, undergraduate students experience persistent difficulties with these functions, and no broadly accepted instructional approach has emerged to address these challenges (Kenney, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Kuper \u0026amp; Carlson, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Research on understanding the inverse relationship between exponential and logarithmic functions is particularly limited. This study examines a video-based assessment designed to support students' understanding of this inverse relationship with a focus on graphing.\u003c/p\u003e\n\u003ch3\u003ePurpose of the Study\u003c/h3\u003e\n\u003cp\u003eThis study explores whether and how video-based assessments affect learning of the inverse relationship between exponential and logarithmic functions across online and face-to-face (F2F) modalities. Video recordings serve as tools to assess students’ procedural and conceptual knowledge in intermediate algebra courses, a prerequisite for students pursuing STEM careers. By comparing these modalities, this research addresses how video-based assessments function in diverse learning environments as institutions increasingly offer mathematics courses in multiple formats. Four research questions guide this investigation:\u003c/p\u003e \u003cp\u003eRQ1: How does students’ conceptual knowledge of the inverse relationship between exponential and logarithmic functions, as demonstrated through video projects, differ between online and F2F courses?\u003c/p\u003e \u003cp\u003eRQ2: How does students’ procedural knowledge of the inverse relationship between exponential and logarithmic functions, as demonstrated through video projects, differ between online and F2F courses?\u003c/p\u003e \u003cp\u003eRQ3: How does unit test performance on exponential and logarithmic functions differ between online and F2F courses, and how do video project scores relate to unit test performance within each modality?\u003c/p\u003e \u003cp\u003eRQ4: How do students in online versus F2F courses perceive the effectiveness of video-based assessment for learning exponential and logarithmic functions?\u003c/p\u003e "},{"header":"Theoretical Framework","content":"\u003cp\u003eThis study examines how video-based assessment supports learning of exponential and logarithmic functions across online and face-to-face instructional modalities. We integrate four theoretical perspectives that together explain how, why, and under what conditions video-based assessment supports mathematical learning across modalities. First, video creation engages students in self-explanation, the process of articulating understanding in their own words. Self-explanation is a constructive learning activity that promotes deeper understanding than passive or active engagement (Chi \u0026amp; Wylie, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). This constructive process should operate similarly regardless of modality, as the cognitive demand remains constant. This generates our first prediction: conceptual knowledge should develop comparably across modalities.\u003c/p\u003e\u003cp\u003eSecond, mathematical proficiency encompasses conceptual knowledge (understanding principles) and procedural knowledge (facility with procedures), which develop iteratively (National Research Council, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Rittle-Johnson \u0026amp; Alibali, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). However, procedural knowledge takes different forms. Instrumental understanding means executing procedures without understanding why they work, while relational understanding means procedural fluency grounded in conceptual comprehension (Skemp, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e1976\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). These forms have different transfer properties: instrumental knowledge remains situation-bound, while relational knowledge transfers across situations (Greeno, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). Video projects allow resource access, enabling success through either form. The distinction emerges on timed tests without resources. This generates our second prediction: procedural knowledge development may differ across modalities, and transfer patterns will reveal whether students developed instrumental or relational understanding.\u003c/p\u003e\u003cp\u003eThird, online and face-to-face environments provide different regulatory supports (Zimmerman, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Face-to-face instruction offers immediate feedback and gestural grounding that may foster relational understanding through iterative practice with correction. Online instruction requires greater self-regulation; students must independently monitor understanding and identify gaps, which may support conceptual understanding but not necessarily procedural fluency. This generates our third prediction: face-to-face students' access to immediate feedback may support relational procedural knowledge that transfers to tests, while online students may develop instrumental procedural knowledge that succeeds on video projects but not tests.\u003c/p\u003e\u003cp\u003eTo operationalize this framework, three key constructs require explicit definition. Conceptual knowledge encompasses understanding of principles and relationships governing mathematical domains (Rittle-Johnson \u0026amp; Alibali, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). For exponential and logarithmic functions, this includes understanding why functions are inverses, what properties represent mathematically, and how inverse relationships appear graphically. Procedural knowledge involves facility with procedures and algorithms (National Research Council, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), but Skemp’s (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e1976\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) framework distinguishes instrumental (executing without understanding) from relational (grounded in concepts) procedural knowledge. Because both types can produce correct performance when resources are available, we distinguished them through transfer examination. Transfer refers to applying knowledge across situations (Greeno, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). We operationalized this as correlations between video project procedural scores and unit test performance within each modality. Significant correlations indicate relational knowledge that transfers; non-significant correlations suggest instrumental knowledge that fails to transfer when supports are removed.\u003c/p\u003e\n\u003ch3\u003eVideo-Based Assessment: Supporting Knowledge Construction\u003c/h3\u003e\n\u003cp\u003eEmpirical research demonstrates that video-based assessments support mathematical learning across multiple contexts. Studies examining video-based assessment in mathematics education show that these assessments enable both formative and summative evaluation (Bennett, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Borowczak \u0026amp; Burrows, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Kippers et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). When implemented formatively, video-based assessments provide opportunities for students to receive feedback on their explanations and revise their understanding (Bennett, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Summatively, they evaluate students\u0026rsquo; ability to articulate mathematical concepts at the conclusion of instruction (Kippers et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Studies found that video-based assessment enables educators to identify student misconceptions and analyze mathematical thinking from multiple perspectives (Kaiser et al.,2015; Sherin \u0026amp; Dyer, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). Gotwals et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) demonstrated that reviewing student-created videos helps instructors recognize patterns in student reasoning that might not be visible through traditional assessments.\u003c/p\u003e \u003cp\u003eEmpirical and meta-analytic research on self-explanation, learning-by-teaching, and formative assessment indicates that video-based assessment supports learning by prompting students to articulate and reflect on their understanding (Chi et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Fiorella \u0026amp; Mayer, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Black \u0026amp; Wiliam, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Chi et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2001\u003c/span\u003e) found that students who explain content to others demonstrate deeper understanding than those who passively review material. Similarly, Fiorella and Mayer\u0026rsquo;s (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) meta-analysis of learning-by-teaching studies showed that explanation enhances both understanding and retention, with effect sizes ranging from moderate to large across content domains. Black and Wiliam (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) further demonstrated that assessment approaches requiring explanation and reflection produce stronger learning gains than traditional testing formats.\u003c/p\u003e \u003cp\u003eHowever, research on video-based assessment has focused predominantly on preservice teacher education programs. Kaiser et al. (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) examined preservice teachers\u0026rsquo; use of video to analyze classroom instruction, while Sherin and Dyer (\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) studied how video analysis supports the development of pedagogical knowledge in teacher candidates. To date, there appears to be limited research on video-based assessment in undergraduate mathematics courses outside teacher preparation programs. More critically, there appears to be a lack of systematic research examining whether video-based assessment functions similarly across online and face-to-face instructional modalities. This gap is significant because the instructional conditions under which students prepare and complete video-based assessments vary across modalities, even when the cognitive demand of self-explanation remains consistent. This evidence establishes that video creation engages self-explanation processes, but whether these processes operate similarly across different instructional modalities remains unexplored.\u003c/p\u003e\n\u003ch3\u003eConceptual and Procedural Knowledge: Development and Challenges\u003c/h3\u003e\n\u003cp\u003eStudies document how conceptual and procedural knowledge develop in mathematics learning (Rittle-Johnson \u0026amp; Alibali, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Rittle-Johnson \u0026amp; Schneider, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Dorner et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2025\u003c/span\u003e; Hiebert \u0026amp; Lefevre, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1986\u003c/span\u003e; Kilpatrick et al., 2001). Rittle-Johnson and Alibali\u0026rsquo;s (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) longitudinal study of elementary students found that conceptual understanding and procedural skill develop iteratively, with gains in one domain predicting subsequent gains in the other. Extending this work, Rittle-Johnson and Schneider (\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) synthesized evidence across mathematical domains and age groups and concluded that relations between conceptual and procedural knowledge are often bidirectional and iterative, but that the strength and symmetry of these relations depend on instructional conditions and task design. Importantly, this synthesis also documents that conceptual and procedural knowledge can develop independently when instruction emphasizes procedural execution without explicit conceptual connections. Hiebert and Lefevre (\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e1986\u003c/span\u003e) found that students often acquire procedural skills through rote memorization without developing corresponding conceptual understanding, resulting in fragile knowledge that does not transfer to novel problems.\u003c/p\u003e \u003cp\u003eThe distinction between instrumental and relational procedural understanding has substantial empirical support. Skemp\u0026rsquo;s (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e1976\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) original work documented students who could execute algebraic procedures correctly but could not explain why those procedures worked or when to apply them. Subsequent research has repeatedly confirmed this distinction. Star (\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) found that students with relational understanding of equation solving could flexibly adapt procedures to different problem types, while students with instrumental understanding could only apply memorized procedures to familiar problem formats. Rittle-Johnson et al. (2001) demonstrated that students taught procedures with conceptual explanations showed better transfer to novel problems than students taught procedures alone.\u003c/p\u003e\n\u003ch3\u003eTransfer of Mathematical Knowledge\u003c/h3\u003e\n\u003cp\u003eResearch on transfer demonstrates that instrumental and relational knowledge differ in how they apply across different situations and assessment formats. Greeno (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1998\u003c/span\u003e) demonstrated that knowledge acquired in specific situations often fails to transfer when contextual supports change. Students may succeed on familiar problems but struggle when problem features or available resources differ, even when the underlying mathematics remains identical. This situation-dependence characterizes instrumental knowledge, where students rely on memorized procedures tied to specific formats without understanding underlying principles.\u003c/p\u003e \u003cp\u003eIn contrast, transfer occurs when students develop understanding of general principles that can be applied flexibly across different problem types and formats. Singley and Anderson (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1989\u003c/span\u003e) found that when students understand underlying principles rather than memorizing surface-level procedures, they successfully transfer knowledge to problems with different features. Rittle-Johnson et al. (2017) provided empirical support through classroom experiments, showing that comparing multiple solution methods for the same problem fostered procedural flexibility and transfer to new equation types, whereas focusing on comparing different problem types resulted in more rigid, format-specific knowledge.\u003c/p\u003e \u003cp\u003eInstructional design influences transfer outcomes. Renkl et al. (2002) demonstrated that gradually reducing support from complete worked examples to independent problem solving promoted transfer by helping students develop abstract understanding without cognitive overload. Similarly, research on analogical problem solving shows that students who develop abstract schemas transfer solution procedures more successfully than students who focus on superficial problem similarities (Gentner et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). These transfer patterns are particularly relevant for understanding how students apply procedural knowledge across different assessment formats. Video projects that allow resource access and rehearsal provide contextual supports that may enable success through either instrumental or relational knowledge. In contrast, timed tests without resources require independent retrieval and flexible application, revealing whether students developed transferable understanding or situation-bound procedures.\u003c/p\u003e\n\u003ch3\u003eStudents’ Understanding of Exponential and Logarithmic Functions\u003c/h3\u003e\n\u003cp\u003eResearch on exponential and logarithmic functions documents persistent student difficulties with both conceptual understanding and procedural facility (Confrey \u0026amp; Smith, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Weber, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Kuper \u0026amp; Carlson, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Makgakga \u0026amp; Sepeng, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Campo-Meneses \u0026amp; Garc\u0026iacute;a-Garc\u0026iacute;a, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Kuper and Carlson (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) interviewed 12 undergraduate students and found sustained difficulty reasoning about covariation in exponential functions. Students were unable to explain how changes in the base influence function behavior. Makgakga and Sepeng (\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) studied 64 South African students and found that only 23% correctly identified the inverse relationship between exponential and logarithmic functions when translating between representations. Campo-Meneses and Garc\u0026iacute;a-Garc\u0026iacute;a (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) reported that students frequently failed to connect algebraic, graphical, and numerical representations, instead treating each representation as an isolated topic rather than as expressions of a single mathematical relationship.\u003c/p\u003e \u003cp\u003eAdditional evidence highlights weaknesses in students\u0026rsquo; understanding of logarithmic functions. Confrey and Smith (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1995\u003c/span\u003e) examined calculus students\u0026rsquo; knowledge and found substantial gaps in foundational understanding. On a placement examination, only 48% of students correctly identified the graph of a logarithmic function. Many students confused exponential and logarithmic graphs, could not explain domain and range constraints, and did not recognize that logarithms represent exponents. Weber (\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) observed that common instructional approaches emphasize procedural tasks such as converting between exponential and logarithmic forms and applying logarithmic rules, with limited attention to conceptual meaning. As a result, students often acquire procedural competence without developing an understanding of what logarithms represent or why the procedures are valid, which restricts their ability to transfer logarithmic reasoning across different representations and problem types.\u003c/p\u003e \u003cp\u003eThe persistent difficulties students experience with exponential and logarithmic functions, particularly the tendency to develop procedural fluency without conceptual understanding (Weber, \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), make this domain especially appropriate for examining how video-based assessments support different types of knowledge development across instructional modalities.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eLearning Across Instructional Modalities: Self-Regulation and Support\u003c/h2\u003e \u003cp\u003eResearch comparing online and face-to-face mathematics learning has produced inconsistent findings, indicating that learning outcomes vary according to instructional conditions rather than instructional modality alone (Eggert, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Jones, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Lynch-Newberg, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Ryan, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Wiggers et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Xu \u0026amp; Jaggars, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Early studies reported no significant differences in achievement. Ryan (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2001\u003c/span\u003e) compared web-based, video-based telecourse, and classroom-based statistics instruction and found no differences in final course grades. Eggert (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) similarly reported no significant differences in completion rates between online and classroom-based developmental mathematics courses. In contrast, later studies identified modality-related differences. Lynch-Newberg (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) found higher success rates for developmental mathematics students enrolled in online courses than for students in traditional lecture formats. However, Xu and Jaggars (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), analyzing data from more than 40,000 community college students, found that enrollment in online mathematics courses was associated with lower grades and reduced course completion. Jones (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) found that face-to-face students achieved higher mean grades than online students, although this difference decreased over time. Wiggers et al. (\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) concluded that well-designed online mathematics instruction can yield outcomes comparable to face-to-face instruction, while noting that average achievement in online courses remains slightly lower.\u003c/p\u003e \u003cp\u003eThese mixed findings suggest that direct comparisons of instructional modality obscure important differences in learning conditions. Face-to-face instruction provides immediate instructor feedback during problem solving, which supports learning by identifying errors early and reducing repeated practice of incorrect procedures (Francis et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Alibali and Nathan (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) found that mathematics instructors frequently use gestures to connect symbolic notation to physical actions, supporting conceptual understanding and procedural execution. These gestures include pointing gestures that link related information, representational gestures that model mathematical actions, and metaphoric gestures that convey abstract processes. This immediate feedback and gestural support may promote procedural knowledge that is grounded in conceptual understanding and therefore more likely to transfer.\u003c/p\u003e \u003cp\u003eOnline mathematics instruction creates different learning conditions. Ward et al. (\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) found that online students must regulate their learning more independently, monitoring understanding and progress without immediate instructor observation. Broadbent and Poon (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) reported that successful online learners demonstrate strong metacognitive monitoring and strategic planning skills, while students with weaker self-regulation skills experience greater difficulty in online environments. Research also indicates that online mathematics students spend more time on coursework than face-to-face students. Artino and Stephens (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2009\u003c/span\u003e, as cited in Al-Zohbi \u0026amp; Pilotti, 2022) and Park (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) found that online learners spent substantially more time on learning activities, reflecting the increased planning and monitoring required in the absence of real-time instructional guidance. Increased time investment alone, however, does not guarantee improved learning outcomes.\u003c/p\u003e \u003cp\u003eDifferences in mathematical communication further distinguish instructional modalities. Jaggars (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) found that communication in online mathematics courses occurs primarily through written text, with limited opportunities for synchronous verbal interaction. In contrast, face-to-face courses provide frequent verbal exchanges between students and instructors. This difference is relevant for assessments requiring spoken explanation. Research found that verbal explanation supports deeper learning than written explanation alone, suggesting that students\u0026rsquo; prior opportunities for oral mathematical communication may influence performance on explanation-based assessments (Chi et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Roscoe \u0026amp; Chi, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Despite extensive research comparing online and face-to-face mathematics learning, assessment practices requiring explanation remain largely unexamined across modalities. Most comparative studies focus on traditional assessments such as exams, quizzes, and homework. Video-based assessments in online courses may face additional challenges.\u003c/p\u003e \u003cp\u003eThe literature reveals three well-established findings: video-based assessment supports mathematical learning through self-explanation; conceptual and procedural knowledge are distinct constructs with different development pathways and transfer properties; and online and face-to-face mathematics learning differ in regulatory supports and communication opportunities. However, these three lines of research have not been integrated: prior research has examined video-based assessment and modality differences independently, with little is known about how video-based assessments across modalities for mathematically demanding topics requiring both conceptual understanding and procedural fluency. This gap has important implications. Mathematics courses are increasingly offered across instructional modalities, often using common assessments without evidence that they function equivalently. Although video-based assessment may support conceptual understanding through self-explanation, its effects on procedural knowledge development and transfer may depend on modality-specific regulatory supports and communication practices.\u003c/p\u003e \u003cp\u003eThis study addresses this gap by examining how video-based assessments of exponential and logarithmic functions operate in online versus face-to-face intermediate algebra courses. Drawing on the integrated theoretical framework, this research investigates four questions. First, does video-based assessment support conceptual knowledge development similarly across modalities, as predicted by theories of self-explanation and constructive learning? Second, does procedural knowledge development differ across modalities, as self-regulated learning theory suggests? Third, do different modalities foster different types of procedural knowledge (instrumental versus relational) as evidenced by transfer patterns from video projects to unit tests? Fourth, how do students in each modality experience and approach video project creation, and do these experiences reflect predicted differences in self-regulatory demands between modalities? By examining both performance outcomes and student experiences, this research provides empirical evidence on how video-based assessment supports mathematical learning across instructional modalities.\u003c/p\u003e \u003c/div\u003e"},{"header":"Methods","content":"\u003cp\u003eA mixed-methods comparative design was used to investigate students\u0026rsquo; understanding of the inverse relationship between exponential and logarithmic functions across online and F2F instructional modalities. Quantitative data included video project scores (conceptual and procedural knowledge) and unit test performance. Qualitative data were collected through open-ended survey questions examining student perceptions of the video project.\u003c/p\u003e\n\u003ch3\u003eParticipants\u003c/h3\u003e\n\u003cp\u003eParticipants were recruited from intermediate algebra courses at a 4-year university in the Western United States during Fall 2023, Spring 2024, and Summer 2024. All students provided informed consent before participating in the study. The final sample consisted of 99 students enrolled in either online (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;29) or F2F (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;70) sections of the course. Among the participants, 56 (56.6%) identified as male and 43 (43.4%) identified as female. Gender distribution differed notably across modalities: the online group included 10 males (34.5%) and 19 females (65.5%), while the F2F group included 46 males (65.7%) and 24 females (34.3%).\u003c/p\u003e\n\u003cp\u003eThe smaller online sample size (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;29) reflected fewer online course sections offered rather than differential consent rates. Across the three semesters, two online sections enrolled approximately 58 students, with 29 (50%) providing consent. In comparison, four F2F sections enrolled approximately 120 students, with 70 (58%) providing consent. The similar consent rates across modalities (50% vs. 58%) suggest that selection bias due to nonresponse is unlikely to differentially affect the two groups. Chi-square analysis confirmed no significant difference in consent rates between modalities (\u003cem\u003e\u0026chi;\u0026sup2;\u003c/em\u003e = 1.01, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.31), indicating that selection bias due to differential nonresponse is unlikely.\u003c/p\u003e\n\u003cp\u003eIntermediate Algebra is an undergraduate mathematics course and a prerequisite for higher-level mathematics courses for students pursuing careers in STEM fields. Topics covered include linear, polynomial, quadratic, exponential, logarithmic, and rational functions from algebraic and graphical perspectives. The course used Lumen Online Homework Manager (OHM), a digital course platform, rather than a traditional textbook.\u003c/p\u003e\n\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\n\u003ch2\u003eProcedure\u003c/h2\u003e\n\u003cp\u003eStudents in both online and F2F sections completed a video project assignment involving exponential and logarithmic functions. Students received a problem set of nine problems requiring them to find key properties of given functions (domain, range, asymptotes, inverse function using algebraic methods, and x- and y-intercepts) and sketch graphs to visualize the inverse relationship between exponential and logarithmic functions. While recording themselves on video, students solved these problems and explained their mathematical reasoning. Videos were limited to approximately 5 minutes and submitted through Canvas. Following the video project, students took a Unit Test covering exponential and logarithmic functions. The test used the same problem types as the video project but with different numerical values and was worth 15 points total.\u003c/p\u003e\n\u003cp\u003eStudents were then invited to complete an optional follow-up survey exploring their experiences with the video project. Of the 99 participants, 80 students (20 online, 60 F2F) completed the survey, which included five open-ended questions addressing preparation strategies, engagement, challenges, confidence, and time investment. All students provided informed consent for their video project scores, unit test scores, and survey responses to be used for research purposes. Obtaining informed consent from online students presented additional logistical challenges, as consent forms were distributed and collected electronically rather than in person.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n\u003ch2\u003eInstruments\u003c/h2\u003e\n\u003cp\u003eThree instruments were used to examine students\u0026rsquo; understanding of the inverse relationship between exponential and logarithmic functions: (a) a problem set with rubric for the video project, (b) an open-ended survey questionnaire assessing students\u0026rsquo; experiences with the video project, and (c) a unit exam assessing retention of mathematical knowledge.\u003c/p\u003e\n\u003cp\u003eStudents completed a problem set requiring them to find properties of exponential and logarithmic functions (domain, range, asymptotes, x- and y-intercepts, and inverse functions) and sketch graphs of these functions while recording themselves using tools such as Kaltura, Windows Media Player, or QuickTime Player.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eRubric\u003c/strong\u003e. Videos were assessed using a 100-point rubric with two components. Video skills (20 points) evaluated presentation quality, including structure (introductions, conclusions, transitions) and delivery (pacing, editing). Content knowledge (80 points; see Fig.\u0026nbsp;1) assessed conceptual understanding (36 points) and procedural knowledge (44 points). Conceptual knowledge measured students\u0026rsquo; ability to explain the meaning of domains, ranges, asymptotes, and intercepts; describe relationships between functions and their inverses; and interpret graphical representations. Procedural knowledge evaluated students\u0026rsquo; ability to correctly calculate these same elements using appropriate mathematical notation, find inverse functions algebraically, and produce accurate graphs showing all key features. The rubric also provided personalized feedback to clarify concepts and direct students to additional resources.\u0026nbsp;\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n\u003cp\u003e\u003cstrong\u003eFollow-up Survey\u003c/strong\u003e. An open-ended follow-up survey was used to collect students\u0026rsquo; perceptions of their experience with the video project. The following questions were included in the survey:\u003c/p\u003e\n\u003col\u003e\n\u003cli\u003e\n\u003cp\u003eHow did you prepare to complete this video project assignment to solve the problem set, and what resources did you use in your problem-solving process?\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eDid you find the video project more engaging than traditional assignments? Why or why not?\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eWas there anything you found particularly challenging about creating a video presentation?\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eHow confident do you feel about the material learned after completing this video project compared to traditional assignments?\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp\u003eHow much time did you spend on preparing and creating the video presentation?\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003e\u003cstrong\u003eRetention Measure\u003c/strong\u003e. After completing the video project, students took a unit exam with problems on the inverse relationship between exponential and logarithmic functions. The exam used the same problem types as the video project but with different numerical values.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n\u003ch2\u003eData Analysis\u003c/h2\u003e\n\u003cp\u003eThese analytical choices directly operationalize the theoretical constructs and predictions outlined in our framework. To address RQ1 regarding conceptual knowledge, descriptive statistics were calculated for video project conceptual knowledge scores (36 points possible) for both online and F2F groups. An independent samples \u003cem\u003et\u003c/em\u003e-test examined differences between groups. Effect sizes (Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e) were calculated to assess the practical significance of any difference. Prior to conducting the \u003cem\u003et\u003c/em\u003e-test, assumptions of normality and homogeneity of variance were tested using Shapiro-Wilk and Levene\u0026rsquo;s tests, respectively, and were satisfied.\u003c/p\u003e\n\u003cp\u003eTo address RQ2 regarding procedural knowledge, parallel analyses were conducted using the procedural knowledge scores from the video project rubric (44 points possible). Descriptive statistics and an independent samples t-test for group comparisons were performed for both online and F2F sections. Effect sizes (Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e) were calculated to assess practical significance.\u003c/p\u003e\n\u003cp\u003eTo address RQ3 regarding unit test performance and relationships among variables, an independent samples t-test was conducted to examine the difference in mean unit test scores between online and F2F groups. Effect sizes (Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e) were calculated to assess practical significance. Additionally, Pearson correlation analyses were conducted separately for each instructional group to examine the relationships among video project conceptual knowledge scores, procedural knowledge scores, and unit test performance. Correlation matrices were generated to identify patterns of association within each learning modality.\u003c/p\u003e\n\u003cp\u003eTo address RQ4 regarding student perceptions, responses from open-ended follow-up survey questionnaires were analyzed using six-phase framework for thematic analysis (Braun \u0026amp; Clarke, 2006): (a) familiarization with data, (b) generating initial codes, (c) searching for themes, (d) reviewing themes, (e) defining and naming themes, and (f) producing the report. To identify potential differences in perceptions across instructional modalities, responses from online and F2F students were analyzed separately, allowing for both within-group theme identification and between-group comparison of emerging patterns. The analysis proceeded iteratively, with constant comparison used to identify themes common to both groups as well as modality-specific themes.\u003c/p\u003e\n\u003cp\u003eTo establish coding reliability, two researchers independently coded a preliminary subset of responses and met to discuss emergent themes, resolve discrepancies, and develop a unified coding scheme. Following codebook refinement, both researchers independently coded all responses to assess inter-rater reliability. Cohen\u0026rsquo;s kappa coefficients ranged from moderate to almost perfect agreement across both modalities (see Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Any remaining discrepancies were resolved through consensus discussion between the two researchers.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\u0026nbsp;\u003c/div\u003e\n\u003ctable id=\"Tab1\" border=\"1\"\u003e\u003ccaption\u003e\n\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n\u003cdiv class=\"CaptionContent\"\u003e\n\u003cp\u003e\u003cem\u003eInter-Rater Reliability Coefficients by Question and Course Modality\u003c/em\u003e\u003c/p\u003e\n\u003c/div\u003e\n\u003c/caption\u003e\n\u003cthead\u003e\n\u003ctr\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eQuestion\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eOnline Course\u003c/p\u003e\n\u003c/th\u003e\n\u003cth align=\"left\"\u003e\n\u003cp\u003eF2F Course\u003c/p\u003e\n\u003c/th\u003e\n\u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eQ1\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.886\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.687\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eQ2\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.505\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.452\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eQ3\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.860\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.953\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eQ4\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.640\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.783\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003eQ5\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.855\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.910\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003ctr\u003e\n\u003ctd align=\"left\"\u003e\n\u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.749\u003c/p\u003e\n\u003c/td\u003e\n\u003ctd align=\"char\" char=\".\"\u003e\n\u003cp\u003e0.757\u003c/p\u003e\n\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003ctfoot\u003e\n\u003ctr\u003e\n\u003ctd colspan=\"3\"\u003e\u003cem\u003eNote.\u003c/em\u003e All values represent Cohen\u0026rsquo;s kappa coefficients. Interpretation based on Landis and Koch (1977): \u0026kappa;\u0026thinsp;\u0026lt;\u0026thinsp;0.00\u0026thinsp;=\u0026thinsp;poor, 0.00\u0026ndash;0.20\u0026thinsp;=\u0026thinsp;slight, 0.21\u0026ndash;0.40\u0026thinsp;=\u0026thinsp;fair, 0.41\u0026ndash;0.60\u0026thinsp;=\u0026thinsp;moderate, 0.61\u0026ndash;0.80\u0026thinsp;=\u0026thinsp;substantial, 0.81\u0026ndash;1.00\u0026thinsp;=\u0026thinsp;almost perfect.\u003c/td\u003e\n\u003c/tr\u003e\n\u003c/tfoot\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e"},{"header":"Results","content":"\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eRQ1: Conceptual Knowledge\u003c/h2\u003e \u003cp\u003eAn independent samples \u003cem\u003et\u003c/em\u003e-test was conducted to compare conceptual knowledge scores between online and F2F groups. Descriptive statistics are presented in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The F2F group (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;27.59, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.52) scored slightly higher than the online group (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;26.29, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;4.78), but this difference was not statistically significant, \u003cem\u003et(\u003c/em\u003e97)\u0026thinsp;=\u0026thinsp;1.484, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.141, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.33. The small-to-medium effect size suggests a minor practical difference favoring F2F instruction.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eDescriptive Statistics for Video Project Conceptual Knowledge Scores by Instructional Group\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eSD\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003edf\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003et\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF2F\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e27.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.484\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.141\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOnline\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e26.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003e\u003cem\u003eNote.\u003c/em\u003e F2F\u0026thinsp;=\u0026thinsp;face-to-face. Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e calculated using pooled standard deviation.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003eRQ2: Procedural Knowledge\u003c/h2\u003e \u003cp\u003eAn independent samples \u003cem\u003et\u003c/em\u003e-test was conducted to compare procedural knowledge scores between online and F2F groups. Descriptive statistics are presented in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The F2F group (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;39.75, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.80) scored significantly higher than the online group (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;38.02, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.91), \u003cem\u003et\u003c/em\u003e(97)\u0026thinsp;=\u0026thinsp;2.02, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.046, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.54. This medium effect size indicates a meaningful practical difference, suggesting that video projects may be more effective for developing procedural knowledge in F2F courses compared to online courses.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eDescriptive Statistics for Video Project Procedural Knowledge Scores by Instructional Group\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eSD\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003edf\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003et\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF2F\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e39.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e.54\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOnline\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e38.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003eRQ3: Unit Test Performance and Relationships Among Variables\u003c/h2\u003e \u003cp\u003eAn independent samples \u003cem\u003et\u003c/em\u003e-test was conducted to compare unit test performance on exponential and logarithmic functions between online and F2F groups after completing video projects. Descriptive statistics are presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eDescriptive Statistics for Unit Test Performance by Instructional Group\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eM\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eSD\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003edf\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003et\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003ep\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003ed\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF2F\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e10.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-\\)\u003c/span\u003e\u003c/span\u003e1.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e.068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e\u0026minus;0.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOnline\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e11.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e2.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"8\"\u003e\u003cem\u003eNote.\u003c/em\u003e Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e calculated using pooled standard deviation. Maximum possible score\u0026thinsp;=\u0026thinsp;15 points.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe online group (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;11.74, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.98) scored slightly higher than the F2F group (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;10.35, \u003cem\u003eSD\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.61), but this difference was not statistically significant, \u003cem\u003et\u003c/em\u003e (97) = \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:-\\)\u003c/span\u003e\u003c/span\u003e1.85, \u003cem\u003ep\u003c/em\u003e = .068, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.44. The small effect size suggests a minor practical difference favoring online instruction, though the groups performed similarly overall on the unit test.\u003c/p\u003e \u003cp\u003eTo examine the relationships among video project performance and unit test outcomes, Pearson correlation analyses were conducted separately for each group. Correlation matrices are presented in Tables\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFor the online group \u003cb\u003e(\u003c/b\u003esee Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e), conceptual knowledge and procedural knowledge were moderately positively correlated (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.45, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.017), suggesting that students who performed well on conceptual tasks also tended to perform well on procedural tasks. However, neither conceptual knowledge (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.17, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.379) nor procedural knowledge (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.01, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.964) showed significant correlations with unit test performance. These findings indicate that video project performance in online courses was not predictive of subsequent unit test scores.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eIntercorrelations Among Video Project Scores and Unit Test Performance for Online Group\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOnline\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1. Conceptual Knowledge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2. Procedural Knowledge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.45*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3. Unit Test Performance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cem\u003eNote. n\u003c/em\u003e\u0026thinsp;=\u0026thinsp;29. *\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.05.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFor the F2F group (see Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), conceptual knowledge and procedural knowledge were also moderately positively correlated (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.45, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001), demonstrating a similar pattern to the online group. Notably, procedural knowledge showed a significant moderate positive correlation with unit test performance (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.34, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.004), indicating that students who demonstrated stronger procedural skills on video projects tended to perform better on the unit test. However, conceptual knowledge was not significantly correlated with unit test performance (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.06, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.628).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eIntercorrelations Among Video Project Scores and Unit Test Performance for F2F Group\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eF2F\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1. Conceptual Knowledge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2. Procedural Knowledge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.45***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3. Unit Test Performance\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.34**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026mdash;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003e\u003cem\u003eNote. n\u003c/em\u003e\u0026thinsp;=\u0026thinsp;70. **\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.01. ***\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;.001.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003eRQ4: Student Perceptions of Video-Based Assessment Effectiveness by Course Modality\u003c/h2\u003e \u003cp\u003eTo address RQ4, we analyzed student responses to five open-ended questions about their experiences with the video project. Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e presents themes related to student preparation strategies and resource use for the video project.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eOpen-Ended Question 1: Themes in Student Preparation and Resource Use\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eThemes\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eOnline\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eF2F\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eExample from Student Response\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;1: Review of Instructional Materials\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eStudents reviewed their notebooks, textbooks, class notes, or course materials to prepare for their video project\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e70%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e65%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;To prepare to complete this video project assignment I read through all of my notes that had to do with the assigned questions and solved for those questions. I used the textbook, past homework assignments and my notes as resources\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;For this project, I utilized the notes I'd taken in class and the examples I'd completed in the Canvas assignments. Therefore, I used the course materials and resources available in Canvas.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;2: External Resources\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eStudents used resources outside the course materials, such as Photomath, ChatGPT, YouTube videos, or other online tools.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e55%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e58%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;Math is always a struggle for me, I did find this difficult. I asked my coworkers to teach me the concepts. I also relooked at the assignments and the chapter reading/practices/ I watched YouTube videos for clarity\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I used chat ChatGPT to come up with problems for me to solve\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;3: Preparing to Explain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eStudents prepared the video presentation by writing scripts, rehearsing explanations, organizing steps for clarity, or practicing their verbal delivery.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e75%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e55%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I prepared by writing out step by step for each question being asked and then reviewing my steps to simplify them when explaining. I used Desmos to help with graphing both the original equation and the inverse equation.\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I practiced problems from our class worksheets to make sure I didn\u0026rsquo;t mess up the steps in the video and had good point to talk about.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u0026ndash;4: Interact with others\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eStudents worked with classmates or tutors in the Math Lab.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e15%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I prepared by going to the math lab and working with classmates to study and learn the material.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cem\u003eNote.\u003c/em\u003e Students often mentioned multiple preparation and resource use strategies in their responses (e.g., reviewing notes while also using YouTube videos and practicing their explanation). Therefore, percentages exceed 100% as codes are not mutually exclusive. Online \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20; F2F \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;60.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eBoth online and F2F students reported similar patterns of preparation, with the majority reviewing instructional materials (online: 70%; F2F: 65%) and approximately half using external resources such as ChatGPT, YouTube, or Photomath (online: 55%; F2F: 58%). The primary difference between modalities emerged in the \u003cem\u003ePreparing to Explain\u003c/em\u003e theme (1\u0026ndash;3), which was substantially more prevalent among online students (75%) compared to F2F students (55%). Online students frequently reported writing scripts, rehearsing explanations, and organizing their presentation strategies before recording. A notable finding was the \u003cem\u003eInteract with Others\u003c/em\u003e theme (1\u0026ndash;4), which appeared exclusively among F2F students (15%), who reported working with classmates or tutors in the Math Lab to prepare their videos. This resource was not mentioned by any online students.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e presents themes related to student engagement with the video project. The majority of students in both modalities found the video project more engaging than traditional assignments, though patterns of engagement differed by modality. The most prevalent theme was \u003cem\u003eDeeper Understanding Required\u003c/em\u003e (1-a), reported by 70% online and 58% F2F students, respectively. Notable differences emerged in several themes. \u003cem\u003eCreative Engagement\u003c/em\u003e (1-b) was more common among F2F students (23%) than online students (10%), with F2F students appreciating the different form of assignment. \u003cem\u003eReflection on Weaknesses\u003c/em\u003e (1-e) was substantially higher among online students (20%) compared to F2F students (3%), suggesting online students used the video project to identify areas needing improvement. \u003cem\u003eBetter Retention\u003c/em\u003e (1-g) appeared exclusively among F2F students (10%), with no online students mentioning this benefit.\u003c/p\u003e \u003cp\u003eAmong students who did not find the video more engaging, the primary concern was \u003cem\u003eTime-Consuming Technical Issues\u003c/em\u003e (2-b), reported by 2% of F2F students but absent among online student responses.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eOpen-Ended Question 2: Comparison of Student Engagement Themes\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThemes\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eOnline\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eF2F\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eExample from student responses\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eYES: MORE ENGAGING\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e1-a: Deeper understanding required\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVideo required deeper understanding to explain concepts\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e70%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e58%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I found it more engaging because I had to know the information well enough to teach it, so I had to redo the questions multiple times.\u0026rdquo;\u003c/p\u003e \u003cp\u003e \u003cb\u003eF2F\u003c/b\u003e:\u0026rdquo; I think it was pretty engaging and made sure that we could explain and understand these concepts.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e1-b: Creative engagement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVideo project allowed different ways to present content\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e23%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I would prefer to do something like this rather than traditional assignments, It is interactive, and traditional assignments feel overdone and repetitive.\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;It was engaging in a different way; I wouldn't say it was more engaging...\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e1-c: Showing\u003c/p\u003e \u003cp\u003ework clearly\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStudents showed their problem-solving written work clearly while explaining\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnlin\u003c/b\u003ee: \u0026ldquo;\u0026hellip;it allowed us to visually show what we know rather than just from work written on a paper. It allows our teachers to actually hear us when we are going step by step and see how we process what is being taught to us\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;The project was very engaging sense I had to write out all of the equations and film myself explaining it all.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e1-d: Confidence/\u003c/p\u003e \u003cp\u003ecomfortable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCompleting this project increased students\u0026rsquo; confidence and comfort with the content\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I did because I wanted to make it perfect so I made sure I understood what I was solving so I could present it professionally and it makes me proud when I know what I am talking about\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;...What most compelled me to do was to show off my skills and what I learned in the unit. Of course, it wasn\u0026rsquo;t perfect, but I felt good...\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e1-e: Reflection\u003c/p\u003e \u003cp\u003eon weaknesses\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVideo project helped them identify area needed improvement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003e3%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;\u0026hellip;it did help me to identify what I need improvement on\u0026hellip;\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F: \u0026ldquo;...\u003c/b\u003eexplaining them allowed me to pay closer attention to the mistakes and errors I made during the process.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e1-f: Enjoyable\u003c/p\u003e \u003cp\u003eand fun\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStudents found this project enjoyable and fun\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e20%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e17%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;Yes, I thoroughly enjoyed creating the video and watching it back over to see my thought process on things and to see how much sense I made\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e:\u0026rdquo; It was more engaging, I found it pretty fun.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e1-g: Better\u003c/p\u003e \u003cp\u003eretention\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eExplaining improved content retention\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e10%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;...This helps improve the memorization of formulas and solution methods...\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e1-h: Challenging\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVideo project was challenging but engaging\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e15%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e15%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;Yes, it was more engaging, but there was an added level of difficulty to match the rubric\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I found it much more engaging, and a little bit more frustrating because I had to create a video for this assignment where I show I my work....\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e1-i: No further explanation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStudents provided no reason why engaging\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F: \u0026ldquo;\u003c/b\u003eI liked the video project.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"7\" nameend=\"c7\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNO: NOT MORE ENGAGING\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e2-a: Just change from routine\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStudent found it different but not significantly more engaging\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo; \u0026hellip;Just change from routine\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: None\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e2-b Time consuming because of tech issue or difficulties\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTechnical or preparing difficulties reduced engagement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;It definitely took a lot more out of me to complete this assignment I wasn't the biggest fan of having to do a lot of research for something that doesn't involve learning math, like spending an hour trying to figure out how I can record and things of that nature.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003e2-c: Speaking replaces written work\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eVideo simply substituted verbal for written explanation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I found the project to be about the same engagement as compared to traditional assignments. I think if we were to have more problems to explain, then I think it would make it more engaging and encouraging to do more work to present\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: none\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cem\u003eNote.\u003c/em\u003e Percentages exceed 100% because students could mention multiple preparation strategies (codes are not mutually exclusive). Online \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20; F2F \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;60.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e presents challenges students encountered when creating their video presentations.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eOpen-Ended Question 3: Challenges in Creating Video Presentation\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThemes\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOnline\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eF2F\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eExample from Student Responses\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3-a: Time constraint\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents struggled to fit content within 5-minute time limit\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e45%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e43%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;\u0026hellip;It was hard to show all of my work with every step in just a 5 min time frame.\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e:\u0026ldquo;The most challenging part of the video project for me was trying to keep the video within that 3\u0026ndash;5 minute mark...\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3-b: Technical difficulties\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents encountered technology or recording issues\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e37%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I found making the video the hardest part, even though the math was hard I just couldn't get my video to look good\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I wasn\u0026rsquo;t sure how it should have been filmed so I had to refill and submit it.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3-c: Remembering rubric requirement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents found it difficult to remember all rubric points while recording\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;The only thing I found really challenging was trying to remember all the points I wanted to hit on the rubric because it is hard to remember it all when I was talking\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;The thing I found challenging was remembering everything, like remembering how to solve each problem.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3-d: Explaining content clearly\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents struggled to explain concepts clearly and concisely\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e40%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e13%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;Creating the content was difficult, trying to figure out. My explanation tends to be long, and I can work on my presentation skills to make it more concise.\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;The most challenging thing about the video presentation was smoothly explaining everything in the allotted amount of time.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3-e: Anxiety\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents felt anxious or nervous about recording themselves.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e20%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e15%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I just get anxious when it comes to presenting and math isn't my strong suit so I second guess myself.\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I get anxious when doing videos for assignments, presentations, and just things that other people will see so doing the video what challenging in general,\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3-f: Time-consuming\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents spent more time than expected on this project.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e13%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;...Another obstacle was the time it took to record and re-record sections to make them clearer.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3-g: No challenges\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents did not find anything challenging.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I do not think I found anything too challenging about creating this video presentation\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;No i felt like the assignment wasn't difficult and rather fun\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003e\u003cem\u003eNote.\u003c/em\u003e Students often mentioned multiple challenges in their responses. Percentages may exceed 100% because codes are not mutually exclusive. Online \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;20; F2F \u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;60.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe most commonly reported challenge across both modalities was \u003cem\u003eTime Constraint\u003c/em\u003e (3-a), with online students (45%) and F2F students (43%) struggling to fit content within the 5-minute time limit. The second most prevalent challenge was \u003cem\u003eExplaining Content Clearly\u003c/em\u003e (3-d), with online students reporting this substantially more frequently (40% vs. 13%). Online students found it more difficult to articulate explanations concisely and clearly on camera. Notably, \u003cem\u003eTechnical Difficulties\u003c/em\u003e (3-b) were more common among F2F students (37% vs. 25%), with F2F students reporting challenges with technology and recording issues. \u003cem\u003eAnxiety\u003c/em\u003e (3-e) was somewhat higher among online students (20% vs. 15%), with students expressing nervousness about recording themselves. \u003cem\u003eTime-Consuming\u003c/em\u003e (3-f) was reported exclusively by F2F students (13% vs. 0%). Interestingly, a small percentage of students in both groups reported No Challenges (3-g: online 5%, F2F 8%).\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e presents themes related to student confidence in solving similar problems after completing the video project. Most students in both modalities reported feeling very confident, though online students demonstrated substantially higher confidence levels. \u003cem\u003eUnderstanding Both Conceptually and in Depth\u003c/em\u003e (4-1-a) was the most prevalent theme among online students (70%) and F2F students (50%). Online students expressed strong confidence in their ability to solve similar problems, attributing this to the deep understanding gained through teaching the material. \u003cem\u003eHelped Knowledge Retention\u003c/em\u003e (4-1-d) appeared more frequently among online students (20%) than F2F students (7%). Notably, the theme \u003cem\u003eNo Further Explanation\u003c/em\u003e (4-1-e) appeared exclusively among F2F students (23%), who expressed confidence without elaborating on the reasons.\u003c/p\u003e \u003cp\u003eWithin the \u0026ldquo;Somewhat Confident\u0026rdquo; category, small percentages of F2F students indicated they \u003cem\u003eStill Need Practice\u003c/em\u003e (8%) or felt confident \u003cem\u003eOnly for Similar Problems in the Project\u003c/em\u003e (3%). Among students who were \u0026ldquo;Not More Confident,\u0026rdquo; small percentages indicated the project had \u003cem\u003eSame as a Standard Assignment\u003c/em\u003e (4-3-a) (online 0% vs. F2F 7%) or that \u003cem\u003ethey Still Cannot Solve Without Class Resources\u003c/em\u003e (4-3-b) (online 0% vs. F2F 2%).\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e11\u003c/span\u003e presents the time students spent preparing and creating their video presentations. The most common time range for both modalities was \u003cem\u003eBetween 1 and 3 Hours\u003c/em\u003e (5-b: online 45%, F2F 52%). The second most prevalent range was \u003cem\u003eMore Than 6 Hours\u003c/em\u003e (5-d), with online students reporting this substantially more frequently (25% vs. 5%). Notable differences emerged across time categories. Online students were more likely to spend extended time: 25% spent \u003cem\u003e3\u0026ndash;6 Hours\u003c/em\u003e (5-c) versus 15% of F2F students, and 25% spent \u003cem\u003eMore Than 6 Hours\u003c/em\u003e (5-d) versus 5% of F2F students. Conversely, F2F students more frequently completed assignments in \u003cem\u003eLess Than 1 Hour\u003c/em\u003e (5-a: 13% vs. 5%). Overall, online students invested considerably more time in the video project than F2F students, with 50% of online students spending more than 3 hours compared to 20% of F2F students spending comparable time.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eOpen-Ended Question 4: Student Confidence in Solving Similar Problems\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThemes\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003eOnline\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eF2F\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003eExample from Student Responses\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"9\" nameend=\"c9\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eVery Confident\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-1-a: Understanding both conceptually and in depth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eStudents gained deep conceptual understanding through teaching.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e70%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e50%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I feel very confident that I know the material because I was able to teach it.\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I feel much more confident than I did previously. It makes me feel better about taking the exam.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-1-b: Requiring a lot of practice\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eThe project required a lot of practice, which helped build confidence in learning.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e7%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I feel pretty confident and this helped me practice a lot.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-1-c: identify areas for improvement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eIdentifying areas for improvement from the video gave students the opportunity to correct themselves.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I feel more confident with the material after completing the video project. ...helped me consolidate my understanding and identify areas where I needed to clarify my knowledge.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-1-d: Helped knowledge retention\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eVideo project helped retain knowledge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e20%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e7%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I feel more confident, which allowed me to dive deeper into the set, and explaining helped me retain the information better.\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I am pretty confident with what i know and my knowledge retention\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-1-e: No further explanation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eStudents provided no explanation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e23%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;A lot more confident that before!\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"9\" nameend=\"c9\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eSomewhat Confident\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-2-a: Still need practice\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eStudents gained confidence while recognizing the need for further practice.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e8%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I feel a little bit more prepared, but I still need to study.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-2-b: Only for similar questions in the project\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eConfidence limited to similar problems\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e3%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I feel a little more confident about the material I learned after completing this project. I also believe I can answer another question that is similar to the one that was provided for this project.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-2-c: Remember better\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eStudents built confidence by improving their memory\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F: \u0026ldquo;...\u003c/b\u003eI do think it'll help me remember for the test, though.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"9\" nameend=\"c9\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eNot More Confident\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"1\" nameend=\"c10\" namest=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-3-a: Same as a standard assignment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eThe project has the same effect as a standard assignment.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e7%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I feel the same, maybe a little more refreshed on the topic but that is all.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4-3-b: Still cannot solve without class resources\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eStudents still need class resources to solve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e0%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c8\" namest=\"c7\"\u003e \u003cp\u003e2%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c10\" namest=\"c9\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: None\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I still feel like unless I look at my notes I'm not sure how to solve for it.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"10\"\u003e\u003cem\u003eNote.\u003c/em\u003e Students within each confidence level could mention multiple reasons. Percentages within sub-themes may exceed the total for that confidence level because codes are not mutually exclusive.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eOpen-Ended Question 5: Time Spent on Video Presentation\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThemes\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eOnline\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eF2F\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eExample from Student Responses\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5-a: Less than 1 hour\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents spent less than 1 hour\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e13%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I spent about an hour preparing for the assignment, mostly just polishing up on my ability to solve\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I spent around 30 minutes.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5-b: Between 1 and 3 hours\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents spent 1\u0026ndash;3 hours\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e45%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e52%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;I would say I spent about 2 hours overall preparing, explaining, and editing the video to make sure it fit the time frame and that everything was explained to the best of my abilities.\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;In total I probably spent about an hour and a half on this assignment.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5-c: 3\u0026ndash;6 hours\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents spent 3\u0026ndash;6 hours\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e15%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;For preparation, it took me about 45 minutes to do the worksheet, and all the work. It took about 3 hours for me to put the presentation together, and it took me about 30 minutes to film, as I needed a couple of takes!\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I spent about 4 hours learning the material and explaining it to my classmates to be able to take the video.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5-d: More than 6 hours\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStudents spent more than 6 hours\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e25%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eOnline\u003c/b\u003e: \u0026ldquo;It took me about a day to prepare for this video project. I worked out the 9 questions for a few hours and then it took about two hours to record. I kept messing up the videos so it took me a while since I had to start over numerous times.\u0026rdquo;\u003c/p\u003e \u003cp\u003e\u003cb\u003eF2F\u003c/b\u003e: \u0026ldquo;I think I spent between 8 hours, about 4 hours solving the exercise, organizing, and planning, 1 hour recording, and about 3 practicing my speech.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study examines how video-based assessments function in undergraduate mathematics courses across online and F2F modalities, integrating four theoretical perspectives: self-explanation, iterative knowledge development, instrumental versus relational understanding, and self-regulation. Three key findings emerged that illuminate these theoretical predictions. First, video-based assessments supported conceptual understanding equally well in both modalities, consistent with self-explanation theory predicting that constructive learning processes operate similarly regardless of instructional format. Second, F2F students demonstrated stronger procedural knowledge development, consistent with predictions about differential regulatory supports across modalities. Third, transfer patterns revealed modality-based differences in the type of procedural knowledge developed. F2F students showed significant correlations between video and test performance, suggesting relational procedural understanding, while online students showed non-significant correlations, suggesting instrumental procedural knowledge that succeeded when resources were available but did not transfer to timed assessments. These patterns reveal that video-based assessment operates differently across instructional modalities in theoretically predictable ways.\u003c/p\u003e \u003cp\u003eNo statistically significant difference emerged in conceptual knowledge scores between F2F and online students who completed video projects, though a small-to-medium effect size favored F2F instruction (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.33). This equivalence indicates that video projects supported conceptual learning similarly across modalities, consistent with research demonstrating that appropriately designed online and F2F mathematics instruction can yield comparable outcomes (Edwards et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Russell et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2009\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe similarity in conceptual knowledge may reflect the self-explaining demands inherent in video creation, which require students to articulate mathematical ideas in their own words regardless of modality (Niess \u0026amp; Walker, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Within the ICAP framework, self-explaining constitutes a constructive learning activity that promotes deeper conceptual understanding than passive or active engagement (Chi \u0026amp; Wylie, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Both groups demonstrated comparable gains (F2F: \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;27.59; online: \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;26.29, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.141, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.33), though the effect size suggests F2F interaction may confer modest benefits.\u003c/p\u003e \u003cp\u003eIn contrast, F2F students demonstrated significantly higher procedural knowledge (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;39.75 vs. \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;38.02, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.046, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.54). This difference may reflect instructional supports more readily available in F2F settings, where mathematics instruction often incorporates gestures that ground procedures in physical action and make abstract ideas concrete (Alibali \u0026amp; Nathan, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Additionally, procedural development is supported by iterative practice with immediate feedback (Rittle-Johnson \u0026amp; Alibali, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) and hands-on manipulation (Moyer et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), both more consistently available when instructors can observe students\u0026rsquo; work in real time. These findings align with self-regulated learning theory (Zimmerman, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), which predicts that different instructional modalities provide different regulatory supports. F2F instruction offers external regulation through instructor observation and correction, while online instruction requires students to self-regulate more independently.\u003c/p\u003e \u003cp\u003eThe relationship between video project performance and unit test outcomes provides critical evidence about the type of procedural knowledge students developed in each modality. Skemp (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e1976\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) distinguished two forms of procedural understanding: instrumental understanding, which involves performing procedures without understanding why they work, and relational understanding, which involves procedural fluency grounded in conceptual comprehension. These two forms have different transfer properties. Instrumental knowledge remains situation-bound and does not transfer when supports change, while relational knowledge transfers across different assessment formats (Greeno, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1998\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOur findings support this theoretical distinction. For F2F students, procedural knowledge scores on video projects correlated significantly with unit test performance (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.34, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.004). This indicates that students who demonstrated procedural fluency on video projects also succeeded on timed tests. This pattern suggests relational procedural understanding that transferred even when supports such as resources and extra time were removed.\u003c/p\u003e \u003cp\u003eIn contrast, online students showed no significant correlation between video procedural scores and test performance (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.01, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.964). This pattern suggests instrumental procedural knowledge. Online students could perform procedures successfully when resources were available during video creation, but this knowledge did not transfer to the resource-restricted test environment. Notably, these differential transfer patterns emerged despite comparable unit test scores between groups (online: \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;11.74; F2F: \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;10.35, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.068, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u0026minus;\u0026thinsp;0.44). This indicates that both groups achieved similar test outcomes but through different knowledge development pathways.\u003c/p\u003e \u003cp\u003eThese knowledge transfer differences were reflected in how students experienced the video project. Open-ended survey responses revealed substantial modality-based differences. Online students more frequently reported scripting and rehearsing (75% vs. 55%), identifying weaknesses (20% vs. 3%), struggling with clear explanation (40% vs. 13%), attributing confidence to conceptual understanding (70% vs. 50%), and investing over three hours (50% vs. 20%). F2F students more often cited retention benefits (10% vs. 0%), experienced technical difficulties (37% vs. 25%), and expressed confidence without elaboration (23% vs. 0%).\u003c/p\u003e \u003cp\u003eOnline students\u0026rsquo; emphasis on scripting and rehearsing (75% vs. 55%) indicates they recognized the need to transform mathematical understanding into teachable explanations, a process that requires verbalization and supports deeper conceptual understanding (Roscoe \u0026amp; Chi, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). Explaining content engages learners in constructive activities (Chi et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2001\u003c/span\u003e) and enhances learning outcomes (Fiorella \u0026amp; Mayer, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Moreover, preparing to explain made knowledge gaps more visible, prompting online students to identify areas needing improvement at substantially higher rates (20% vs. 3%). This pattern of planning explanations through scripting, monitoring understanding, and reflecting on gaps represents self-regulated learning. In such processes, metacognitive activities promote deeper understanding (Zimmerman, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). This extensive metacognitive engagement may help explain why online students achieved similar conceptual knowledge scores despite different learning environments (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;26.29 vs. \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;27.59, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.141). In contrast, F2F students\u0026rsquo; emphasis on retention benefits (10% vs. 0%) suggests they used video projects as study tools rather than diagnostic opportunities.\u003c/p\u003e \u003cp\u003eChallenges differed by modality: 40% of online students reported difficulty explaining content clearly compared to 13% of F2F students, consistent with their greater preparation through scripting. F2F students experienced technical difficulties more frequently (37% vs. 25%) despite investing less time overall. Despite online students\u0026rsquo; extensive preparation, F2F students achieved higher procedural knowledge scores (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;39.75 vs. \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;38.02, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.046), indicating that time investment and metacognitive reflection, while supporting conceptual understanding, did not automatically translate to procedural fluency. Conceptual understanding and procedural fluency are distinct yet related strands of mathematical proficiency that develop through different instructional pathways (Jbeili, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; National Research Council, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), with F2F students\u0026rsquo; access to immediate instructor feedback potentially supporting greater procedural fluency (Francis et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOnline students more frequently attributed confidence to conceptual understanding gained through teaching (70% vs. 50%) and to improved retention (20% vs. 7%), consistent with research showing that explaining to others enhances both (Fiorella \u0026amp; Mayer, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). F2F students more often expressed confidence without elaboration (23% vs. 0%). These differing approaches were reflected in time investment: 50% of online students spent over 3 hours compared to 20% of F2F students, with online students more likely to invest substantial time (25% spent 3\u0026ndash;6 hours; 25% over 6 hours) than F2F students (15% spent 3\u0026ndash;6 hours; 5% over 6 hours). These patterns directly support our theoretical prediction that online students demand greater self-regulatory effort (Zimmerman, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), while F2F students benefited from external regulatory supports through instructor presence and peer interaction. Research indicates that online environments demand greater self-regulation, leading students to devote more time to planning, monitoring, and evaluating (Artino \u0026amp; Stephens, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2009\u003c/span\u003e, as cited in Al-Zohbi \u0026amp; Pilotti, 2022; Cardinale \u0026amp; Johnson, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Park, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eResearch indicates that online environments demand greater self-regulation, leading students to devote more time to planning, monitoring, and evaluating (Artino \u0026amp; Stephens, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2009\u003c/span\u003e, as cited in Al- Zohbi \u0026amp; Pilotti, 2022; Cardinale \u0026amp; Johnson, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Park, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). That F2F students spent less time despite higher technical difficulties (37% vs. 25%) suggests technical challenges do not fully explain the difference; rather, online learners chose extended engagement (Al-Zohbi \u0026amp; Pilotti, 2022; Park, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), with both groups relying on self-regulation enacted differently across modalities (Glenn, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe relationship between video performance and unit test scores differed by modality. In F2F courses, procedural knowledge correlated significantly with test performance (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.34, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.004), whereas online students' video scores showed no such relationship (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.01, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.964). Although online students developed strong metacognitive awareness through scripting and self-assessment, this preparation did not translate to improved test performance, possibly because extended preparation reinforced deliberate problem solving rather than the procedural fluency required under time pressure. In contrast, F2F students\u0026rsquo; regular verbal mathematical explanations during class may have supported both conceptual understanding and efficient problem solving. These patterns align with evidence that online video assignments promote metacognitive awareness and self-regulated learning through planning, explanation, and reflection (Cardinale \u0026amp; Johnson, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Cardace et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), whereas F2F instruction provides immediate feedback that supports procedural fluency (Al-Zohbi \u0026amp; Pilotti, 2022; Park, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTaken together, these findings demonstrate that video-based assessment operates differently across instructional modalities in theoretically predictable ways. Self-explanation through video creation supported conceptual knowledge development equally across modalities, as predicted by constructivist learning theory. However, procedural knowledge development and transfer varied by modality in ways consistent with self-regulated learning theory and Skemp's instrumental-relational framework. Online students engaged in extensive metacognitive planning and developed conceptual understanding but often developed instrumental procedural knowledge. F2F students benefited from immediate feedback and iterative correction that supported relational procedural understanding with stronger transfer. These findings reveal that video-based assessment effectiveness depends not only on self-explanation demands but also on how instructional modality shapes regulatory supports available during knowledge construction.\u003c/p\u003e \u003cdiv id=\"Sec21\" class=\"Section2\"\u003e \u003ch2\u003eLimitations and Future Research\u003c/h2\u003e \u003cp\u003eSeveral limitations should be considered. The study was conducted at a single institution with undergraduate mathematics students, limiting generalizability. The smaller online sample (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;29) relative to the F2F group (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;70) reflected fewer online sections offered rather than differential consent rates. Because students were not randomly assigned to instructional modality, observed differences may reflect both instructional context and pre-existing characteristics; accordingly, the study emphasizes patterns of performance and knowledge transfer rather than causal comparisons. Despite reduced power for some analyses, the study detected medium-to-large effects, including a significant difference in procedural knowledge (\u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.54). Additionally, the study examined video projects focused on a single topic, limiting generalizability to other content areas. Future research should investigate video-based assessments across diverse mathematical topics and student populations and explore instructional scaffolds that support procedural knowledge transfer in online environments. Despite these limitations, the findings indicate that video projects support conceptual learning comparably across modalities while revealing modality-based differences in procedural knowledge development and transfer.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study demonstrates that video projects effectively support conceptual understanding of exponential and logarithmic functions in both F2F and online mathematics courses. However, the type of procedural knowledge developed differed by modality. F2F students appeared to develop relational procedural knowledge that transferred to timed assessments, while online students appeared to develop instrumental procedural knowledge alongside strong metacognitive awareness but with limited transfer to unsupported testing contexts. By revealing how video-based assessments function differently across modalities, this study contributes to the understanding how innovative assessment approaches can support mathematics learning in diverse instructional environments.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cul type=\"disc\"\u003e\n \u003cli\u003eCompeting Interests: The authors have no relevant financial or non-financial interests to disclose.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eEthics Approval: This study was approved by the Utah Valley University Institutional Review Board.\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eInformed Consent: Informed consent was obtained from all participants included in the study.\u003c/li\u003e\n\u003c/ul\u003e\n\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAlibali, M. 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Becoming a self-regulated learner: An overview. \u003cem\u003eTheory Into Practice\u003c/em\u003e, \u003cem\u003e41\u003c/em\u003e(2), 64\u0026ndash;70. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1207/s15430421tip4102_2\u003c/span\u003e\u003cspan address=\"10.1207/s15430421tip4102_2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"video-based assessment, online learning, face-to-face instruction, procedural knowledge, conceptual knowledge, exponential functions, logarithmic functions","lastPublishedDoi":"10.21203/rs.3.rs-8634003/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8634003/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis mixed-methods study examined video-based assessments across online (\u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;29) and face-to-face (F2F, \u003cem\u003en\u003c/em\u003e\u0026thinsp;=\u0026thinsp;70) undergraduate mathematics courses. Students created videos explaining exponential and logarithmic functions and their inverse relationship. Data included video project scores (conceptual and procedural knowledge), unit test performance, and open-ended surveys. Conceptual knowledge was comparable across modalities (F2F: \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;27.59; online: \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;26.29, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.141), but F2F students demonstrated higher procedural knowledge (\u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;39.75 vs. \u003cem\u003eM\u003c/em\u003e\u0026thinsp;=\u0026thinsp;38.02, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.046, \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.54). Despite similar unit test performance, only F2F students\u0026rsquo; procedural knowledge correlated with test scores (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.34, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.004), while online students\u0026rsquo; video performance showed no relationship to test outcomes (\u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.01, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;.964). Qualitative analysis revealed online students engaged in more extensive preparation through scripting (75% vs. 55%), self-assessment (20% identified weaknesses vs. 3% F2F), and time investment (50% spent 3\u0026thinsp;+\u0026thinsp;hours vs. 20% F2F). F2F students emphasized retention benefits without elaboration. Findings indicate video-based assessments support conceptual learning across modalities while revealing modality-based differences in procedural knowledge development and transfer.\u003c/p\u003e","manuscriptTitle":"Video-Based Assessment and Learning of Exponential and Logarithmic Functions Across Instructional Modalities","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-29 17:33:53","doi":"10.21203/rs.3.rs-8634003/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"883b73de-2a73-455a-bfde-92f4590e1833","owner":[],"postedDate":"January 29th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-29T18:23:54+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-29 17:33:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8634003","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8634003","identity":"rs-8634003","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}