Bridging Mindfulness and Mathematics-Related Affect: Extending the Role of Conditional Task

Bridging Mindfulness and Mathematics-Related Affect: Extending the Role of Conditional Task | 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 Bridging Mindfulness and Mathematics-Related Affect: Extending the Role of Conditional Task Gyuhee Yi, Jihyun Lee This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8708945/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 study presents a secondary analysis of experimental data from Yi et al. ( 2024 ), shifting the focus to the cumulative affective consequences of a ten-lesson intervention. While the previous study established that conditional tasks embedded with uncertainty foster students’ mindfulness, it remained unclear how such cognitive shifts translate into broader affective outcomes. Using a quasi-experimental design, students were assigned to one of three groups in regular mathematics classes: a control group (conventional textbook-based tasks), and two experimental groups receiving different frequences of conditional tasks (one per lesson vs. three to four per lesson). A repeated measures two-way ANOVA revealed a significant discrepancy in developmental trajectories: while the control group’s mathematics-related affect declined, both experimental groups exhibited significant increases. These findings suggest that the pedagogical benefits of conditional tasks extend beyond mindfulness, offering a robust intervention to enhance students’ overall affective experiences in mathematics. mindfulness mathematics-related affect conditional mathematics task uncertainty classroom Figures Figure 1 Figure 2 Introduction Recent research in mathematics education has increasingly emphasized that, beyond the development of cognitive competencies, students’ affect plays a crucial role in shaping both their learning of mathematics and their long-term relationship with the subject (Di Martino & Zan, 2001 , 2014 ; Hannula, 2019 , 2020 ). Affect such as enjoyment, self-efficacy, and valuing are widely recognized as central factors of mathematics learning, influencing persistence, creativity, and achievement (Dowker et al., 2019 ; Goldin, 2014 ; Schukajlow et al., 2012 ; Singh et al., 2002 ). Accordingly, designing learning environments that nurture positive affective experiences has emerged as a challenge for mathematics educators (Winberg et al., 2014 ). Mathematics, unlike other academic disciplines, possesses a certainty that enables it to withstand doubts or challenges more effectively than other fields of study. Because it derives results through a logical process of proof from axioms, rather than relying on experiments or observation. However, in educational contexts, uncertainty is not merely a cognitive obstacle but a constitutive and productive element that promotes active knowledge construction (English, 2005; Sriraman, 2019 , 2022 ). Learners encountering incomplete, ambiguous, or conflicting information can consider the degree of uncertainty and potential ambiguities while engaging in learning (Leitner & Buttenfield, 2000 ; Padilla et al., 2021 ). Such engagement can foster transfer of knowledge across contexts (Lamnina & Chase, 2021 ) and elicit emotional responses such as curiosity, cognitive flexibility, and a relativistic attitude, enhancing motivation and persistence (Bohm et al., 2024; Jirout, 2020 ). In mathematics education, introducing uncertainty has been identified as a defining feature of productive mathematical tasks (Feldman et al., 2020 ). From this perspective, the conditional tasks proposed by Yi et al. ( 2024 ) serve as learning activities that deliberately embed uncertainty, inviting learners to explore various possibilities under under-determined conditions. Grounded in Langer’s ( 1993 ) theory of mindfulness, these tasks are designed to move beyond traditional certainties by integrating conditional language, diverse strategies and representations, and unfamiliar perspectives. By shifting the focus from finding a single correct answer to navigating multiple mathematical alternatives, these tasks aim to foster mindfulness, curiosity, and cognitive flexibility (Langer et al., 1989 ; Ritchhart & Langer, 1997 ; Yi et al., 2024 ). Consequently, exploring the impact of such tasks on students' affective orientations provides a crucial pathway for rethinking classroom instruction. Educational research is needed to develop theoretical concepts and pedagogical approaches that explore the possibilities of recognizing, welcoming, and even intentionally introducing disciplinary uncertainty in the classroom (Gomez & Lachuk, 2019). Building on this theoretical foundation, the present study extends the work of Yi et al. ( 2024 ) by shifting the focus from mindfulness to mathematics-related affect. Although recent educational research has reported meaningful effects of uncertainty on learning, studies on mathematical tasks embedding uncertainty are still limited. Feldman et al. ( 2020 ) investigated how uncertainty can be designed and incorporated into mathematical tasks; however, their study focused on prospective elementary teachers and provided concrete examples based on Zaslavsky’s ( 2005 ) three types of uncertainty—competing claims, unknown path or questionable conclusion, and non-readily verifiable outcomes—which differs from the theoretical approach to uncertainty embedded in mathematical tasks pursued in the present study. Accordingly, this study conducts a secondary analysis using the same experimental data as Yi et al. ( 2024 ) but employing mathematics-related affect measures. This analysis, it examines the effects of conditional tasks on students’ enjoyment, self-efficacy, and valuing, and further investigates whether the frequency of conditional tasks (one per lesson vs. three to four per lesson) differentially affects students’ affective outcomes. Accordingly, this study addresses the following research questions: RQ1. How do conditional tasks influence students’ mathematics-related affect? RQ2. Does the frequency of conditional tasks (one per lesson vs. three to four per lesson) lead to differential effects on students’ affective outcomes? Theoretical background Affect in Mathematics learning Mathematics education has long been regarded as education for thinking, with the underlying premise that the rationality cultivated through mathematics is essential for sustaining an open and democratic society (Heymann, 2013 ; Skovsmose, 1998 ). Ideally, the mathematics classroom serves as a primary domain for developing high-level cognitive processes and robust understanding (Schoenfeld, 2018 , 2020 ). However, as Lakatos ( 1976 ) critically observed, school mathematics is often presented as a finished product—a fixed system of knowledge devoid of historical debate or dialectical process. This static presentation limits students' opportunities to exercise mathematical agency, often fostering passive or even negative dispositions. To address this gap between ideal cognitive goals and actual classroom reality, it is necessary to look beyond cognitive outcomes and recognize the affective domain as a fundamental shaper of students’ mathematical experiences. Negative mathematics-related affect has been increasingly recognized as a significant societal concern, as it may limit future career opportunities and diminish the human capital necessary for a technologically advanced society (Hodgen et al., 2020 ; OECD, 2022 ). Accordingly, there is a global need for pedagogical interventions that can foster more positive mathematical experiences beyond mere cognitive success. This challenge is well illustrated in several high-performing East Asian systems, most notably in South Korea. While consistently achieving top-tier rankings in international assessments such as TIMSS 2023, students in these contexts often report relatively lower levels of enjoyment, self-efficacy, and valuing (von Davier et al., 2024 ). This discrepancy between high cognitive achievement and reserved affective orientation provides a unique opportunity to investigate the pedagogical roots of student engagement in mathematics. The construct of mathematics-related affect has been conceptualized in diverse ways. Some scholars define it as a unidimensional construct representing the degree of positive or negative emotions toward mathematics (McLeod, 1992 ). Others adopt a multidimensional perspective, encompassing enjoyment, self-efficacy, and valuing (Di Martino & Zan, 2001 , 2014 ). In the present study, we adopt the TIMSS perspective to operationalize and measure students’ mathematics-related affect. Specifically, affect was measured using a survey instrument developed and validated by Yi et al. ( 2017 ), which was adapted from the TIMSS framework and has demonstrated strong reliability and validity. Prior research has established that enjoyment, self-efficacy, and valuing are significant predictors of mathematics learning. For instance, enjoyment—the positive affective experience during learning—and self-efficacy—the belief in one’s capability to execute required actions (Zimmerman, 2000 )—are positively correlated with academic achievement (Bartimote-Aufflick et al., 2016 ; Schukajlow et al., 2021 ). Similarly, valuing, referring to the perceived importance and utility of the subject, deeply influences students’ choices and persistence (Seah, 2019 ). According to Schindler and Bakker ( 2020 ), it is plausible to assume that different cognitive experiences in the classroom, such as those provided by novel task designs, may impact students’ affective orientations, thereby shaping their enjoyment, self-efficacy, and valuing. Uncertainty and Conditional Tasks Despite the established importance of uncertainty in mathematical discovery and creativity, this element remains underexplored within the field of mathematics education (Sriraman, 2019 , 2022 ). Mathematicians often describe doubt, exploration, and moments of multiple possibilities as essential to generating new ideas. While proofs ultimately provide certainty, the path leading to them is often filled with uncertainty, and the certainty achieved through proof is itself relative, contingent on given conditions (Rott et al, 2014 ). This dual nature - certainty of results and uncertainty of processes - constitutes a central tension in mathematics (Greiffenhagen & Sharrock, 2011 ; Hersh, 1991 ), yet it is rarely addressed in school contexts (Sriraman, 2019 , 2022 ; Yi et al., 2017 ). In contrast to the creative practices of professional mathematicians, school mathematics has traditionally focused on certainty and correct answers. Lessons often emphasize procedures with clear solutions, leaving little room for ambiguity, exploration, or multiple problem-solving approaches. Classroom mathematics cultures tend to reward speed and accuracy over reflective thinking and flexibility, which can lead students to perceive mathematics as a rigid set of rules rather than an evolving discipline (Lampert, 1990 ; Star et al., 2015 ). This focus on certainty is further reinforced by assessment practices, which frequently reduce mathematical learning to the ability to reproduce correct solutions. Errors are penalized, and the value of exploring alternative approaches is minimized. Consequently, students may find it difficult to perceive uncertainty as a productive aspect of mathematics or to recognize engagement with the unknown as an essential mathematical activity (Alrø & Skovsmose, 1996 ; Beghetto & Schreiber, 2017). Research suggests that restricting mathematics solely to certainty can negatively impact students’ affective orientations. When uncertainty is excluded, opportunities for curiosity, creativity, and enjoyment are diminished. In particular, Sriraman ( 2022 ) argues that uncertainty serves as a critical catalyst for mathematical creativity; while his work primarily offers theoretical or conceptual foundations, our experimental study aims to provide empirical evidence to support this claim by examining how different frequencies of uncertainty-inducing tasks influence students' affective outcomes. More recent research has shown that students who experience uncertainty tend to develop a more positive mathematical identity and are more likely to perceive mathematics as an explorative discipline (Buckley & Sullivan, 2023 ). This gap between school mathematics and actual mathematical practice highlights the need to reconsider the role of uncertainty in classroom instruction. One way to address this gap is to intentionally design tasks that embed uncertainty. Conditional tasks serve as a prime example, distinguished from conventional open tasks by their specific structural design. While open tasks primarily focus on multiple correct answers, conditional tasks are characterized by: (1) the use of conditional language in task statements to signal uncertainty and stimulate hypothesis consideration (Langer et al., 1989 ; Langer & Piper, 1987 ); (2) the encouragement of multiple strategies and representations to support the exploration of alternative possibilities (Ritchhart & Langer, 1997 ; Schukajlow et al., 2015 ); and (3) the highlighting of unfamiliar perspectives to foster cognitive flexibility (Langer et al., 1985 ; Lee & Ryu, 2015 ; Maymin & Langer, 2021 ; Sullivan et al., 2012). Rather than simply seeking predetermined answers, students are invited to navigate under-determined information where the mathematical outcomes depend on the conditions they identify. Through this process, uncertainty is experienced as an integral part of authentic mathematical reasoning (Yi et al., 2018 , 2024 ). As will be illustrated in the methodology, these features transform a routine calculation into a reflective inquiry where students must manage the logical relationship between varied conditions and their corresponding possibilities. By navigating these features, students experience uncertainty not as a permanent state of confusion, but as a dynamic catalyst for cognitive development. Similar to Piaget’s ( 1977 ) mechanism of equilibration, the learning process through conditional tasks can be viewed as a continuous cycle of certainty and uncertainty. When students encounter uncertainty (disequilibrium) through under-determined information, they are driven to refine their reasoning and seek new justifications to reach a higher level of mathematical certainty (re-equilibration). In this sense, uncertainty in the learning process is an essential pedagogical moment that transforms a routine calculation into a reflective inquiry. Thus, by intentionally balancing these states, conditional tasks provide a structured yet open environment that supports both the cognitive and affective growth necessary for authentic mathematical practice. Mindfulness learning: Linking Conditional Tasks and Mathematics-Related Affect The concept of mindfulness, as defined by Langer ( 2000 ), provides a powerful psychological framework for linking conditional tasks with student affect in mathematics. Langer describes mindfulness as a state of active awareness characterized by the creation of new categories and openness to multiple perspectives. Conversely, mindlessness involves a rigid reliance on fixed categories, often leading to a passive engagement with knowledge. To facilitate a transition from mindlessness to mindfulness, Langer and colleagues have explored various intervention strategies, such as varying the context of information, highlighting the perspective-dependent nature of facts, and encouraging the exploration of alternative possibilities (Langer, 2000 ; Langer & Moldoveanu, 2000 ). Among these methodologies, conditional instruction serves as a primary work for fostering a mindful state in educational settings. A central component of this approach is the strategic use of conditional language. Traditional education tends to convey knowledge in absolute language (e.g., “is true”) as fixed and context-free, even when truths are only conditionally valid (Herbel-Eisenma, 2007). Langer’s experiments demonstrated that conditional phrasing (e.g., “could be true”) encourages learners to adopt more flexible, creative, and open modes of thinking. For instance, participants introduced to objects with conditional language were more likely to repurpose them in creative ways (Langer & Piper, 1987 ), and students exposed to conditional instructions produced more creative poems (Langer et al., 1989 ), demonstrated higher conceptual understanding, and generated novel mathematical strategies compared to peers taught with absolute language (Ritchart & Langer, 1997). These studies collectively highlight that uncertainty, when introduced through conditional instruction, fosters creativity, problem-solving, and deeper engagement with learning. From this perspective, conditional tasks can be understood as structured opportunities to elicit mindful engagement, aligning with the principle of Learning Mathematics by Doing Mathematics (Leinwand et al., 2014 ). Unlike memorization tasks that focus on the passive reproduction of fixed procedures (Stein & Lane, 1996 ), conditional tasks shift the focus toward active mathematical practices, such as making sense of problems and reasoning abstractly. Central to this shift is the transition from closed directions to open suggestions through the strategic use of conditional language. By replacing absolute mandates with ‘could be’ scenarios, these tasks embed uncertainty as an invitation for students to explore rather than follow. This framing transforms the task from a rigid command into a reflective inquiry where open suggestions (allowing for varied premises) and incomplete information (requiring students to identify necessary constraints) necessitate cognitive flexibility. This resonates with Langer’s notion that conditional framing induces a participatory mental state, enabling learners to see themselves as mathematical thinkers. Empirically, Yi et al. ( 2024 ) demonstrated that tasks designed with such embedded uncertainty cultivate mindfulness by encouraging an exploratory stance. By situating conditional tasks as opportunities for genuine doing, this research highlights their potential to reshape both the cognitive and affective experiences of students. The implications for mathematics-related affect are significant. As reviewed earlier, affective dimensions such as enjoyment, self-efficacy and valuing are strong predictors of achievement and long-term engagement (Di Martino & Zan, 2014 ). Yet, in traditional certainty-oriented classrooms, affect is often undermined by rigid practices that restrict exploration and amplify performance anxiety. By contrast, conditional tasks based on mindful learning can foster curiosity, intrinsic motivation, and engagement, thereby contributing positively to students’ affective orientations. In addition, mindfulness through conditional tasks reflects the dual nature of mathematics: certainty at the level of results and uncertainty at the level of processes (Sriraman, 2022 ). This structural balance reinforces the aforementioned cycle of equilibration; the process-level uncertainty acts as the necessary disequilibrium that drives students toward a more robust, justified certainty. By navigating this recursive movement between doubt and proof, students not only encounter uncertainty productively but also experience the satisfaction of resolving it through logical reasoning. This process supports a holistic synergy between cognitive development and affective growth. Moreover, the impact of such experiences may depend on the frequency of implementation. Investigating whether varying the number of conditional tasks per lesson leads to distinct changes in enjoyment, self-efficacy, and valuing provides further insights into the optimal pedagogical dosage required for sustainable engagement. By considering both the structural design and the quantitative frequency of task implementation, this perspective highlights how thoughtfully sequenced uncertainty can foster students’ holistic development in mathematics. Taken together, the body of work on conditional instruction (Langer, 1993 ; Langer & Piper, 1987 ; Langer et al., 1989 ; Ritchart & Langer, 1997; Lee & Ryu, 2015 ) demonstrates that mindfulness interventions are both practical and effective in educational contexts. Building on these insights, conditional tasks in mathematics can be intentionally designed to introduce uncertainty, thereby fostering creativity, affective engagement, and epistemological openness. In this way, mindfulness provides not only a psychological framework but also a pedagogical strategy for aligning conditional tasks with the development of positive affective orientations in mathematics education. Method This study builds on the experimental design reported in Yi, Lee, and Hwang ( 2024 ), which examined whether conditional mathematics tasks that embed uncertainty could cultivate students’ mindfulness. While the earlier study focused on mindfulness as the dependent variable, the present research maintains the same interventions and procedures but investigates a different outcome. Specifically, this study examines the impact of conditional mathematics tasks on students’ mathematics-related affect. In this way, the study reports a second set of findings from the same intervention, thereby contributing to a broader understanding of the educational potential of conditional tasks. Research design and sample The present study employed a teaching experiment integrated into the regular Grade 7 mathematics curriculum, maintaining the prescribed content and objectives. Two public middle schools located in Gyeonggi Province, a metropolitan region surrounding Seoul, South Korea, participated in the study. Both institutions demonstrate academic performance consistent with the national average in mathematics. In each school, two teachers with approximately four years of experience taught the experimental groups. For comparison, students taught by two other teachers at the same grade level served as control groups. The control group teachers varied in experience: one had slightly more than one year, while the other had more than ten years of teaching experience. Because the primary focus of the study was the influence of task design, groups were distinguished solely by the types of mathematical tasks provided. One experimental group (EG1, n = 71) received one conditional task per lesson, while another (EG2, n = 62) received three to four conditional tasks. These proportions correspond to roughly 20% and 60–80% of the total tasks typically covered in a lesson. The distinction between EG1 and EG2 not only allowed for examining the effects of conditional tasks in general but also provided an opportunity to investigate whether the frequency of conditional tasks per lesson leads to differential changes in students’ mathematics-related affect. In contrast, the control groups (n = 49) were taught using traditional textbook problems and standard worksheets. For analytical purposes, the two control groups were merged into a single control group, enabling more robust statistical comparisons with the experimental groups. To ensure consistency across the intervention, all participating teachers followed a standardized instructional schedule, while the researchers remained non-interventive except for the administration of pre- and post-tests. The final dataset included 182 participants who provided informed consent. Figure 1 provides an overview of the study design. Figure 1 Overview of the Study Design (Yi et al., 2024 , p.386 ) Instruments To investigate students’ mathematics-related affect, a scale was constructed consisting of three subscales: Enjoyment, Self-efficacy, and Valuing. This instrument underwent a validation process during the development phase, including development planning, item development, pilot testing, and main testing. This validation process ensured the instrument's validity. During this process, the fifteen preliminary questions were reduced to ten (Yi et al., 2018 ). Enjoyment subscale measured students’ emotional responses to mathematics classes. Self-efficacy subscale addressed students’ beliefs about their competence and confidence in mathematics. Valuing subscale measured the degree to which students perceived mathematics as useful and meaningful for their future. Table 1 illustrates items for each subscale. This scale was assessed through statements rated on a 7-point Likert-type scale (1 = strongly disagree to 7 = strongly agree). Negative-worded items were reverse-coded so that higher values reflected a more positive affective orientation. Table 1 Items of mathematics-related affect ( Yi, Lee, & Choi, 2017 ) Subscale Items Enjoyment I think studying mathematics is boring. a I look forward to mathematics class. I enjoy mathematics. Self-efficacy I am good at mathematics. I have more difficulty with mathematics than my classmates. a I feel nervous during mathematics class. a I learn mathematics quickly. Valuing I believe studying mathematics will help me. I believe learning mathematics is important for preparing for the future. I believe math is needed to study other subjects. a Reverse item The internal consistency of the mathematics-related affect scale was examined using Cronbach’s alpha. As shown in Table 2 , alpha values for the subscales ranged from 0.702 (EG2, self-efficacy, Post-test) to .0.907 (EG2, self-efficacy, Pre-test), with the total score demonstrating an alpha of 0.826. These results indicate that the scale exhibits acceptable to excellent internal consistency, supporting its reliability for measuring students’ mathematics-related affect within the context of this study. Table 2 Reliability of Mathematics-Related Affect Subscale Reliability (Cronbach’s alpha) CG EG1 EG2 Sum Enjoyment Pre-test 0.823 0.860 0.883 0.865 Post-test 0.839 0.795 0.871 0.842 Self-efficacy Pre-test 0.731 0.744 0.907 0.769 Post-test 0.798 0.789 0.702 0.761 Valuing Pre-test 0.887 0.880 0.814 0.891 Post-test 0.779 0.841 0.815 0.813 Sum Pre-test 0.872 0.830 0.886 0.865 Post-test 0.822 0.800 0.854 0.826 Table 3 presents the pre- and post-test correlations of mathematics-related affect for each group and subscale. Notably, the total score demonstrated consistently strong positive correlations across groups (r = 0.719–0.779), indicating good overall test–retest reliability of the scale. At the subscale level, significant positive correlations were also observed between pre- and post-test scores, suggesting that students’ relative rankings on enjoyment, self-efficacy, and valuing remained stable over time. Specifically, correlations for enjoyment ranged from r = 0.667 to 0.723, for self-efficacy from r = 0.632 to 0.809, and for valuing from r = 0.382 to 0.786. All correlations were statistically significant at p < .01, further supporting the reliability of the mathematics-related affect measures. Table 3 Pre-and Post-Test Correlation of Mathematics-Related Affect Subscale CG EG1 EG2 Sum Enjoyment 0.723** 0.701** 0.667** 0.706** Self-efficacy 0.632** 0.786** 0.809** 0.747** Valuing 0.701** 0.382** 0.786** 0.414** Sum 0.726** 0.779** 0.719** 0.739** ** p < 0.01 Task Development The independent variable in this study was the implementation of conditional mathematics tasks. Rather than redefining the theoretical principles of conditional instruction previously discussed, this section focuses on how those principles were operationalized into the specific mathematical tasks used in the intervention. Specifically, the design followed Langer’s framework to shift students from a mindless to a mindful state. To achieve this, the tasks were developed to intentionally deviate from conventional textbook problems by: (1) replacing absolute phrasing with conditional language to signal uncertainty; (2) structuring problems to necessitate multiple strategies and representations; and (3) introducing unfamiliar perspectives that require students to manage under-determined information. While these design features are often associated with fostering a mindful state in a general sense, the present study specifically examines their role in stimulating students’ affective responses, such as enjoyment and self-efficacy, within the context of mathematical problem-solving. To identify a contrasting baseline, we analyzed Korean mathematics textbooks focusing on integers and rational numbers. Consistent with earlier studies (Woo & Choi, 2007 ; Yoo, 2007 ), we found that these textbooks typically introduce negative numbers through direct definition, present operation rules with formal justification, and rely heavily on procedural practice. For example, tasks such as “Calculate \(\:(-3)\times\:(-5)\) ” (Kim et al., 2016 , p.45) exemplify the emphasis on rote application of rules without opportunities for exploration or reflection. In contrast, conditional tasks were designed to invite students to think deeply about mathematical ideas from new or different perspectives. For instance, to open a new perspective on negative numbers, we asked, “We typically call 1, 2, 3, and 4 integers. However, why could we also consider them to be rational numbers?”. To encourage multiple expressions in algebraic operations, we asked students to reconfigure a given numerical expression into as many equivalent forms as possible by strategically changing the signs of numbers or the operations (addition and subtraction). For example, students were tasked with finding multiple ways to represent expressions such as (1) \(\:8+(-10)\) and (2) \(\:(-25)+(-44)\) by exploring the logical relationships between signs and operations. Additionally, we developed a task using a number line model to introduce the concept of symmetry—a perspective rarely emphasized in traditional textbooks for this topic. In this task, students were asked to visualize negative numbers and their operations as symmetrical movements or reflections across the origin (zero) on the number line. In classroom implementation, experimental group teachers typically allowed students individual time to explore the tasks before facilitating whole-class discussion. Since the conditional tasks in the present study were identical to those Yi et al. ( 2024 ), representative tasks for Experiment Group 1 and 2 are presented in Tables 4 and 5 , respectively, while the complete set of tasks can be found in the previous study. In classroom implementation, teachers in the experimental groups typically provided students with individual time to explore these tasks before facilitating whole-class discussions. The complete set of conditional tasks used in this study follows the design established by Yi et al. ( 2024 ). Since the detailed structure and full inventory of these tasks have been documented in the previous work, we direct readers to that publication for the complete instrument. Data Analysis Data were analyzed using a two-way repeated measures analysis of variance (RM-ANOVA) with SPSS Statistics 21. The dependent variable was mathematics-related affect, which was examined at two levels: (a) separately for each of the three subscales (enjoyment, self-efficacy, valuing) and (b) as a total score representing students’ overall mathematics-related affect. Independent variables were group (EG1, EG2, CG) and time (pre-test, post-test). Levene’s tests confirmed the assumption of homogeneity of variances at the 5% significance level across all subscales and the total score. While normality was not directly tested, RM-ANOVA is generally robust to violations of this assumption, especially with balanced designs. The assumption of sphericity did not apply, as only two measurement points were used (Blanca et al., 2023). This analytic approach allowed for examination of both main effects and interaction effects, providing evidence on whether the introduction of conditional tasks influenced students’ mathematics-related affect, both at the level of specific subscales and in terms of the overall total score, over the course of the intervention. Specifically, interaction effects between group (EG1, EG2, CG) and time (pre-test, post-test) were examined not only to identify overall differences in mathematics-related affect but also to explore whether the frequency of conditional tasks influenced affective changes differently between the experimental groups. Results Overall, the students’ mathematics-related affect exhibited different patterns of change from pre-test to post-test across the three groups. In the control group, most subscales and the total score showed slight decreases, with the exception of Enjoyment, which remained relatively stable. In contrast, both experimental groups demonstrated consistent positive shifts in their total scores and subscales. For instance, Enjoyment increased in EG1 (11.66 to 12.00) and EG2 (10.56 to 11.68), whereas the CG remained relatively unchanged. Self-efficacy followed a similar upward trend, particularly in EG2 (15.21 to 16.48). Notably, the total score (Sum) for the experimental groups showed modest improvements (EG1: 46.11 to 47.34; EG2: 43.48 to 46.10), while the CG exhibited a slight decline (48.88 to 47.98). Standard deviations in EG2 generally decreased from pre-test to post-test, indicating that students’ scores became somewhat more consistent after the intervention. Finally, the pre-test means indicate that initial scores varied across groups, which should be taken into account in subsequent analyses of group differences. Table 4 presents the descriptive statistics of the pre- and post-test scores for each group and subscale, providing a detailed overview of these trends. Table 4 Descriptive Statistics of Mathematics-Related Affect Subscale Group Pre-test Post-test Mean Standard Deviation Mean Standard Deviation Enjoyment CG 13.47 4.01 13.61 3.98 EG1 11.66 4.11 12.00 3.83 EG2 10.56 4.44 11.68 4.18 Self-efficacy CG 16.53 3.51 16.51 2.94 EG1 16.58 3.60 17.21 2.76 EG2 15.21 4.62 16.48 3.28 Valuing CG 18.88 4.71 17.86 4.98 EG1 17.87 4.88 18.13 4.68 EG2 17.71 5.64 17.94 4.78 Sum CG 48.88 10.13 47.98 9.14 EG1 46.11 9.55 47.34 8.18 EG2 43.48 11.87 46.10 9.74 Note . CG: Control Group, EG1: Experimental Group 1, EG2: Experimental Group 2 A repeated measures ANOVA (RM-ANOVA) confirmed these observations (Table 5 ). For the total score (Sum), although the main effect of Time was not significant (p = 0.071), the Time*Group interaction effect was statistically significant, F(2, 179) = 3.267, p = 0.040. This indicates that the trajectory of affective change differed significantly among the groups, with the experimental groups showing favorable growth compared to the control group. Furthermore, EG2, which received a higher frequency of conditional tasks, tended to show slightly greater gains than EG1, providing preliminary evidence that task frequency may influence the magnitude of affective development. For Self-efficacy, neither the main effect of Time, F(1,179) = 0.472, p = 0.493, nor the Time*Group interaction, F(2,179) = 2.325, p = 0.101, was significant. The between-subjects effect of group was also not significant, F(2,179) = 0.193, p = 0.825. These results suggest that Self-efficacy remained relatively stable across time and did not differ significantly between groups. Valuing showed a significant main effect of Time, F(1,179) = 4.730, p = 0.031, indicating that there was an overall change in scores from pre-test to post-test. However, when examined by group, the experimental groups exhibited slight increases, whereas the control group showed a decreasing trend. The Time*Group interaction was not significant, F(2,179) = 1.548, p = 0.215, suggesting that the differences in Valuing changes between groups were not statistically significant. Finally, for the total score (Sum), the main effect of Time was not significant, F(1,179) = 3.296, p = 0.071, but the Time*Group interaction was significant, F(2,179) = 3.267, p = 0.040. This indicates that the overall change in mathematics-related affect differed across groups, with the experimental groups showing modest improvements relative to the control group. The between-subjects effect of group was not significant, F(2,179) = 2.209, p = 0.113. Moreover, although both experimental groups exhibited improvements in mathematics-related affect, EG2, which received a higher frequency of conditional tasks, tended to show slightly greater gains than EG1. This pattern suggests that the frequency of conditional tasks may influence the magnitude of affective changes, providing partial support for the second research question. In summary, the conditional mathematics tasks appear to have had small but meaningful effects on students’ mathematics-related affect, particularly in terms of overall scores, while changes in individual subscales were more limited. Table 5 RM-ANOVA Results LMS-Y Source Sum of Squares df Mean Square F p-value Enjoyment Within-Subjects Time 25.090 1 25.090 4.865 0.029 Time*Group 15.479 2 7.739 1.501 0.226 Error(time) 923.049 179 5.157 Between-Subjects Treatment(group) 331.644 2 165.822 5.839 0.003 Error 5083.466 179 28.399 Self-efficacy Within-Subjects Time 2.892 1 2.892 0.472 0.493 Time*Group 28.482 2 14.241 2.325 0.101 Error(time) 1096.627 179 6.126 Between-Subjects Treatment(group) 16.589 2 8.295 0.193 0.825 Error 7692.872 179 42.977 Valuing Within-Subjects Time 35.192 1 35.192 4.730 0.031 Time*Group 23.038 2 11.519 1.548 0.215 Error(time) 1331.899 179 7.441 Between-Subjects Treatment(group) 73.583 2 36.792 2.143 0.120 Error 3073.463 179 17.170 Sum Within-Subjects Time 85.392 1 85.392 3.296 0.071 Time*Group 169.250 2 84.625 3.267 0.040 Error(time) 4636.797 179 25.904 Between-Subjects Treatment(group) 733.940 2 366.970 2.209 0.113 Error 29737.337 179 166.130 To visually illustrate the statistically significant total score (Sum) results, Fig. 2 presents the pre- and post-test mean scores for each group, with lines connecting the points to indicate the direction of change. The figure highlights the Time*Group interaction, showing modest increases in the experimental groups and a slight decrease in the control group. Figure 2 Changes in Mathematics-Related Affect by Groups Note CG: Control Group, EG1: Experimental Group 1, EG2: Experimental Group 2 Discussion and Conclusion The present study offers valuable insights how conditional mathematics tasks designed to embed uncertainty may influence students’ affective orientations in mathematics classrooms. Prior research has consistently demonstrated that conditional instruction can foster creativity, flexibility, and mindfulness (Langer, 2000 ; Langer et al., 1985 ; Langer et al., 1989 ; Langer & Piper, 1987 ; Ritchhart & Langer, 1997 ; Yi et al., 2018 , 2024 ). For instance, Ritchhart and Langer ( 1997 ) reported that conditional instruction of newly defined arithmetic operations significantly enhanced problem-solving ability and creativity compared to absolute instruction. Although their findings were situated in a controlled context, they provided critical early evidence that uncertainty-based instruction could move students beyond rote procedural thinking. Building on this foundation, recent studies in authentic mathematics classrooms (Yi et al., 2018 , 2024 ) have confirmed that such tasks improve cognitive flexibility and promote a mindful state. The present study shifts the focus of this line of inquiry from the state of mindfulness itself to students’ mathematics-related affective orientations. By demonstrating that conditional tasks can contribute to meaningful changes in students’ affect within a regular school setting, this research bridges the gap between earlier experimental findings and the practical goals of holistic mathematics education. Most notably, the experimental groups in this study, who engaged with uncertainty-embedded conditional tasks, exhibited small but statistically significant improvements in mathematics-related affect, whereas the control group tended to decline over time. Although the control group maintained the highest absolute scores, the pattern of change highlights the potential of conditional tasks to prevent affective deterioration and to sustain or promote more positive orientations toward mathematics. These findings suggest that embedding uncertainty within conditional mathematics tasks may help students engage in productive exploration, aligning classroom experiences more closely with authentic mathematical practices where doubt and multiple possibilities are integral (Sriraman, 2019 , 2022 ). In contexts where affect is often overshadowed by cognitive performance, this result suggests that carefully designed uncertainty-embedded mathematics tasks can have the dual function of fostering conceptual growth and nurturing affective engagement. Conditional tasks, in this sense, emerge not only as tools for promoting diverse thinking and flexibility, but also as instructional strategies that can help students develop and maintain more positive relationships with mathematics. Moreover, although both experimental groups exhibited improvements in mathematics-related affect, EG2, which received a higher frequency of conditional tasks, tended to show slightly greater gains than EG1. This pattern suggests that the frequency of conditional tasks may influence the magnitude of affective changes. These findings carry several implications. First, from a theoretical perspective, the study extends Langer’s framework of mindful learning into the domain of mathematics education. While previous research was largely situated in psychological experiments or general learning contexts, this study demonstrates that the principles of mindful learning operate meaningfully within a discipline-specific setting. By doing so, it underscores the relevance of mindfulness not only as a general educational orientation but also as a framework for designing domain-sensitive interventions (Lee & Ryu, 2015 ). Furthermore, the study establishes concrete design principles for conditional mathematics instruction and provides specific task examples that effectively embed uncertainty. This contribution is particularly significant because it illustrates how theoretical constructs—such as conditionality and mindfulness—can be operationalized into tangible instructional materials. Specifically, it offers mathematics educators a practical model for transforming abstract cognitive theories into classroom-ready tasks that stimulate both reflective inquiry and affective engagement. More broadly, the results resonate with the growing recognition in mathematics education that cognition and affect are deeply intertwined, and that theoretical models must account for both dimensions in order to capture the complexity of learning. Second, in terms of practical implications, this study shows that uncertainty-embedded conditional tasks can be implemented effectively within regular classroom instruction as part of the official mathematics curriculum. Much of the innovation in instructional approaches often remains confined to controlled laboratory settings or isolated pilot studies (e.g., Langer & Piper, 1987 ; Ritchhart & Langer, 1997 ). By contrast, the present study demonstrates that conditional tasks can be seamlessly integrated into everyday lessons, providing empirical evidence of their feasibility. This is particularly significant given the widespread concern in global mathematics education regarding students’ declining affective orientations. International assessments repeatedly report that as students progress through formal schooling, their interest, enjoyment, and self-efficacy in mathematics tend to diminish, even among those with high cognitive proficiency (OECD, 2022 ). Against this backdrop, conditional tasks hold promise not only as tools for promoting cognitive flexibility but also as a pedagogical strategy for sustaining and improving students’ emotional engagement. Teachers, therefore, can utilize uncertainty-embedded instruction to design lessons that simultaneously cultivate cognitive and affective growth, fostering a more balanced and human-centered mathematics education. Third, the study carries important methodological implications while also acknowledging its limitations. Although the findings confirm that uncertainty-embedded conditional tasks exert a measurable effect on affective outcomes, the complexity of the mathematics classroom must be considered. Specifically, a critical challenge in authentic classroom research is that the impact of a task depends not only on its design but also on how it is enacted by the teacher (e.g., Baumert et al., 2010 ; Wayne & Youngs, 2003 ). In this study, while the tasks were standardized, the pedagogical implementation—including the teacher’s framing, scaffolding, and classroom management—was not fully controlled. For instance, the high level of engagement observed in some groups may have been influenced by the individual teacher’s instructional delivery rather than the task design alone. This underscores that task development and task implementation are distinct dimensions, and future research should focus on monitoring the fidelity of implementation to better isolate the effects of the tasks themselves. Additionally, as one of the earliest attempts to apply Langer’s mindfulness theory to mathematics education, these results should be interpreted with caution. Further replication across diverse grade levels, mathematical domains, and longitudinal time frames is necessary to establish the robustness and generalizability of the findings. Despite these limitations, the present study provides valuable insights into how uncertainty-embedded conditional mathematics tasks can influence students’ cognitive and affective engagement in mathematics classrooms, and it points to the potential for further active research on conditional mathematics tasks informed by Langer’s mindfulness framework. Declarations Ethics Approval The study was approved by the Institutional Review Board of Seoul National University. Consent for Participation and Publication Informed consent was obtained from all individual participants included in the study. Availability of data and materials The datasets generated during the current study are not publicly available due to IRB restrictions regarding participant privacy. Competing interests The authors have no competing interests to declare. Funding No funding was received. Authors' contributions G.Y. contributed to the design and implementation of the teaching experiment, statistical analysis, and drafting the manuscript. J. L. contributed to literature review, the design and implementation of the teaching experiment, data collection, and revision. Acknowledgements The authors would like to express their deepest gratitude to Professor Younggi Choi of the Department of Mathematics Education at Seoul National University for his invaluable guidance, continuous support, and profound inspiration throughout this project. His insightful perspectives were instrumental in the development of this research. Clinical Trial Registration Not applicable References Alrø, H., & Skovsmose, O. (1996). On the right track. For the Learning of Mathematics, 16 (1), 2-22. Bartimote-Aufflick, K., Bridgeman, A., Walker, R., Sharma, M., & Smith, L. (2016). 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Self-efficacy: An essential motive to learn. Contemporary educational psychology , 25 (1), 82-91. 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8708945","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":592983579,"identity":"68c6a7eb-77f9-4e0d-b9f7-64685cbc34b9","order_by":0,"name":"Gyuhee Yi","email":"","orcid":"","institution":"Inhun High School","correspondingAuthor":false,"prefix":"","firstName":"Gyuhee","middleName":"","lastName":"Yi","suffix":""},{"id":592983580,"identity":"0fa3bd4d-8421-4fac-bd4f-d032212d3c96","order_by":1,"name":"Jihyun Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYBACxmYeEGXBwMDe2AAR4iFOiwRQ5UEitUBVALVIJCAL4AHM7bzHpHl3SMjxSz5ue8zDYCfPwHP2AQGH8aVJ856RMJacndhuzMOQbNjA225AQAuPmTRvm0TihtuJbdI8DMwJDPxs+B0G01K//+ZBkJZ64rUkGEgwgrQcTmDgbSOoxdhybpuE4YwziW2ScwyOG7bxHMOvxbD/jOGNt2028vztx59JvKmolufnSSOgpYGBRQLBBYYVAZ8wMMgDo+YDIUWjYBSMglEwwgEAiWE0TjjnFZQAAAAASUVORK5CYII=","orcid":"","institution":"Incheon National University","correspondingAuthor":true,"prefix":"","firstName":"Jihyun","middleName":"","lastName":"Lee","suffix":""}],"badges":[],"createdAt":"2026-01-27 10:20:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8708945/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8708945/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103505960,"identity":"ff10c473-e5a2-42d9-b6e6-d679015bc27a","added_by":"auto","created_at":"2026-02-26 13:33:39","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":69882,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eOverview of the Study Design (Yi et al., 2024, p.386 )\u003c/em\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8708945/v1/46092f6edb0989e78d2a532f.png"},{"id":103257454,"identity":"bc484e4b-3957-47a7-be5e-6654f8290905","added_by":"auto","created_at":"2026-02-23 17:11:39","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":46500,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eChanges in Mathematics-Related Affect by Groups\u003c/em\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8708945/v1/1d0c1e733eef8c7d82edbc39.png"},{"id":104779143,"identity":"294265ea-9d6f-4b2d-8761-cde8e2d88c47","added_by":"auto","created_at":"2026-03-17 07:35:42","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1000543,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8708945/v1/b4c432fb-4082-4add-9525-9cba112c375f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bridging Mindfulness and Mathematics-Related Affect: Extending the Role of Conditional Task","fulltext":[{"header":"Introduction","content":"\u003cp\u003eRecent research in mathematics education has increasingly emphasized that, beyond the development of cognitive competencies, students\u0026rsquo; affect plays a crucial role in shaping both their learning of mathematics and their long-term relationship with the subject (Di Martino \u0026amp; Zan, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2001\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Hannula, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Affect such as enjoyment, self-efficacy, and valuing are widely recognized as central factors of mathematics learning, influencing persistence, creativity, and achievement (Dowker et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Goldin, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Schukajlow et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Singh et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Accordingly, designing learning environments that nurture positive affective experiences has emerged as a challenge for mathematics educators (Winberg et al., \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eMathematics, unlike other academic disciplines, possesses a certainty that enables it to withstand doubts or challenges more effectively than other fields of study. Because it derives results through a logical process of proof from axioms, rather than relying on experiments or observation. However, in educational contexts, uncertainty is not merely a cognitive obstacle but a constitutive and productive element that promotes active knowledge construction (English, 2005; Sriraman, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Learners encountering incomplete, ambiguous, or conflicting information can consider the degree of uncertainty and potential ambiguities while engaging in learning (Leitner \u0026amp; Buttenfield, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Padilla et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Such engagement can foster transfer of knowledge across contexts (Lamnina \u0026amp; Chase, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) and elicit emotional responses such as curiosity, cognitive flexibility, and a relativistic attitude, enhancing motivation and persistence (Bohm et al., 2024; Jirout, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn mathematics education, introducing uncertainty has been identified as a defining feature of productive mathematical tasks (Feldman et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). From this perspective, the conditional tasks proposed by Yi et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) serve as learning activities that deliberately embed uncertainty, inviting learners to explore various possibilities under under-determined conditions. Grounded in Langer\u0026rsquo;s (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1993\u003c/span\u003e) theory of mindfulness, these tasks are designed to move beyond traditional certainties by integrating conditional language, diverse strategies and representations, and unfamiliar perspectives. By shifting the focus from finding a single correct answer to navigating multiple mathematical alternatives, these tasks aim to foster mindfulness, curiosity, and cognitive flexibility (Langer et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1989\u003c/span\u003e; Ritchhart \u0026amp; Langer, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Yi et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Consequently, exploring the impact of such tasks on students' affective orientations provides a crucial pathway for rethinking classroom instruction.\u003c/p\u003e \u003cp\u003eEducational research is needed to develop theoretical concepts and pedagogical approaches that explore the possibilities of recognizing, welcoming, and even intentionally introducing disciplinary uncertainty in the classroom (Gomez \u0026amp; Lachuk, 2019). Building on this theoretical foundation, the present study extends the work of Yi et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) by shifting the focus from mindfulness to mathematics-related affect. Although recent educational research has reported meaningful effects of uncertainty on learning, studies on mathematical tasks embedding uncertainty are still limited. Feldman et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) investigated how uncertainty can be designed and incorporated into mathematical tasks; however, their study focused on prospective elementary teachers and provided concrete examples based on Zaslavsky\u0026rsquo;s (\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) three types of uncertainty\u0026mdash;competing claims, unknown path or questionable conclusion, and non-readily verifiable outcomes\u0026mdash;which differs from the theoretical approach to uncertainty embedded in mathematical tasks pursued in the present study. Accordingly, this study conducts a secondary analysis using the same experimental data as Yi et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) but employing mathematics-related affect measures. This analysis, it examines the effects of conditional tasks on students\u0026rsquo; enjoyment, self-efficacy, and valuing, and further investigates whether the frequency of conditional tasks (one per lesson vs. three to four per lesson) differentially affects students\u0026rsquo; affective outcomes.\u003c/p\u003e \u003cp\u003eAccordingly, this study addresses the following research questions:\u003c/p\u003e \u003cp\u003eRQ1. How do conditional tasks influence students\u0026rsquo; mathematics-related affect?\u003c/p\u003e \u003cp\u003eRQ2. Does the frequency of conditional tasks (one per lesson vs. three to four per lesson) lead to differential effects on students\u0026rsquo; affective outcomes?\u003c/p\u003e\n\u003ch3\u003eTheoretical background\u003c/h3\u003e\n\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eAffect in Mathematics learning\u003c/h2\u003e \u003cp\u003eMathematics education has long been regarded as education for thinking, with the underlying premise that the rationality cultivated through mathematics is essential for sustaining an open and democratic society (Heymann, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Skovsmose, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). Ideally, the mathematics classroom serves as a primary domain for developing high-level cognitive processes and robust understanding (Schoenfeld, \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). However, as Lakatos (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1976\u003c/span\u003e) critically observed, school mathematics is often presented as a finished product\u0026mdash;a fixed system of knowledge devoid of historical debate or dialectical process. This static presentation limits students' opportunities to exercise mathematical agency, often fostering passive or even negative dispositions. To address this gap between ideal cognitive goals and actual classroom reality, it is necessary to look beyond cognitive outcomes and recognize the affective domain as a fundamental shaper of students\u0026rsquo; mathematical experiences.\u003c/p\u003e \u003cp\u003eNegative mathematics-related affect has been increasingly recognized as a significant societal concern, as it may limit future career opportunities and diminish the human capital necessary for a technologically advanced society (Hodgen et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; OECD, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Accordingly, there is a global need for pedagogical interventions that can foster more positive mathematical experiences beyond mere cognitive success. This challenge is well illustrated in several high-performing East Asian systems, most notably in South Korea. While consistently achieving top-tier rankings in international assessments such as TIMSS 2023, students in these contexts often report relatively lower levels of enjoyment, self-efficacy, and valuing (von Davier et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). This discrepancy between high cognitive achievement and reserved affective orientation provides a unique opportunity to investigate the pedagogical roots of student engagement in mathematics.\u003c/p\u003e \u003cp\u003eThe construct of mathematics-related affect has been conceptualized in diverse ways. Some scholars define it as a unidimensional construct representing the degree of positive or negative emotions toward mathematics (McLeod, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1992\u003c/span\u003e). Others adopt a multidimensional perspective, encompassing enjoyment, self-efficacy, and valuing (Di Martino \u0026amp; Zan, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2001\u003c/span\u003e, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). In the present study, we adopt the TIMSS perspective to operationalize and measure students\u0026rsquo; mathematics-related affect. Specifically, affect was measured using a survey instrument developed and validated by Yi et al. (\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2017\u003c/span\u003e), which was adapted from the TIMSS framework and has demonstrated strong reliability and validity.\u003c/p\u003e \u003cp\u003ePrior research has established that enjoyment, self-efficacy, and valuing are significant predictors of mathematics learning. For instance, enjoyment\u0026mdash;the positive affective experience during learning\u0026mdash;and self-efficacy\u0026mdash;the belief in one\u0026rsquo;s capability to execute required actions (Zimmerman, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2000\u003c/span\u003e)\u0026mdash;are positively correlated with academic achievement (Bartimote-Aufflick et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Schukajlow et al., \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Similarly, valuing, referring to the perceived importance and utility of the subject, deeply influences students\u0026rsquo; choices and persistence (Seah, \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). According to Schindler and Bakker (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), it is plausible to assume that different cognitive experiences in the classroom, such as those provided by novel task designs, may impact students\u0026rsquo; affective orientations, thereby shaping their enjoyment, self-efficacy, and valuing.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eUncertainty and Conditional Tasks\u003c/h3\u003e\n\u003cp\u003eDespite the established importance of uncertainty in mathematical discovery and creativity, this element remains underexplored within the field of mathematics education (Sriraman, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Mathematicians often describe doubt, exploration, and moments of multiple possibilities as essential to generating new ideas. While proofs ultimately provide certainty, the path leading to them is often filled with uncertainty, and the certainty achieved through proof is itself relative, contingent on given conditions (Rott et al, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). This dual nature - certainty of results and uncertainty of processes - constitutes a central tension in mathematics (Greiffenhagen \u0026amp; Sharrock, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Hersh, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1991\u003c/span\u003e), yet it is rarely addressed in school contexts (Sriraman, \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Yi et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn contrast to the creative practices of professional mathematicians, school mathematics has traditionally focused on certainty and correct answers. Lessons often emphasize procedures with clear solutions, leaving little room for ambiguity, exploration, or multiple problem-solving approaches. Classroom mathematics cultures tend to reward speed and accuracy over reflective thinking and flexibility, which can lead students to perceive mathematics as a rigid set of rules rather than an evolving discipline (Lampert, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1990\u003c/span\u003e; Star et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis focus on certainty is further reinforced by assessment practices, which frequently reduce mathematical learning to the ability to reproduce correct solutions. Errors are penalized, and the value of exploring alternative approaches is minimized. Consequently, students may find it difficult to perceive uncertainty as a productive aspect of mathematics or to recognize engagement with the unknown as an essential mathematical activity (Alr\u0026oslash; \u0026amp; Skovsmose, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1996\u003c/span\u003e; Beghetto \u0026amp; Schreiber, 2017).\u003c/p\u003e \u003cp\u003eResearch suggests that restricting mathematics solely to certainty can negatively impact students\u0026rsquo; affective orientations. When uncertainty is excluded, opportunities for curiosity, creativity, and enjoyment are diminished. In particular, Sriraman (\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) argues that uncertainty serves as a critical catalyst for mathematical creativity; while his work primarily offers theoretical or conceptual foundations, our experimental study aims to provide empirical evidence to support this claim by examining how different frequencies of uncertainty-inducing tasks influence students' affective outcomes. More recent research has shown that students who experience uncertainty tend to develop a more positive mathematical identity and are more likely to perceive mathematics as an explorative discipline (Buckley \u0026amp; Sullivan, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This gap between school mathematics and actual mathematical practice highlights the need to reconsider the role of uncertainty in classroom instruction.\u003c/p\u003e \u003cp\u003eOne way to address this gap is to intentionally design tasks that embed uncertainty. Conditional tasks serve as a prime example, distinguished from conventional open tasks by their specific structural design. While open tasks primarily focus on multiple correct answers, conditional tasks are characterized by: (1) the use of conditional language in task statements to signal uncertainty and stimulate hypothesis consideration (Langer et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1989\u003c/span\u003e; Langer \u0026amp; Piper, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1987\u003c/span\u003e); (2) the encouragement of multiple strategies and representations to support the exploration of alternative possibilities (Ritchhart \u0026amp; Langer, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e1997\u003c/span\u003e; Schukajlow et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2015\u003c/span\u003e); and (3) the highlighting of unfamiliar perspectives to foster cognitive flexibility (Langer et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1985\u003c/span\u003e; Lee \u0026amp; Ryu, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Maymin \u0026amp; Langer, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Sullivan et al., 2012). Rather than simply seeking predetermined answers, students are invited to navigate under-determined information where the mathematical outcomes depend on the conditions they identify. Through this process, uncertainty is experienced as an integral part of authentic mathematical reasoning (Yi et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). As will be illustrated in the methodology, these features transform a routine calculation into a reflective inquiry where students must manage the logical relationship between varied conditions and their corresponding possibilities.\u003c/p\u003e \u003cp\u003eBy navigating these features, students experience uncertainty not as a permanent state of confusion, but as a dynamic catalyst for cognitive development. Similar to Piaget\u0026rsquo;s (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e1977\u003c/span\u003e) mechanism of equilibration, the learning process through conditional tasks can be viewed as a continuous cycle of certainty and uncertainty. When students encounter uncertainty (disequilibrium) through under-determined information, they are driven to refine their reasoning and seek new justifications to reach a higher level of mathematical certainty (re-equilibration). In this sense, uncertainty in the learning process is an essential pedagogical moment that transforms a routine calculation into a reflective inquiry. Thus, by intentionally balancing these states, conditional tasks provide a structured yet open environment that supports both the cognitive and affective growth necessary for authentic mathematical practice.\u003c/p\u003e\n\u003ch3\u003eMindfulness learning: Linking Conditional Tasks and Mathematics-Related Affect\u003c/h3\u003e\n\u003cp\u003eThe concept of mindfulness, as defined by Langer (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2000\u003c/span\u003e), provides a powerful psychological framework for linking conditional tasks with student affect in mathematics. Langer describes mindfulness as a state of active awareness characterized by the creation of new categories and openness to multiple perspectives. Conversely, mindlessness involves a rigid reliance on fixed categories, often leading to a passive engagement with knowledge. To facilitate a transition from mindlessness to mindfulness, Langer and colleagues have explored various intervention strategies, such as varying the context of information, highlighting the perspective-dependent nature of facts, and encouraging the exploration of alternative possibilities (Langer, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Langer \u0026amp; Moldoveanu, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2000\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAmong these methodologies, conditional instruction serves as a primary work for fostering a mindful state in educational settings. A central component of this approach is the strategic use of conditional language. Traditional education tends to convey knowledge in absolute language (e.g., \u0026ldquo;is true\u0026rdquo;) as fixed and context-free, even when truths are only conditionally valid (Herbel-Eisenma, 2007). Langer\u0026rsquo;s experiments demonstrated that conditional phrasing (e.g., \u0026ldquo;could be true\u0026rdquo;) encourages learners to adopt more flexible, creative, and open modes of thinking. For instance, participants introduced to objects with conditional language were more likely to repurpose them in creative ways (Langer \u0026amp; Piper, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1987\u003c/span\u003e), and students exposed to conditional instructions produced more creative poems (Langer et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1989\u003c/span\u003e), demonstrated higher conceptual understanding, and generated novel mathematical strategies compared to peers taught with absolute language (Ritchart \u0026amp; Langer, 1997). These studies collectively highlight that uncertainty, when introduced through conditional instruction, fosters creativity, problem-solving, and deeper engagement with learning.\u003c/p\u003e \u003cp\u003eFrom this perspective, conditional tasks can be understood as structured opportunities to elicit mindful engagement, aligning with the principle of \u003cem\u003eLearning Mathematics by Doing Mathematics\u003c/em\u003e (Leinwand et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Unlike memorization tasks that focus on the passive reproduction of fixed procedures (Stein \u0026amp; Lane, \u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e1996\u003c/span\u003e), conditional tasks shift the focus toward active mathematical practices, such as making sense of problems and reasoning abstractly. Central to this shift is the transition from closed directions to open suggestions through the strategic use of conditional language. By replacing absolute mandates with \u0026lsquo;could be\u0026rsquo; scenarios, these tasks embed uncertainty as an invitation for students to explore rather than follow. This framing transforms the task from a rigid command into a reflective inquiry where open suggestions (allowing for varied premises) and incomplete information (requiring students to identify necessary constraints) necessitate cognitive flexibility. This resonates with Langer\u0026rsquo;s notion that conditional framing induces a participatory mental state, enabling learners to see themselves as mathematical thinkers. Empirically, Yi et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) demonstrated that tasks designed with such embedded uncertainty cultivate mindfulness by encouraging an exploratory stance. By situating conditional tasks as opportunities for genuine doing, this research highlights their potential to reshape both the cognitive and affective experiences of students.\u003c/p\u003e \u003cp\u003eThe implications for mathematics-related affect are significant. As reviewed earlier, affective dimensions such as enjoyment, self-efficacy and valuing are strong predictors of achievement and long-term engagement (Di Martino \u0026amp; Zan, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Yet, in traditional certainty-oriented classrooms, affect is often undermined by rigid practices that restrict exploration and amplify performance anxiety. By contrast, conditional tasks based on mindful learning can foster curiosity, intrinsic motivation, and engagement, thereby contributing positively to students\u0026rsquo; affective orientations.\u003c/p\u003e \u003cp\u003eIn addition, mindfulness through conditional tasks reflects the dual nature of mathematics: certainty at the level of results and uncertainty at the level of processes (Sriraman, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). This structural balance reinforces the aforementioned cycle of equilibration; the process-level uncertainty acts as the necessary disequilibrium that drives students toward a more robust, justified certainty. By navigating this recursive movement between doubt and proof, students not only encounter uncertainty productively but also experience the satisfaction of resolving it through logical reasoning. This process supports a holistic synergy between cognitive development and affective growth. Moreover, the impact of such experiences may depend on the frequency of implementation. Investigating whether varying the number of conditional tasks per lesson leads to distinct changes in enjoyment, self-efficacy, and valuing provides further insights into the optimal pedagogical dosage required for sustainable engagement. By considering both the structural design and the quantitative frequency of task implementation, this perspective highlights how thoughtfully sequenced uncertainty can foster students\u0026rsquo; holistic development in mathematics.\u003c/p\u003e \u003cp\u003eTaken together, the body of work on conditional instruction (Langer, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1993\u003c/span\u003e; Langer \u0026amp; Piper, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Langer et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1989\u003c/span\u003e; Ritchart \u0026amp; Langer, 1997; Lee \u0026amp; Ryu, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2015\u003c/span\u003e) demonstrates that mindfulness interventions are both practical and effective in educational contexts. Building on these insights, conditional tasks in mathematics can be intentionally designed to introduce uncertainty, thereby fostering creativity, affective engagement, and epistemological openness. In this way, mindfulness provides not only a psychological framework but also a pedagogical strategy for aligning conditional tasks with the development of positive affective orientations in mathematics education.\u003c/p\u003e"},{"header":"Method","content":"\u003cp\u003eThis study builds on the experimental design reported in Yi, Lee, and Hwang (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), which examined whether conditional mathematics tasks that embed uncertainty could cultivate students\u0026rsquo; mindfulness. While the earlier study focused on mindfulness as the dependent variable, the present research maintains the same interventions and procedures but investigates a different outcome. Specifically, this study examines the impact of conditional mathematics tasks on students\u0026rsquo; mathematics-related affect. In this way, the study reports a second set of findings from the same intervention, thereby contributing to a broader understanding of the educational potential of conditional tasks.\u003c/p\u003e\n\u003ch3\u003eResearch design and sample\u003c/h3\u003e\n\u003cp\u003eThe present study employed a teaching experiment integrated into the regular Grade 7 mathematics curriculum, maintaining the prescribed content and objectives. Two public middle schools located in Gyeonggi Province, a metropolitan region surrounding Seoul, South Korea, participated in the study. Both institutions demonstrate academic performance consistent with the national average in mathematics.\u003c/p\u003e \u003cp\u003eIn each school, two teachers with approximately four years of experience taught the experimental groups. For comparison, students taught by two other teachers at the same grade level served as control groups. The control group teachers varied in experience: one had slightly more than one year, while the other had more than ten years of teaching experience.\u003c/p\u003e \u003cp\u003eBecause the primary focus of the study was the influence of task design, groups were distinguished solely by the types of mathematical tasks provided. One experimental group (EG1, n\u0026thinsp;=\u0026thinsp;71) received one conditional task per lesson, while another (EG2, n\u0026thinsp;=\u0026thinsp;62) received three to four conditional tasks. These proportions correspond to roughly 20% and 60\u0026ndash;80% of the total tasks typically covered in a lesson. The distinction between EG1 and EG2 not only allowed for examining the effects of conditional tasks in general but also provided an opportunity to investigate whether the frequency of conditional tasks per lesson leads to differential changes in students\u0026rsquo; mathematics-related affect.\u003c/p\u003e \u003cp\u003eIn contrast, the control groups (n\u0026thinsp;=\u0026thinsp;49) were taught using traditional textbook problems and standard worksheets. For analytical purposes, the two control groups were merged into a single control group, enabling more robust statistical comparisons with the experimental groups. To ensure consistency across the intervention, all participating teachers followed a standardized instructional schedule, while the researchers remained non-interventive except for the administration of pre- and post-tests. The final dataset included 182 participants who provided informed consent. Figure\u0026nbsp;1 provides an overview of the study design.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure 1\u003c/b\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eOverview of the Study Design (Yi et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e, p.386 )\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eInstruments\u003c/h3\u003e\n\u003cp\u003eTo investigate students\u0026rsquo; mathematics-related affect, a scale was constructed consisting of three subscales: Enjoyment, Self-efficacy, and Valuing. This instrument underwent a validation process during the development phase, including development planning, item development, pilot testing, and main testing. This validation process ensured the instrument's validity. During this process, the fifteen preliminary questions were reduced to ten (Yi et al., \u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eEnjoyment subscale measured students\u0026rsquo; emotional responses to mathematics classes. Self-efficacy subscale addressed students\u0026rsquo; beliefs about their competence and confidence in mathematics. Valuing subscale measured the degree to which students perceived mathematics as useful and meaningful for their future. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates items for each subscale. This scale was assessed through statements rated on a 7-point Likert-type scale (1\u0026thinsp;=\u0026thinsp;strongly disagree to 7\u0026thinsp;=\u0026thinsp;strongly agree). Negative-worded items were reverse-coded so that higher values reflected a more positive affective orientation.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eItems of mathematics-related affect (\u003c/em\u003eYi, Lee, \u0026amp; Choi, \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2017\u003c/span\u003e\u003cem\u003e)\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubscale\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eItems\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnjoyment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eI think studying mathematics is boring. \u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eI look forward to mathematics class.\u003c/p\u003e \u003cp\u003eI enjoy mathematics.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSelf-efficacy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eI am good at mathematics.\u003c/p\u003e \u003cp\u003eI have more difficulty with mathematics than my classmates. \u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eI feel nervous during mathematics class. \u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003cp\u003eI learn mathematics quickly.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eValuing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eI believe studying mathematics will help me.\u003c/p\u003e \u003cp\u003eI believe learning mathematics is important for preparing for the future.\u003c/p\u003e \u003cp\u003eI believe math is needed to study other subjects.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"2\"\u003e\u003csup\u003ea\u003c/sup\u003e Reverse item\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe internal consistency of the mathematics-related affect scale was examined using Cronbach\u0026rsquo;s alpha. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, alpha values for the subscales ranged from 0.702 (EG2, self-efficacy, Post-test) to .0.907 (EG2, self-efficacy, Pre-test), with the total score demonstrating an alpha of 0.826. These results indicate that the scale exhibits acceptable to excellent internal consistency, supporting its reliability for measuring students\u0026rsquo; mathematics-related affect within the context of this study.\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\u003eReliability of Mathematics-Related Affect\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSubscale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003eReliability (Cronbach\u0026rsquo;s alpha)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEG1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eEG2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSum\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eEnjoyment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.823\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.860\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.883\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.865\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePost-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.839\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.795\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.871\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.842\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSelf-efficacy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.731\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.744\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.907\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.769\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePost-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.798\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.789\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.702\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.761\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eValuing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.880\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.814\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.891\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePost-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.779\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.841\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.815\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.813\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePre-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.872\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.830\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.886\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.865\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePost-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.822\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.854\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.826\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the pre- and post-test correlations of mathematics-related affect for each group and subscale. Notably, the total score demonstrated consistently strong positive correlations across groups (r\u0026thinsp;=\u0026thinsp;0.719\u0026ndash;0.779), indicating good overall test\u0026ndash;retest reliability of the scale. At the subscale level, significant positive correlations were also observed between pre- and post-test scores, suggesting that students\u0026rsquo; relative rankings on enjoyment, self-efficacy, and valuing remained stable over time. Specifically, correlations for enjoyment ranged from r\u0026thinsp;=\u0026thinsp;0.667 to 0.723, for self-efficacy from r\u0026thinsp;=\u0026thinsp;0.632 to 0.809, and for valuing from r\u0026thinsp;=\u0026thinsp;0.382 to 0.786. All correlations were statistically significant at p \u0026lt; .01, further supporting the reliability of the mathematics-related affect measures.\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\u003ePre-and Post-Test Correlation of Mathematics-Related Affect\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=\"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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubscale\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCG\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEG1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEG2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSum\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnjoyment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.723**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.701**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.667**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.706**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSelf-efficacy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.632**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.786**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.809**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.747**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eValuing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.701**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.382**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.786**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.414**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.726**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.779**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.719**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.739**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003e** p\u0026thinsp;\u0026lt;\u0026thinsp;0.01\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003eTask Development\u003c/h2\u003e \u003cp\u003eThe independent variable in this study was the implementation of conditional mathematics tasks. Rather than redefining the theoretical principles of conditional instruction previously discussed, this section focuses on how those principles were operationalized into the specific mathematical tasks used in the intervention. Specifically, the design followed Langer\u0026rsquo;s framework to shift students from a mindless to a mindful state.\u003c/p\u003e \u003cp\u003eTo achieve this, the tasks were developed to intentionally deviate from conventional textbook problems by: (1) replacing absolute phrasing with conditional language to signal uncertainty; (2) structuring problems to necessitate multiple strategies and representations; and (3) introducing unfamiliar perspectives that require students to manage under-determined information. While these design features are often associated with fostering a mindful state in a general sense, the present study specifically examines their role in stimulating students\u0026rsquo; affective responses, such as enjoyment and self-efficacy, within the context of mathematical problem-solving.\u003c/p\u003e \u003cp\u003eTo identify a contrasting baseline, we analyzed Korean mathematics textbooks focusing on integers and rational numbers. Consistent with earlier studies (Woo \u0026amp; Choi, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Yoo, \u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), we found that these textbooks typically introduce negative numbers through direct definition, present operation rules with formal justification, and rely heavily on procedural practice. For example, tasks such as \u0026ldquo;Calculate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(-3)\\times\\:(-5)\\)\u003c/span\u003e\u003c/span\u003e\u0026rdquo; (Kim et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e, p.45) exemplify the emphasis on rote application of rules without opportunities for exploration or reflection.\u003c/p\u003e \u003cp\u003eIn contrast, conditional tasks were designed to invite students to think deeply about mathematical ideas from new or different perspectives. For instance, to open a new perspective on negative numbers, we asked, \u0026ldquo;We typically call 1, 2, 3, and 4 integers. However, why could we also consider them to be rational numbers?\u0026rdquo;. To encourage multiple expressions in algebraic operations, we asked students to reconfigure a given numerical expression into as many equivalent forms as possible by strategically changing the signs of numbers or the operations (addition and subtraction). For example, students were tasked with finding multiple ways to represent expressions such as (1) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:8+(-10)\\)\u003c/span\u003e\u003c/span\u003e and (2) \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:(-25)+(-44)\\)\u003c/span\u003e\u003c/span\u003e by exploring the logical relationships between signs and operations. Additionally, we developed a task using a number line model to introduce the concept of symmetry\u0026mdash;a perspective rarely emphasized in traditional textbooks for this topic. In this task, students were asked to visualize negative numbers and their operations as symmetrical movements or reflections across the origin (zero) on the number line.\u003c/p\u003e \u003cp\u003eIn classroom implementation, experimental group teachers typically allowed students individual time to explore the tasks before facilitating whole-class discussion. Since the conditional tasks in the present study were identical to those Yi et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), representative tasks for Experiment Group 1 and 2 are presented in Tables\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, respectively, while the complete set of tasks can be found in the previous study.\u003c/p\u003e \u003cp\u003eIn classroom implementation, teachers in the experimental groups typically provided students with individual time to explore these tasks before facilitating whole-class discussions. The complete set of conditional tasks used in this study follows the design established by Yi et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Since the detailed structure and full inventory of these tasks have been documented in the previous work, we direct readers to that publication for the complete instrument.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eData Analysis\u003c/h2\u003e \u003cp\u003eData were analyzed using a two-way repeated measures analysis of variance (RM-ANOVA) with SPSS Statistics 21. The dependent variable was mathematics-related affect, which was examined at two levels: (a) separately for each of the three subscales (enjoyment, self-efficacy, valuing) and (b) as a total score representing students\u0026rsquo; overall mathematics-related affect. Independent variables were group (EG1, EG2, CG) and time (pre-test, post-test).\u003c/p\u003e \u003cp\u003eLevene\u0026rsquo;s tests confirmed the assumption of homogeneity of variances at the 5% significance level across all subscales and the total score. While normality was not directly tested, RM-ANOVA is generally robust to violations of this assumption, especially with balanced designs. The assumption of sphericity did not apply, as only two measurement points were used (Blanca et al., 2023).\u003c/p\u003e \u003cp\u003eThis analytic approach allowed for examination of both main effects and interaction effects, providing evidence on whether the introduction of conditional tasks influenced students\u0026rsquo; mathematics-related affect, both at the level of specific subscales and in terms of the overall total score, over the course of the intervention. Specifically, interaction effects between group (EG1, EG2, CG) and time (pre-test, post-test) were examined not only to identify overall differences in mathematics-related affect but also to explore whether the frequency of conditional tasks influenced affective changes differently between the experimental groups.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eOverall, the students’ mathematics-related affect exhibited different patterns of change from pre-test to post-test across the three groups. In the control group, most subscales and the total score showed slight decreases, with the exception of Enjoyment, which remained relatively stable. In contrast, both experimental groups demonstrated consistent positive shifts in their total scores and subscales.\u003c/p\u003e \u003cp\u003eFor instance, Enjoyment increased in EG1 (11.66 to 12.00) and EG2 (10.56 to 11.68), whereas the CG remained relatively unchanged. Self-efficacy followed a similar upward trend, particularly in EG2 (15.21 to 16.48). Notably, the total score (Sum) for the experimental groups showed modest improvements (EG1: 46.11 to 47.34; EG2: 43.48 to 46.10), while the CG exhibited a slight decline (48.88 to 47.98).\u003c/p\u003e \u003cp\u003eStandard deviations in EG2 generally decreased from pre-test to post-test, indicating that students’ scores became somewhat more consistent after the intervention. Finally, the pre-test means indicate that initial scores varied across groups, which should be taken into account in subsequent analyses of group differences. Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e presents the descriptive statistics of the pre- and post-test scores for each group and subscale, providing a detailed overview of these trends.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003ctable id=\"Tab4\" border=\"1\"\u003e \u003ccaption\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eDescriptive Statistics of Mathematics-Related Affect\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003c/colgroup\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" rowspan=\"2\"\u003e \u003cp\u003eSubscale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" rowspan=\"2\"\u003e \u003cp\u003eGroup\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\"\u003e \u003cp\u003ePre-test\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\"\u003e \u003cp\u003ePost-test\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eStandard\u003c/p\u003e \u003cp\u003eDeviation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eStandard\u003c/p\u003e \u003cp\u003eDeviation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" rowspan=\"3\"\u003e \u003cp\u003eEnjoyment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eCG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e13.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e13.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e3.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eEG1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e11.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e12.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e3.83\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eEG2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e10.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e11.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" rowspan=\"3\"\u003e \u003cp\u003eSelf-efficacy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eCG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e16.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e3.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e16.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eEG1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e16.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e3.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e17.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2.76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eEG2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e15.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e16.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e3.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" rowspan=\"3\"\u003e \u003cp\u003eValuing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eCG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e18.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e17.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eEG1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e17.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e18.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eEG2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e17.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e5.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e17.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.78\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" rowspan=\"3\"\u003e \u003cp\u003eSum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eCG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e48.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e10.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e47.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e9.14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eEG1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e46.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e9.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e47.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e8.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eEG2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e43.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e11.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e46.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e9.74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003e\u003cem\u003eNote\u003c/em\u003e. CG: Control Group, EG1: Experimental Group 1, EG2: Experimental Group 2\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eA repeated measures ANOVA (RM-ANOVA) confirmed these observations (Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e). For the total score (Sum), although the main effect of Time was not significant (p = 0.071), the \u003cem\u003eTime*Group\u003c/em\u003e interaction effect was statistically significant, F(2, 179) = 3.267, p = 0.040. This indicates that the trajectory of affective change differed significantly among the groups, with the experimental groups showing favorable growth compared to the control group. Furthermore, EG2, which received a higher frequency of conditional tasks, tended to show slightly greater gains than EG1, providing preliminary evidence that task frequency may influence the magnitude of affective development.\u003c/p\u003e \u003cp\u003eFor Self-efficacy, neither the main effect of Time, F(1,179) = 0.472, p = 0.493, nor the \u003cem\u003eTime*Group\u003c/em\u003e interaction, F(2,179) = 2.325, p = 0.101, was significant. The between-subjects effect of group was also not significant, F(2,179) = 0.193, p = 0.825. These results suggest that Self-efficacy remained relatively stable across time and did not differ significantly between groups.\u003c/p\u003e \u003cp\u003eValuing showed a significant main effect of Time, F(1,179) = 4.730, p = 0.031, indicating that there was an overall change in scores from pre-test to post-test. However, when examined by group, the experimental groups exhibited slight increases, whereas the control group showed a decreasing trend. The \u003cem\u003eTime*Group\u003c/em\u003e interaction was not significant, F(2,179) = 1.548, p = 0.215, suggesting that the differences in Valuing changes between groups were not statistically significant.\u003c/p\u003e \u003cp\u003eFinally, for the total score (Sum), the main effect of Time was not significant, F(1,179) = 3.296, p = 0.071, but the \u003cem\u003eTime*Group\u003c/em\u003e interaction was significant, F(2,179) = 3.267, p = 0.040. This indicates that the overall change in mathematics-related affect differed across groups, with the experimental groups showing modest improvements relative to the control group. The between-subjects effect of group was not significant, F(2,179) = 2.209, p = 0.113. Moreover, although both experimental groups exhibited improvements in mathematics-related affect, EG2, which received a higher frequency of conditional tasks, tended to show slightly greater gains than EG1. This pattern suggests that the frequency of conditional tasks may influence the magnitude of affective changes, providing partial support for the second research question.\u003c/p\u003e \u003cp\u003eIn summary, the conditional mathematics tasks appear to have had small but meaningful effects on students’ mathematics-related affect, particularly in terms of overall scores, while changes in individual subscales were more limited.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e\u003cdiv class=\"gridtable\"\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\"\u003e\u003c/div\u003e\u003ctable id=\"Tab5\" border=\"1\"\u003e \u003ccaption\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u003cem\u003eRM-ANOVA Results\u003c/em\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003c/colgroup\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\"\u003e \u003cp\u003eLMS-Y\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eSource\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eSum of Squares\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eMean Square\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003eF\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\"\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" rowspan=\"7\"\u003e \u003cp\u003eEnjoyment\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"6\"\u003e \u003cp\u003eWithin-Subjects\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTime\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e25.090\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e25.090\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.865\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.029\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTime*Group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e15.479\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e7.739\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e1.501\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.226\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eError(time)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e923.049\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e5.157\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\"\u003e \u003cp\u003eBetween-Subjects\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTreatment(group)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e331.644\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e165.822\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e5.839\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.003\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eError\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e5083.466\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e28.399\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" rowspan=\"7\"\u003e \u003cp\u003eSelf-efficacy\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"6\"\u003e \u003cp\u003eWithin-Subjects\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTime\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2.892\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2.892\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.472\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.493\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTime*Group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e28.482\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e14.241\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2.325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.101\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eError(time)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e1096.627\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e6.126\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\"\u003e \u003cp\u003eBetween-Subjects\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTreatment(group)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e16.589\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e8.295\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.193\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.825\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eError\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e7692.872\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e42.977\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" rowspan=\"7\"\u003e \u003cp\u003eValuing\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"6\"\u003e \u003cp\u003eWithin-Subjects\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTime\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e35.192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e35.192\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4.730\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.031\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTime*Group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e23.038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e11.519\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e1.548\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.215\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eError(time)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e1331.899\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e7.441\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\"\u003e \u003cp\u003eBetween-Subjects\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTreatment(group)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e73.583\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e36.792\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2.143\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.120\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eError\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e3073.463\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e17.170\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" rowspan=\"7\"\u003e \u003cp\u003eSum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"6\"\u003e \u003cp\u003eWithin-Subjects\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTime\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e85.392\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e85.392\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e3.296\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.071\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTime*Group\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e169.250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e84.625\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e3.267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e\u003cb\u003e0.040\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eError(time)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e4636.797\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e25.904\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\"\u003e \u003cp\u003eBetween-Subjects\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eTreatment(group)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e733.940\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e366.970\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e2.209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e0.113\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\"\u003e \u003cp\u003eError\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e29737.337\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e \u003cp\u003e166.130\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/table\u003e\u003c/div\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003eTo visually illustrate the statistically significant total score (Sum) results, \u003cb\u003eFig.\u0026nbsp;2\u003c/b\u003e presents the pre- and post-test mean scores for each group, with lines connecting the points to indicate the direction of change. The figure highlights the Time*Group interaction, showing modest increases in the experimental groups and a slight decrease in the control group.\u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure 2\u003c/b\u003e \u003c/p\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eChanges in Mathematics-Related Affect by Groups\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eNote\u003c/strong\u003e \u003c/p\u003e\u003cp\u003eCG: Control Group, EG1: Experimental Group 1, EG2: Experimental Group 2\u003c/p\u003e \u003cp\u003e\u003c/p\u003e \u003c/div\u003e "},{"header":"Discussion and Conclusion","content":"\u003cp\u003eThe present study offers valuable insights how conditional mathematics tasks designed to embed uncertainty may influence students’ affective orientations in mathematics classrooms. Prior research has consistently demonstrated that conditional instruction can foster creativity, flexibility, and mindfulness (Langer, \u003cspan class=\"CitationRef\"\u003e2000\u003c/span\u003e; Langer et al., \u003cspan class=\"CitationRef\"\u003e1985\u003c/span\u003e; Langer et al., \u003cspan class=\"CitationRef\"\u003e1989\u003c/span\u003e; Langer \u0026amp; Piper, \u003cspan class=\"CitationRef\"\u003e1987\u003c/span\u003e; Ritchhart \u0026amp; Langer, \u003cspan class=\"CitationRef\"\u003e1997\u003c/span\u003e; Yi et al., \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e). For instance, Ritchhart and Langer (\u003cspan class=\"CitationRef\"\u003e1997\u003c/span\u003e) reported that conditional instruction of newly defined arithmetic operations significantly enhanced problem-solving ability and creativity compared to absolute instruction. Although their findings were situated in a controlled context, they provided critical early evidence that uncertainty-based instruction could move students beyond rote procedural thinking. Building on this foundation, recent studies in authentic mathematics classrooms (Yi et al., \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e) have confirmed that such tasks improve cognitive flexibility and promote a mindful state. The present study shifts the focus of this line of inquiry from the state of mindfulness itself to students’ mathematics-related affective orientations. By demonstrating that conditional tasks can contribute to meaningful changes in students’ affect within a regular school setting, this research bridges the gap between earlier experimental findings and the practical goals of holistic mathematics education.\u003c/p\u003e\u003cp\u003eMost notably, the experimental groups in this study, who engaged with uncertainty-embedded conditional tasks, exhibited small but statistically significant improvements in mathematics-related affect, whereas the control group tended to decline over time. Although the control group maintained the highest absolute scores, the pattern of change highlights the potential of conditional tasks to prevent affective deterioration and to sustain or promote more positive orientations toward mathematics. These findings suggest that embedding uncertainty within conditional mathematics tasks may help students engage in productive exploration, aligning classroom experiences more closely with authentic mathematical practices where doubt and multiple possibilities are integral (Sriraman, \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). In contexts where affect is often overshadowed by cognitive performance, this result suggests that carefully designed uncertainty-embedded mathematics tasks can have the dual function of fostering conceptual growth and nurturing affective engagement. Conditional tasks, in this sense, emerge not only as tools for promoting diverse thinking and flexibility, but also as instructional strategies that can help students develop and maintain more positive relationships with mathematics. Moreover, although both experimental groups exhibited improvements in mathematics-related affect, EG2, which received a higher frequency of conditional tasks, tended to show slightly greater gains than EG1. This pattern suggests that the frequency of conditional tasks may influence the magnitude of affective changes.\u003c/p\u003e\u003cp\u003eThese findings carry several implications. First, from a theoretical perspective, the study extends Langer’s framework of mindful learning into the domain of mathematics education. While previous research was largely situated in psychological experiments or general learning contexts, this study demonstrates that the principles of mindful learning operate meaningfully within a discipline-specific setting. By doing so, it underscores the relevance of mindfulness not only as a general educational orientation but also as a framework for designing domain-sensitive interventions (Lee \u0026amp; Ryu, \u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e). Furthermore, the study establishes concrete design principles for conditional mathematics instruction and provides specific task examples that effectively embed uncertainty. This contribution is particularly significant because it illustrates how theoretical constructs—such as conditionality and mindfulness—can be operationalized into tangible instructional materials. Specifically, it offers mathematics educators a practical model for transforming abstract cognitive theories into classroom-ready tasks that stimulate both reflective inquiry and affective engagement. More broadly, the results resonate with the growing recognition in mathematics education that cognition and affect are deeply intertwined, and that theoretical models must account for both dimensions in order to capture the complexity of learning.\u003c/p\u003e\u003cp\u003eSecond, in terms of practical implications, this study shows that uncertainty-embedded conditional tasks can be implemented effectively within regular classroom instruction as part of the official mathematics curriculum. Much of the innovation in instructional approaches often remains confined to controlled laboratory settings or isolated pilot studies (e.g., Langer \u0026amp; Piper, \u003cspan class=\"CitationRef\"\u003e1987\u003c/span\u003e; Ritchhart \u0026amp; Langer, \u003cspan class=\"CitationRef\"\u003e1997\u003c/span\u003e). By contrast, the present study demonstrates that conditional tasks can be seamlessly integrated into everyday lessons, providing empirical evidence of their feasibility. This is particularly significant given the widespread concern in global mathematics education regarding students’ declining affective orientations. International assessments repeatedly report that as students progress through formal schooling, their interest, enjoyment, and self-efficacy in mathematics tend to diminish, even among those with high cognitive proficiency (OECD, \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e). Against this backdrop, conditional tasks hold promise not only as tools for promoting cognitive flexibility but also as a pedagogical strategy for sustaining and improving students’ emotional engagement. Teachers, therefore, can utilize uncertainty-embedded instruction to design lessons that simultaneously cultivate cognitive and affective growth, fostering a more balanced and human-centered mathematics education.\u003c/p\u003e\u003cp\u003eThird, the study carries important methodological implications while also acknowledging its limitations. Although the findings confirm that uncertainty-embedded conditional tasks exert a measurable effect on affective outcomes, the complexity of the mathematics classroom must be considered. Specifically, a critical challenge in authentic classroom research is that the impact of a task depends not only on its design but also on how it is enacted by the teacher (e.g., Baumert et al., \u003cspan class=\"CitationRef\"\u003e2010\u003c/span\u003e; Wayne \u0026amp; Youngs, \u003cspan class=\"CitationRef\"\u003e2003\u003c/span\u003e). In this study, while the tasks were standardized, the pedagogical implementation—including the teacher’s framing, scaffolding, and classroom management—was not fully controlled. For instance, the high level of engagement observed in some groups may have been influenced by the individual teacher’s instructional delivery rather than the task design alone. This underscores that task development and task implementation are distinct dimensions, and future research should focus on monitoring the fidelity of implementation to better isolate the effects of the tasks themselves.\u003c/p\u003e\u003cp\u003eAdditionally, as one of the earliest attempts to apply Langer’s mindfulness theory to mathematics education, these results should be interpreted with caution. Further replication across diverse grade levels, mathematical domains, and longitudinal time frames is necessary to establish the robustness and generalizability of the findings.\u003c/p\u003e\u003cp\u003eDespite these limitations, the present study provides valuable insights into how uncertainty-embedded conditional mathematics tasks can influence students’ cognitive and affective engagement in mathematics classrooms, and it points to the potential for further active research on conditional mathematics tasks informed by Langer’s mindfulness framework.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics Approval \u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe study was approved by the Institutional Review Board of Seoul National University.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for Participation and Publication\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eInformed consent was obtained from all individual participants included in the study.\u003cbr\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets generated during the current study are not publicly available due to IRB restrictions regarding participant privacy.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors have no competing interests to declare.\u003cbr\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNo funding was received.\u0026nbsp;\u003cbr\u003e\u003cstrong\u003eAuthors' contributions\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eG.Y. contributed to the design and implementation of the teaching experiment, statistical analysis, and drafting the manuscript. J. L. contributed to literature review, the design and implementation of the teaching experiment, data collection, and revision.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to express their deepest gratitude to Professor Younggi Choi of the Department of Mathematics Education at Seoul National University for his invaluable guidance, continuous support, and profound inspiration throughout this project. His insightful perspectives were instrumental in the development of this research.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eClinical Trial Registration\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAlr\u0026oslash;, H., \u0026amp; Skovsmose, O. (1996). 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(2007).\u0026nbsp;Middle school mathematics textbook research. Kyungmoonsa.\u003c/li\u003e\n \u003cli\u003eZaslavsky, O. (2005). \u003cem\u003eSeizing the opportunity to create uncertainty in learning mathematics.\u003c/em\u003e \u003cem\u003eEducational Studies in Mathematics, 60\u003c/em\u003e(3), 297\u0026ndash;321. https://doi.org/10.1007/s10649-005-0606-5\u003c/li\u003e\n \u003cli\u003eZimmerman, B. J. (2000). Self-efficacy: An essential motive to learn. \u003cem\u003eContemporary educational psychology\u003c/em\u003e, \u003cem\u003e25\u003c/em\u003e(1), 82-91.\u003c/li\u003e\n\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":"mindfulness, mathematics-related affect, conditional mathematics task, uncertainty, classroom","lastPublishedDoi":"10.21203/rs.3.rs-8708945/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8708945/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study presents a secondary analysis of experimental data from Yi et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), shifting the focus to the cumulative affective consequences of a ten-lesson intervention. While the previous study established that conditional tasks embedded with uncertainty foster students\u0026rsquo; mindfulness, it remained unclear how such cognitive shifts translate into broader affective outcomes. Using a quasi-experimental design, students were assigned to one of three groups in regular mathematics classes: a control group (conventional textbook-based tasks), and two experimental groups receiving different frequences of conditional tasks (one per lesson vs. three to four per lesson). A repeated measures two-way ANOVA revealed a significant discrepancy in developmental trajectories: while the control group\u0026rsquo;s mathematics-related affect declined, both experimental groups exhibited significant increases. These findings suggest that the pedagogical benefits of conditional tasks extend beyond mindfulness, offering a robust intervention to enhance students\u0026rsquo; overall affective experiences in mathematics.\u003c/p\u003e","manuscriptTitle":"Bridging Mindfulness and Mathematics-Related Affect: Extending the Role of Conditional Task","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-23 17:11:34","doi":"10.21203/rs.3.rs-8708945/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":"1b734080-0836-403f-9c9f-26626284eb72","owner":[],"postedDate":"February 23rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-15T06:39:20+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-23 17:11:34","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8708945","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8708945","identity":"rs-8708945","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}