The Relationship between Student’s Perception and Knowledge in Learning Related Rates of Change Problems

The Relationship between Student’s Perception and Knowledge in Learning Related Rates of Change Problems | 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 Article The Relationship between Student’s Perception and Knowledge in Learning Related Rates of Change Problems Muhammad Farooq This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6490660/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 investigates the relationship between students' perception and knowledge in learning related rates of change problems. Related rates of change are fundamental concepts in calculus, requiring students to grasp the dynamic nature of variables and their interdependencies. However, students' perception and knowledge regarding these problems can significantly determine their learning outcomes. The study is about relationship which is under correlational study (quantitative), incorporating surveys to gauge students' perceptions and knowledge tests to assess their performance. The findings illuminate the complex interplay between students' perceptions of related rates problems and their actual knowledge levels. Understanding this kinetics can inform instructional strategies and interventions aimed at improving students' comprehension and mastery of related rates concepts. Social science/Education Social science/Science technology and society Related rates of change student perception knowledge calculus learning outcomes instructional strategies Introduction The interplay between students' perceptions and their knowledge is one of the major foci of academic inquiry, particularly into the pedagogy of mathematics. (Wagner & Tamayo, 2024 ). One of the basic concepts within calculus that ordinarily proves problematic from students' perspectives is related rates of change (Santos-Trigo et al., 2024 ). Motion describes the situation of comparing how much one quantity changes concerning the change in another. Facility in those situations would be considered a profound grasp of the principles of calculus and would likely enhance student skills in developing solutions to problems and their logical ability as well (Pelemeniano & Siega, 2023 ). The relationship between students' perceptions about their learning experience and the actual academic knowledge has been one of the factors that psychology and pedagogy pay more and more attention to right now (Uyen et al., 2024 ). It is believed that students' attitudes, beliefs, and perceptions are very important in forming their learning outcomes (Uyen et al., 2024 ). Precisely, how the perceptual factors interact with learners' performance within some very narrow mathematical content areas, say, problems based on related rates of change demands more research (Cohen & Sukenik, 2024 ). This paper is set to articulate the complicated nexus between perception by students and their knowledge when dealing with related rates of change problems. To unearth pedagogical, curriculum, and subscribed mechanism insights for fostering a better calculus education learning experience, the pursuit shall be informed by what will be discovered about this relationship (Díaz et al., 2025 ). This paper first provides an overview of related rates of change problems and the challenges students face in understanding them. Next, it explores the importance of examining students' perceptions and knowledge in learning calculus, particularly in the context of related rates. Finally, the study's objectives and methodology are outlined, highlighting its contribution to the broader discourse on mathematics education and student learning. Through this research, effective strategies are identified for creating a supportive learning environment and enhancing academic success in calculus education. Literature Review Students’ Knowledge in the related rates of change problems Conventional teaching approaches have long been adopting in university-level calculus instruction. However, due to these methods students often grappling to grasp the fundamental concepts of calculus (Kidron, 2020 ). Instructors commonly emphasizes on calculations rather than nurturing a trench understanding of the fundamental principles at play (Mergendoller et al., 2013 ). Students who take conventional teaching methods are 1.5 times more intend to failure compared to their peers in active learning environments (Dzaiy & Abdullah, 2024 ). This is because traditional teaching often prioritizes rote memorization of formulas and mechanical procedures quite than developing a sound understanding of abstract concepts and their interconnections. Consequently, the traditional approach to teaching calculus proves ineffective in fostering a genuine comprehension of its essential principles (Muldoon Brown, 2025 ). Understanding students' perception and knowledge towards learning calculus, particularly related rates of change problems, is vital for informing pedagogical practices and curriculum development (Díaz et al., 2025 ). By identifying factors that influence students' motivation and engagement, educationalists can design interventions to address misconceptions, alleviate anxiety, and heighten students' confidence in handling complex mathematical problems (Subramaniam & Saleh, 2024 ). Students often struggle in calculus during studying related rates of change problems. The instructors who would like to use conventional approach in teaching calculus should realize that traditional teaching methods in calculus does not work even in classes dominated by students majoring in mathematics, science, and engineering since traditional pedagogy yields unsatisfactory results. This includes difficulties with proceedings knowledge as well as abstract understanding, indicating a broader challenge than plainly a lack of one type of knowledge or skill (Turunen & Seppälä, 2025 ). It's imperative for students to cultivate the skill of synthesizing verbal, symbolic, and graphical representations, fostering a holistic understanding of concepts (Honrubia-Montesinos & Otero, 2025 ). It's crucial for calculus students to both decode and encode symbolical representations, recognizing that these skills may reflect varying levels of conceptual understanding (Jain et al., 2025 ). The perception and knowledge of the students towards learning calculus play an important role in their academic achievement and motivation (Bibi et al., 2025 ). Research indicates that beliefs of the students about their mathematical abilities, their interest in the subject, and their perception of the relevance of calculus to their future goals can mold their learning outcomes (Kasa et al., 2024 ). Adverse attitudes towards mathematics, fear of failure, and a lack of trust in their problem-solving abilities may hinder students' engagement and persistence in learning calculus, particularly in challenging topics, for instance related rates of change problems (Saha et al., 2024 ). Calculus serves as a fundamental mathematical discipline essential for students wishing to adopt STEM majors in higher education. The concept of related rates of change is a key focus in single-variable calculus, providing students with a model to employ the fundamental view of instantaneous rates of change in practical scenarios. Past research has shown that students often see related rates of change problems to be challenging (Tulis & Fulmer, 2013 ). Students faced challenges when learning problems involving related rates of change (Domondon et al., 2022 ). The primary challenges initially arise when students try to grasp the problem context instead of understanding the concept. This comprehension significantly affects their ability to make an appropriate mathematical model that defines the connection between relevant quantities and their corresponding rates of change (Kaplan, 2025 ). Students’ Perception of the related rates of change problems and its relationship with knowledge In calculus, many students consider related rates of change problems difficult and challenging (Díaz et al., 2025 ). These problems need a better understanding of how multiple variables are related with each other and how their rates of change impact one another. Students see the related rates of change problems as a complex puzzles that require more attention and an understanding of how different quantities are interconnected (Ahmed, 2024 ). Some students may find related rates of change problems challenging at first. However, for many these problems become interesting when they explore their applications in real-world scenarios, such as physics, engineering, and economics. Through practice and persistence, students develop deep understanding to think and solve these problems as well as enabling them to deal complex scenarios with confidence (Ahmed, 2024 ). In addition, students' perception of related rates of change problems can be affected by numerous factors, including their prior mathematical knowledge, teaching methods, and self-learning styles (Tseng et al., 2013). Visual aids, interactive demonstrations, and real-life examples can boost students' comprehension and engagement with these concepts. Moreover, promoting a helpful learning environment where students feel stimulated to ask questions and discover different problem-solving techniques can foster a deeper understanding and appreciation of related rates of change problems (Muis et al., 2016). As students gain confidence in tackling related rates of change problems, they often show a sense of accomplishment and mastery, recognizing the value of calculus as a powerful tool around for analyzing dynamic systems and phenomena (Faulkner et al., 2019). Perception plays a vital role in determining one's achievement in learning calculus topics (Duran et al., 2024). The attitude of the students towards complexity and relevance of calculus can significantly impact their motivation and approach to learning (Rasmussen et al., 2014). If students take calculus as an unbeatable dilemma or fail to see its practical applications, they may approach the subject with lack of interest, hindering their ability to grasp key concepts and attain academic success. On the other side, a positive perception of calculus as a fascinating discipline with real-world applications can revolutionize students to engage more deeply with the material, leading to greater understanding and knowledge (Akbuga, 2018). Additionally, perception influences attitudes of the students towards challenges and setbacks encountered while learning calculus (Sonnert et al., 2015). Those who comprehend difficulties as opportunities for growth and learning are more probably to persist in their efforts and overcome challenges. Conversely, students who perceive challenges as non-removable barriers may turn discouraged and disengage from the learning process (Flynn et al., 2011). Thus, cultivating an increment mindset and fosterage positive perceptions of calculus as an intellectually stimulating field can enhance knowledge of the students and mastering of calculus topics (Hunt, 2017). By addressing students' perceptions and attitudes towards calculus, educators can make a supportive learning environment helpful to academic success (Hung et al., 2010). In spite of the importance of understanding the relationship between student perceptions and knowledge in learning related rates of change problems, a few studies have particularly addressed this topic. Past researches have primarily focused on exploring students' attitudes towards mathematics in general or investigating instructional strategies for improving calculus learning outcomes without directly examining the influence of student perceptions on their knowledge in related rates of change problems. The current study aims to investigate the connection between the perception of the students and their knowledge in related rates of change problems. By administering surveys to assess students' perception and knowledge in learning related rates problem-solving tasks, this research seeks to identify potential correlations and predictive factors. The results of this study will help to create effective research-based strategies for promoting academic success in calculus education and enhancing students' understanding in related rates of change concepts. Methodology The methodology section includes a description of the research design, samples involved, research instrument, and data analysis. Research Design A cross-sectional survey design was utilized with self-structured questionnaire. The inclusion criteria include all students currently enrolled in engineering majors. All faculty members, instructors and all other majors was excluded during study. Samples A total of 218 students were surveyed during this study. The sample size was calculated using standard sample size calculator with 5% population mean error. 50% distribution error was set during survey distribution. Research Instrument The research instrument was divided into 4 different sections. Section 1 includes demographic features like gender, year of study, current CGPA, and degree program. Section 2 includes questions related to knowledge, with close end questions like Yes and No. While the third section included questions related to perception, and the perception was correlated with the responses of knowledge related questions. While the last section includes knowledge based on current knowledge. The knowledge was assessed by designing a 10 questions quiz, including questions related to solutions of different context statements including equations, symbols and diagrams. Data Analysis All the qualitative data were evaluated using Statistical Package for Social Sciences (SPSS) software version 29. The demographic data was evaluated using mean and standard deviation. The Kruskal-Wallis Test was used to assess the significance of demographic data based on perception level. The reliability analysis of the study data was evaluated using Cronbach alpha values. A Spearmen’s correlation analysis identifies the demographic features with knowledge level. A statistical significance was defined as p-value less than 0.05. Results and Discussion Demographic characteristics of participants According to Table 1 , the study population comprised 102 male (87.2%) and 15 female (12.8%) students, with the majority (78.6%) in first year of their study. This gender distribution suggests that the study cohort is predominantly male, which could be reflective of enrollment trends in engineering fields, followed by 16.2% in second year and smaller proportion (0.9%) in fourth year of their study. This distribution indicates that the majority of respondents are at the beginning stages of their academic journey, which may influence their learning experiences and engagement with argumentation-based teaching strategies. Majority of the students were enrolled in computer science program (29.9%), while only 1.7% were enrolled in chemical engineering program. The diverse academic backgrounds suggest that the study's findings may be applicable across multiple engineering fields, though the high concentration of computing-related disciplines may introduce a disciplinary bias. Regarding academic achievement 8.55% scored CGPA 4.0, and 39.32% scored CGPA between 3.0–3.9, though 18.8% scored CGPA between 2.0–2.9. This suggests a varied academic performance level among participants, which could impact their responsiveness to instructional strategies. Regarding residency, most participants (88.0%) resided in their homes and 12.0% lived in dormitory. This finding may have implications for students' access to peer learning opportunities, study environments, and engagement with course materials outside of class. Assessment of knowledge regarding learning related rates of change problems To assess the knowledge, the responses were translated into 10 different questions. Out of 117 participants, most participants (65.0%) have good knowledge regarding familiarity about related rates of change problems, while 35.0% have poor knowledge regarding familiarity about related rates of change problems. The data indicated lack of confidence to solve related rates of change problems, with 54.7% of participants who are not confident to solve related rates of change problems and 45.3% believing they are confident to solve related rates of change problems. Regarding the knowledge about substituting values of variables after differentiation, 73.5% reported having heard of it, but only 26.5% did not know about its significance. This highlights a knowledge gap, as 26.5% are unaware of the importance of this concept. The Kruskal-Wallis test (Table 2 ) was applied to two variables (knowledge and gender) to access knowledge regarding learning related rates of change problems. The results showed that there was no significant difference (Table 2 ) between gender and knowledge regarding learning related rates of change problems ( p > 0.05). Assessment of perception regarding learning related rates of change problems To assess the perception, the responses were translated into 10 different questions. Out of 117 participants, most participants (46.2%) disagreed regarding to understand the statement of related rates of change problems easily, while only 9.4% were strongly agreed regarding to understand the statement of related rates of change problems easily. The data indicated lack of confidence to sketch diagram when solving related rates of change problems, with 44.4% of participants who are not confident to sketch diagram when solving related rates of change problems and only 12.8% believing they are confident to sketch diagram when solving related rates of change problems. Regarding facing difficulty identifying what is given in the question, the majority (49.6%) reported having difficulty with it, but only 11.1% strongly disagreed with this statement. This highlights a perception gap, as the majority is unaware of the importance of this concept. The Kruskal-Wallis test (Table 3 ) was applied to two variables (perception and gender) to access perception regarding learning related rates of change problems. The results showed that there was no significant difference (Table 3 ) between gender and perception regarding learning related rates of change problems ( p > 0.05). Association of knowledge with achievement Table 4 shows the association of participants' knowledge regarding learning related rates of change problems with achievement. The Kruskal-Wallis H test showed different factors related to the knowledge of participants, which caused a change in their achievement pattern. Participants who have familiarity about related rates of change problems have significant association with achievement ( p < 0.05). In addition, a significant association ( p < 0.05) was found between to solve related rates of change problems confidently and the achievement. This significance association highlights the importance of knowledge with achievement. Association of perception with achievement Table 5 shows the association of participants' perception regarding learning related rates of change problems with achievement. The Kruskal-Wallis H test showed different factors related to the perception of participants, which caused a change in their achievement pattern. Participants who have familiarity about related rates of change problems have significant association with achievement ( p < 0.05). In addition, a significant association ( p < 0.05) was found between to solve related rates of change problems confidently. Another significantly correlated factor ( p < 0.05) was facing difficulty to develop the required equation when solving related rates of change problems. Also, the factor not able to master related rates of change problems and the questions related to related rates of change problems are easy to understand have significant association ( p < 0.05) with achievement. Feeling related rates of change problems is an interesting topic, is another significantly corelated factor (( p < 0.05). These significance associations highlight the importance of perception with achievement. Correlational analysis of perception, knowledge, achievement and gender The correlation analysis reveals several significant relationships among the study variables (Table 6 ). A strong positive correlation was found between perception and knowledge (R 2 = 0.662), indicating that higher knowledge is associated with better perception regarding learning related rates of change problems. Participants' knowledge was also significantly correlated with achievement (R 2 = 0.235), suggesting that informed individuals are more likely to achieve a high CGPA. Meanwhile, the achievement-gender correlation (R 2 = 0.265) indicates a significant positive correlation between gender and achievement. Overall, perception significantly impacts both knowledge and achievement. In addition, gender also has an influence on achievement. The study explored perception and knowledge regarding learning related rates of change problems. According to Engelke (2008), to solve related rates of change problems successfully students are required to possess strong mathematical problem-solving skills. Mkhatshwa (2019) argues that a few studies are available on students' perception and reasoning when solving related rates of change problems. Calculus is a first-year mandatory course for all STEM majors (Sadler & Sonnert, 2018; Schraeder et al., 2019). Students learn the concept of related rates of change, which involves solving problems that connect at least two quantities through an equation, function, or formula. These problems are often challenging for many students in differential calculus (Infante, 2021; Mkhatshwa, 2020). Moreover, researchers have identified that students often struggle with related rates of change problems due to challenges in developing a solid conceptual understanding of the underlying mathematics (Mkhatshwa, 2020; Engelke, 2004). The findings of this study indicate a strong association between perception and knowledge regarding learning related rates of change problems which align with the previous study indicating that students can gain better knowledge about the main concepts of calculus when have a better perception about them (Caltson et al., 2010). Similarly, another study done by Martin (2000) found that 48% of the students could not solve the related rates of change problems due to lower perception about the concept. Conclusion The research highlights that students' perceptions about their learning experiences significantly influence their academic knowledge and outcomes. Positive attitudes and beliefs about their capabilities can lead to better performance in understanding related rates of change problems. The study's demographic analysis indicates that the majority of participants were first-year students, predominantly male, which may affect their engagement and learning experiences. This demographic distribution suggests that early academic experiences are crucial for shaping students' perceptions and knowledge. Utilizing a cross-sectional survey design allowed for a comprehensive assessment of students' perceptions and knowledge levels. The study employed self-structured questionnaires and statistical analyses, such as the Kruskal-Wallis Test and Spearman's correlation, to evaluate the relationships between demographic features and knowledge levels. The findings suggest that understanding the relationship between perception and knowledge can inform the development of effective instructional strategies. By creating supportive learning environments that address students' perceptions, educators can enhance comprehension and mastery of calculus concepts, particularly related rates. The study contributes to the broader discourse on mathematics education by emphasizing the need to consider students' perceptions in instructional design. This approach can lead to improved academic success and a deeper understanding of complex mathematical concepts. In summary, the study underscores the critical role of students' perceptions in their learning processes and outcomes, particularly in the context of calculus education. By addressing these perceptions, educators can foster better learning environments and improve student performance in related rates of change problems. Scope and Limitations The research is primarily concerned with individuals pursuing engineering disciplines at the University. This particular population may restrict the applicability of the results to other academic areas or institutions, as the experiences and viewpoints of engineering students may substantially diverge from those in alternative fields. A total of 218 individuals engaged in the survey, predominantly comprising first-year students, with a notable male predominance (87.2%). This demographic configuration may sway the outcomes, as the perceptions and levels of knowledge among students across various academic years or genders could differ markedly. The investigation adopts a cross-sectional survey methodology, which captures data at a singular temporal snapshot. This methodological approach constrains the capacity to infer shifts in perceptions and knowledge over time, as it fails to incorporate longitudinal data that might illuminate the evolution of these parameters. The study specifically explores related rates of change problems within the realm of calculus. While this emphasis permits a thorough examination of a pivotal sector in mathematics education, it may not encompass other significant mathematical constructs or broader educational elements that could also impact student learning and perceptions. The research employs self-structured questionnaires to collect information regarding perceptions and knowledge. Although this technique yields valuable insights, it may simultaneously introduce biases contingent upon the manner in which questions are articulated and interpreted by respondents. Furthermore, the dependence on self-reported data can potentially compromise the precision of the findings. Table 1 The sociodemographic characteristics of participants Characteristics Frequency (N) Percentage (%) Gender Male 102 87.2 Female 15 12.8 Current Year of Study 1 92 78.6 2 19 16.2 3 5 4.3 4 1 0.9 Degree Program Architecture 8 6.8 Biomedical 7 6.0 Chemical 3 2.6 Civil 2 1.7 Computer 35 29.9 Cybersecurity 21 17.9 Electrical 6 5.1 Industrial 4 3.4 Mechanical 12 10.3 Software 19 16.2 Current CGPA 1.0–1.9 39 33.33 2.0–2.9 22 18.80 3.0–3.9 46 39.32 4.0 10 8.55 Residence Dormitory 14 12.0 Home 103 88.0 Table 2 Association of knowledge with gender Factors Gender Mean Rank H Test p value Are you familiar to related rates of change problems? 0.022 0.882 Male 59.15 Female 58.00 Are you confident to solve related rates of change problems? 0.986 0.321 Male 57.97 Female 66.0 In solving related rates of change problems, we can draw diagram before understanding the statement of the problem? 1.128 0.288 Male 57.90 Female 66.50 In solving related rates of change problems, we can draw diagram after understanding the statement of the problem? 0.396 0.529 Male 58.47 Female 62.60 Integration is involved in solving related rates of change problems intensively. 1.156 0.282 Male 60.12 Female 51.40 Differentiation is involved in solving related rates of change problems intensively. 0.177 0.674 Male 58.68 Female 61.20 Differentiation with respect to time is involved in solving related rates of change problems. 1.309 0.253 Male 59.90 Female 52.90 Implicit differentiation is involved in solving related rates of change problems intensively. 0.070 0.791 Male 58.76 Female 60.60 Table 3 Association of perception with gender Factors Gender Mean Rank H Test p value It is easy to understand the statement of Related Rates of Change question. Male 58.53 0.175 0.675 Female 62.20 It is difficult for me to sketch the diagram when solving the Related Rates of Change problem. Male 58.47 0.222 0.637 Female 62.60 It is difficult for me to identify what is given in the question when solving the Related Rates of Change problem. Male 58.82 0.027 0.870 Female 60.23 It is difficult for me to identify what is required in the question when solving the Related Rates of Change problem. Male 58.65 0.094 0.759 Female 61.37 Related Rates of Change topic has many formulas that make me confuse to use in solving the questions. Male 57.63 1.456 0.228 Female 68.30 It is difficult for me to develop the required equation when solving the Related Rates of Change problem. Male 57.72 1.301 0.254 Female 67.73 It is difficult for me to identify the derivatives rules when solving the Related Rates of Change problem. Male 57.25 2.353 0.125 Female 70.87 I will not able to master the Related Rates of Change topic. Male 58.01 0.742 0.389 Female 65.70 Table 4 Association of knowledge with achievement Factors CGPA Mean Rank H Test p value Are you familiar to related rates of change problems? 1 50.50 8.754 0.033 2 54.45 3 67.75 4 61.90 Are you confident to solve related rates of change problems? 1 46.50 10.872 0.012 2 66.89 3 65.15 4 62.10 In solving related rates of change problems, we can draw diagram before understanding the statement of the problem? 1 51.50 5.659 0.129 2 62.07 3 60.57 4 74.30 In solving related rates of change problems, we can draw diagram after understanding the statement of the problem? 1 60.50 1.712 0.634 2 62.95 3 57.17 4 52.85 Integration is involved in solving related rates of change problems intensively. 1 58.00 2.011 0.570 2 62.57 3 55.98 4 68.95 Differentiation is involved in solving related rates of change problems intensively. 1 57.00 1.336 0.721 2 62.80 3 59.67 4 55.35 Differentiation with respect to time is involved in solving related rates of change problems. 1 56.50 2.448 0.485 2 64.95 3 59.17 4 54.85 Implicit differentiation is involved in solving related rates of change problems intensively. 1 54.00 2.829 0.419 2 60.95 3 62.80 4 56.70 Table 5 Association of perception with achievement Factors CGPA Mean Rank H Test p value It is easy to understand the statement of Related Rates of Change question. 1 70.69 8.156 0.043 2 55.00 3 51.85 4 55.10 It is difficult for me to sketch the diagram when solving the Related Rates of Change problem. 1 50.92 4.540 0.209 2 60.23 3 65.53 4 57.75 It is difficult for me to identify what is given in the question when solving the Related Rates of Change problem. 1 54.12 5.881 0.118 2 67.73 3 62.46 4 42.95 It is difficult for me to identify what is required in the question when solving the Related Rates of Change problem. 1 51.46 6.724 0.081 2 69.73 3 62.86 4 47.05 Related Rates of Change topic has many formulas that make me confuse to use in solving the questions. 1 49.85 6.435 0.092 2 57.36 3 67.40 4 59.65 It is difficult for me to develop the required equation when solving the Related Rates of Change problem. 1 46.18 10.002 0.019 2 65.18 3 66.85 4 59.30 It is difficult for me to identify the derivatives rules when solving the Related Rates of Change problem. 1 48.96 6.928 0.074 2 64.59 3 65.98 4 53.75 I will not able to master the Related Rates of Change topic. 1 47.96 14.356 0.002 2 71.52 3 66.72 4 39.00 Questions related to Related Rates of Change topic are easy to solve. 1 70.49 9.721 0.021 2 54.27 3 49.95 4 66.25 I feel that Related Rates of Change topic is interesting. 1 69.81 8.339 0.040 2 48.16 3 54.42 4 61.75 Table 6 Correlation between knowledge, perception, achievement and gender Variables Correlation coefficient p value Perception-knowledge 0.662 0.001 Knowledge-achievement 0.235 0.011 achievement-gender 0.265 0.004 Declarations Declarations This study has been reviewed and approved by the Institutional Review Board for Human Subjects Research (IRB) at Abu Dhabi University, Abu Dhabi, UAE. The IRB has determined that the research complies with all applicable ethical standards and regulations, ensuring the protection of the rights, welfare, and privacy of human subjects involved in the study. The authors have no relevant financial or non-financial interests to disclose. The authors have no competing interests to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article. The authors have no relevant financial or non-financial interests to disclose. The authors have no competing interests to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article. References Ahmed, J. W. (2024). Problem-Based Learning: A Strategy to Foster 21st Century Critical Thinking and Perseverance in Building Technology Students. BIJOTE-BICHI Journal Of Technology Education , 7 (1), 99-111. Bibi, A., Aurangzeb, W., Tabassum, F., & Ahmad, M. (2025). Modelling the relationship among calculus scholars’ beliefs, critical thinking, elaboration, and problem-solving. International Electronic Journal of Mathematics Education , 20 (1), em0808. Cohen, O., & Sukenik, N. (2024). Mathematical proficiency in adolescents with ASD. Journal of Autism and Developmental Disorders , 1-16. Díaz, B., Luengo‐Aravena, D., Barahona, P., & Felmer, P. (2025). Assessing the impact of online collaborative problem solving on a calculus class for first‐year engineering students: A communities of practice lens. Journal of Engineering Education , 114 (1), e20622. Domondon, C. S., Pardo, C. G., & Rin, E. T. (2022). Analysis of difficulties of students in learning calculus. Science International (Lahore) , 34 (6), 1-4. Dzaiy, A. H. S., & Abdullah, S. A. (2024). The use of active learning strategies to foster effective teaching in higher education institutions. Zanco Journal of Human Sciences , 28 (4), 328-351. Honrubia-Montesinos, C., & Otero, L. A. (2025). Fostering Intercultural Skills Through Geography: A Proposal for Future Primary Education Teachers. In Geography Education and Explorations on Human Development and Culture (pp. 243-264). IGI Global Scientific Publishing. Jain, S., Bharti, M., & Tripathi, S. (2025). Graphical User Interface for Handwritten Mathematical Expression Employing RNN-based Encoder-decoder Model. Recent Advances in Computer Science and Communications , 18 (1), E290524230473. Kaplan, H. A. (2025). ChatGPT's Knowledge in Mathematics Teaching: An Example of Rational Numbers. Pegem Journal of Education and Instruction , 15 (2), 63-75. Kasa, Y., Areaya, S., & Woldemichael, M. (2024). Mathematics Teachers' Beliefs about Mathematics, Its Teaching, and Learning: The Case of Five Teachers. Pedagogical Research , 9 (2). Kidron, I. (2020). Calculus teaching and learning. Encyclopedia of mathematics education , 87-94. Mergendoller, J. R., Markham, T., Ravitz, J., & Larmer, J. (2013). Pervasive management of project-based learning: Teachers as guides and facilitators. In Handbook of classroom management (pp. 593-626). Routledge. Muldoon Brown, T. (2025). Becoming a More Effective Instructor Using Primary Source Projects. The Mathematics Enthusiast , 22 (1), 9-28. Pelemeniano, A. P., & Siega, M. H. (2023). Integrating Mathematical Modeling of Real-Life Problems: A Contextualized Approach to Developing Instructional Material in Basic Calculus. International Journal , 10 (3), 149-163. Saha, M., Islam, S., Akhi, A. A., & Saha, G. (2024). Factors affecting success and failure in higher education mathematics: Students' and teachers’ perspectives. Heliyon , 10 (7). Santos-Trigo, M., Camacho-Machín, M., & Barrera-Mora, F. (2024). Focusing on foundational Calculus ideas to understand the derivative concept via problem-solving tasks that involve the use of a dynamic geometry system. ZDM–Mathematics Education , 1-15. Subramaniam, G., & Saleh, Z. M. (2024). Development of GeoExplorer: A Gamification Platform Utilizing Constructivist Approach to Alleviate Mathematical Anxiety. Semarak International Journal of STEM Education , 3 (1), 1-16. Tulis, M., & Fulmer, S. M. (2013). Students' motivational and emotional experiences and their relationship to persistence during academic challenge in mathematics and reading. Learning and Individual Differences , 27 , 35-46. Turunen, E., & Seppälä, U. (2025). How does it feel to be poor? Resources and strength limiting action. Nordic Social Work Research , 1-14. Uyen, D. P., Nhu, N. T. H., Nghi, D. D., Khanh, V. H., Vy, H. T., Sa, N. T. H., & Vy, N. T. H. (2024). Optimal pedagogical strategies in research methodology: Insights from student experiences. Environment and Social Psychology , 9 (4). Wagner, D., & Tamayo, C. (2024). Invisibilization and Intersectionality in Mathematics Education: A Panoramic View: Invisibilização e Interseccionalidade na Educação Matemática: Uma Visão Panorâmica. In Fourth International Handbook of Mathematics Education (pp. 379-411). Springer. 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-6490660","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":445394195,"identity":"b59c9af1-8f86-4595-a7b3-760f33656c9e","order_by":0,"name":"Muhammad Farooq","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCklEQVRIiWNgGAWjYBAC9gYYSwJMMssZgGkDC5xaeA6gaTE2YGAGaZEgXkviBrAWBjxa2M8+fPChjCHa4Hbz0003aqzTt7P3H93wo0CCgb+9OwGrFp50Y8MZ5xhyN9w5ZnY751h67s6ew2w3e4AOkzhzdgM2LfYMaWzSvG3/czfcSABqYTsMZCSz3eABajGQyMWqhYf/GUgL0JYb6d9u5/w7nG4A1HLzDz4tEmkwLTlmt3PbDieAtNzGa4vEM2awX2beyCm7nduXbrjhzGGz2zIGEjy4/MLDn8YICrHcvhvp227nfLOWNzje+Ozmmz82cvztvVi1QAAbNsNwK8elZRSMglEwCkYBDAAAOCpkOE+V/q8AAAAASUVORK5CYII=","orcid":"","institution":"Abu Dhabi University","correspondingAuthor":true,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Farooq","suffix":""}],"badges":[],"createdAt":"2025-04-20 18:08:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6490660/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6490660/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83477027,"identity":"bad9b3f8-d1b7-4228-96c5-8683118e6da7","added_by":"auto","created_at":"2025-05-27 05:01:49","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1039110,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6490660/v1/1b37e51b-507d-4257-b844-b173dd005872.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Relationship between Student’s Perception and Knowledge in Learning Related Rates of Change Problems","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe interplay between students' perceptions and their knowledge is one of the major foci of academic inquiry, particularly into the pedagogy of mathematics. (Wagner \u0026amp; Tamayo, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). One of the basic concepts within calculus that ordinarily proves problematic from students' perspectives is related rates of change (Santos-Trigo et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Motion describes the situation of comparing how much one quantity changes concerning the change in another. Facility in those situations would be considered a profound grasp of the principles of calculus and would likely enhance student skills in developing solutions to problems and their logical ability as well (Pelemeniano \u0026amp; Siega, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe relationship between students' perceptions about their learning experience and the actual academic knowledge has been one of the factors that psychology and pedagogy pay more and more attention to right now (Uyen et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). It is believed that students' attitudes, beliefs, and perceptions are very important in forming their learning outcomes (Uyen et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Precisely, how the perceptual factors interact with learners' performance within some very narrow mathematical content areas, say, problems based on related rates of change demands more research (Cohen \u0026amp; Sukenik, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis paper is set to articulate the complicated nexus between perception by students and their knowledge when dealing with related rates of change problems. To unearth pedagogical, curriculum, and subscribed mechanism insights for fostering a better calculus education learning experience, the pursuit shall be informed by what will be discovered about this relationship (D\u0026iacute;az et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis paper first provides an overview of related rates of change problems and the challenges students face in understanding them. Next, it explores the importance of examining students' perceptions and knowledge in learning calculus, particularly in the context of related rates. Finally, the study's objectives and methodology are outlined, highlighting its contribution to the broader discourse on mathematics education and student learning. Through this research, effective strategies are identified for creating a supportive learning environment and enhancing academic success in calculus education.\u003c/p\u003e"},{"header":"Literature Review","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eStudents\u0026rsquo; Knowledge in the related rates of change problems\u003c/h2\u003e \u003cp\u003eConventional teaching approaches have long been adopting in university-level calculus instruction. However, due to these methods students often grappling to grasp the fundamental concepts of calculus (Kidron, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Instructors commonly emphasizes on calculations rather than nurturing a trench understanding of the fundamental principles at play (Mergendoller et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Students who take conventional teaching methods are 1.5 times more intend to failure compared to their peers in active learning environments (Dzaiy \u0026amp; Abdullah, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). This is because traditional teaching often prioritizes rote memorization of formulas and mechanical procedures quite than developing a sound understanding of abstract concepts and their interconnections. Consequently, the traditional approach to teaching calculus proves ineffective in fostering a genuine comprehension of its essential principles (Muldoon Brown, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Understanding students' perception and knowledge towards learning calculus, particularly related rates of change problems, is vital for informing pedagogical practices and curriculum development (D\u0026iacute;az et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). By identifying factors that influence students' motivation and engagement, educationalists can design interventions to address misconceptions, alleviate anxiety, and heighten students' confidence in handling complex mathematical problems (Subramaniam \u0026amp; Saleh, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eStudents often struggle in calculus during studying related rates of change problems. The instructors who would like to use conventional approach in teaching calculus should realize that traditional teaching methods in calculus does not work even in classes dominated by students majoring in mathematics, science, and engineering since traditional pedagogy yields unsatisfactory results. This includes difficulties with proceedings knowledge as well as abstract understanding, indicating a broader challenge than plainly a lack of one type of knowledge or skill (Turunen \u0026amp; Sepp\u0026auml;l\u0026auml;, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). It's imperative for students to cultivate the skill of synthesizing verbal, symbolic, and graphical representations, fostering a holistic understanding of concepts (Honrubia-Montesinos \u0026amp; Otero, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). It's crucial for calculus students to both decode and encode symbolical representations, recognizing that these skills may reflect varying levels of conceptual understanding (Jain et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe perception and knowledge of the students towards learning calculus play an important role in their academic achievement and motivation (Bibi et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Research indicates that beliefs of the students about their mathematical abilities, their interest in the subject, and their perception of the relevance of calculus to their future goals can mold their learning outcomes (Kasa et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Adverse attitudes towards mathematics, fear of failure, and a lack of trust in their problem-solving abilities may hinder students' engagement and persistence in learning calculus, particularly in challenging topics, for instance related rates of change problems (Saha et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eCalculus serves as a fundamental mathematical discipline essential for students wishing to adopt STEM majors in higher education. The concept of related rates of change is a key focus in single-variable calculus, providing students with a model to employ the fundamental view of instantaneous rates of change in practical scenarios. Past research has shown that students often see related rates of change problems to be challenging (Tulis \u0026amp; Fulmer, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Students faced challenges when learning problems involving related rates of change (Domondon et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The primary challenges initially arise when students try to grasp the problem context instead of understanding the concept. This comprehension significantly affects their ability to make an appropriate mathematical model that defines the connection between relevant quantities and their corresponding rates of change (Kaplan, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eStudents’ Perception of the related rates of change problems and its relationship with knowledge\u003c/h3\u003e\n\u003cp\u003eIn calculus, many students consider related rates of change problems difficult and challenging (D\u0026iacute;az et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). These problems need a better understanding of how multiple variables are related with each other and how their rates of change impact one another. Students see the related rates of change problems as a complex puzzles that require more attention and an understanding of how different quantities are interconnected (Ahmed, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Some students may find related rates of change problems challenging at first. However, for many these problems become interesting when they explore their applications in real-world scenarios, such as physics, engineering, and economics. Through practice and persistence, students develop deep understanding to think and solve these problems as well as enabling them to deal complex scenarios with confidence (Ahmed, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eIn addition, students' perception of related rates of change problems can be affected by numerous factors, including their prior mathematical knowledge, teaching methods, and self-learning styles (Tseng et al., 2013). Visual aids, interactive demonstrations, and real-life examples can boost students' comprehension and engagement with these concepts. Moreover, promoting a helpful learning environment where students feel stimulated to ask questions and discover different problem-solving techniques can foster a deeper understanding and appreciation of related rates of change problems (Muis et al., 2016). As students gain confidence in tackling related rates of change problems, they often show a sense of accomplishment and mastery, recognizing the value of calculus as a powerful tool around for analyzing dynamic systems and phenomena (Faulkner et al., 2019).\u003c/p\u003e \u003cp\u003ePerception plays a vital role in determining one's achievement in learning calculus topics (Duran et al., 2024). The attitude of the students towards complexity and relevance of calculus can significantly impact their motivation and approach to learning (Rasmussen et al., 2014). If students take calculus as an unbeatable dilemma or fail to see its practical applications, they may approach the subject with lack of interest, hindering their ability to grasp key concepts and attain academic success. On the other side, a positive perception of calculus as a fascinating discipline with real-world applications can revolutionize students to engage more deeply with the material, leading to greater understanding and knowledge (Akbuga, 2018). Additionally, perception influences attitudes of the students towards challenges and setbacks encountered while learning calculus (Sonnert et al., 2015). Those who comprehend difficulties as opportunities for growth and learning are more probably to persist in their efforts and overcome challenges. Conversely, students who perceive challenges as non-removable barriers may turn discouraged and disengage from the learning process (Flynn et al., 2011). Thus, cultivating an increment mindset and fosterage positive perceptions of calculus as an intellectually stimulating field can enhance knowledge of the students and mastering of calculus topics (Hunt, 2017). By addressing students' perceptions and attitudes towards calculus, educators can make a supportive learning environment helpful to academic success (Hung et al., 2010).\u003c/p\u003e \u003cp\u003eIn spite of the importance of understanding the relationship between student perceptions and knowledge in learning related rates of change problems, a few studies have particularly addressed this topic. Past researches have primarily focused on exploring students' attitudes towards mathematics in general or investigating instructional strategies for improving calculus learning outcomes without directly examining the influence of student perceptions on their knowledge in related rates of change problems.\u003c/p\u003e \u003cp\u003eThe current study aims to investigate the connection between the perception of the students and their knowledge in related rates of change problems. By administering surveys to assess students' perception and knowledge in learning related rates problem-solving tasks, this research seeks to identify potential correlations and predictive factors. The results of this study will help to create effective research-based strategies for promoting academic success in calculus education and enhancing students' understanding in related rates of change concepts.\u003c/p\u003e"},{"header":"Methodology","content":"\u003cp\u003eThe methodology section includes a description of the research design, samples involved, research instrument, and data analysis.\u003c/p\u003e\n\u003ch3\u003eResearch Design\u003c/h3\u003e\n\u003cp\u003eA cross-sectional survey design was utilized with self-structured questionnaire. The inclusion criteria include all students currently enrolled in engineering majors. All faculty members, instructors and all other majors was excluded during study.\u003c/p\u003e\n\u003ch3\u003eSamples\u003c/h3\u003e\n\u003cp\u003eA total of 218 students were surveyed during this study. The sample size was calculated using standard sample size calculator with 5% population mean error. 50% distribution error was set during survey distribution.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003eResearch Instrument\u003c/h2\u003e \u003cp\u003eThe research instrument was divided into 4 different sections. Section 1 includes demographic features like gender, year of study, current CGPA, and degree program. Section 2 includes questions related to knowledge, with close end questions like Yes and No. While the third section included questions related to perception, and the perception was correlated with the responses of knowledge related questions. While the last section includes knowledge based on current knowledge. The knowledge was assessed by designing a 10 questions quiz, including questions related to solutions of different context statements including equations, symbols and diagrams.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003eData Analysis\u003c/h2\u003e \u003cp\u003eAll the qualitative data were evaluated using Statistical Package for Social Sciences (SPSS) software version 29. The demographic data was evaluated using mean and standard deviation. The Kruskal-Wallis Test was used to assess the significance of demographic data based on perception level. The reliability analysis of the study data was evaluated using Cronbach alpha values. A Spearmen\u0026rsquo;s correlation analysis identifies the demographic features with knowledge level. A statistical significance was defined as p-value less than 0.05.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results and Discussion","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003eDemographic characteristics of participants\u003c/h2\u003e \u003cp\u003eAccording to Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the study population comprised 102 male (87.2%) and 15 female (12.8%) students, with the majority (78.6%) in first year of their study. This gender distribution suggests that the study cohort is predominantly male, which could be reflective of enrollment trends in engineering fields, followed by 16.2% in second year and smaller proportion (0.9%) in fourth year of their study. This distribution indicates that the majority of respondents are at the beginning stages of their academic journey, which may influence their learning experiences and engagement with argumentation-based teaching strategies. Majority of the students were enrolled in computer science program (29.9%), while only 1.7% were enrolled in chemical engineering program. The diverse academic backgrounds suggest that the study's findings may be applicable across multiple engineering fields, though the high concentration of computing-related disciplines may introduce a disciplinary bias. Regarding academic achievement 8.55% scored CGPA 4.0, and 39.32% scored CGPA between 3.0\u0026ndash;3.9, though 18.8% scored CGPA between 2.0\u0026ndash;2.9. This suggests a varied academic performance level among participants, which could impact their responsiveness to instructional strategies. Regarding residency, most participants (88.0%) resided in their homes and 12.0% lived in dormitory. This finding may have implications for students' access to peer learning opportunities, study environments, and engagement with course materials outside of class.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003eAssessment of knowledge regarding learning related rates of change problems\u003c/h2\u003e \u003cp\u003eTo assess the knowledge, the responses were translated into 10 different questions. Out of 117 participants, most participants (65.0%) have good knowledge regarding familiarity about related rates of change problems, while 35.0% have poor knowledge regarding familiarity about related rates of change problems. The data indicated lack of confidence to solve related rates of change problems, with 54.7% of participants who are not confident to solve related rates of change problems and 45.3% believing they are confident to solve related rates of change problems.\u003c/p\u003e \u003cp\u003eRegarding the knowledge about substituting values of variables after differentiation, 73.5% reported having heard of it, but only 26.5% did not know about its significance. This highlights a knowledge gap, as 26.5% are unaware of the importance of this concept.\u003c/p\u003e \u003cp\u003eThe Kruskal-Wallis test (Table \u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) was applied to two variables (knowledge and gender) to access knowledge regarding learning related rates of change problems. The results showed that there was no significant difference (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) between gender and knowledge regarding learning related rates of change problems (\u003cem\u003ep\u0026thinsp;\u0026gt;\u003c/em\u003e\u0026thinsp;0.05).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003eAssessment of perception regarding learning related rates of change problems\u003c/h2\u003e \u003cp\u003eTo assess the perception, the responses were translated into 10 different questions. Out of 117 participants, most participants (46.2%) disagreed regarding to understand the statement of related rates of change problems easily, while only 9.4% were strongly agreed regarding to understand the statement of related rates of change problems easily. The data indicated lack of confidence to sketch diagram when solving related rates of change problems, with 44.4% of participants who are not confident to sketch diagram when solving related rates of change problems and only 12.8% believing they are confident to sketch diagram when solving related rates of change problems.\u003c/p\u003e \u003cp\u003eRegarding facing difficulty identifying what is given in the question, the majority (49.6%) reported having difficulty with it, but only 11.1% strongly disagreed with this statement. This highlights a perception gap, as the majority is unaware of the importance of this concept.\u003c/p\u003e \u003cp\u003eThe Kruskal-Wallis test (Table \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) was applied to two variables (perception and gender) to access perception regarding learning related rates of change problems. The results showed that there was no significant difference (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) between gender and perception regarding learning related rates of change problems (\u003cem\u003ep\u0026thinsp;\u0026gt;\u003c/em\u003e\u0026thinsp;0.05).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003eAssociation of knowledge with achievement\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the association of participants' knowledge regarding learning related rates of change problems with achievement. The Kruskal-Wallis H test showed different factors related to the knowledge of participants, which caused a change in their achievement pattern. Participants who have familiarity about related rates of change problems have significant association with achievement (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05).\u003c/p\u003e \u003cp\u003eIn addition, a significant association (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) was found between to solve related rates of change problems confidently and the achievement. This significance association highlights the importance of knowledge with achievement.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003eAssociation of perception with achievement\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e shows the association of participants' perception regarding learning related rates of change problems with achievement. The Kruskal-Wallis H test showed different factors related to the perception of participants, which caused a change in their achievement pattern. Participants who have familiarity about related rates of change problems have significant association with achievement (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05).\u003c/p\u003e \u003cp\u003eIn addition, a significant association (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) was found between to solve related rates of change problems confidently. Another significantly correlated factor (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) was facing difficulty to develop the required equation when solving related rates of change problems. Also, the factor not able to master related rates of change problems and the questions related to related rates of change problems are easy to understand have significant association (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05) with achievement. Feeling related rates of change problems is an interesting topic, is another significantly corelated factor ((\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05). These significance associations highlight the importance of perception with achievement.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003eCorrelational analysis of perception, knowledge, achievement and gender\u003c/h2\u003e \u003cp\u003eThe correlation analysis reveals several significant relationships among the study variables (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). A strong positive correlation was found between perception and knowledge (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.662), indicating that higher knowledge is associated with better perception regarding learning related rates of change problems. Participants' knowledge was also significantly correlated with achievement (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.235), suggesting that informed individuals are more likely to achieve a high CGPA. Meanwhile, the achievement-gender correlation (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.265) indicates a significant positive correlation between gender and achievement. Overall, perception significantly impacts both knowledge and achievement. In addition, gender also has an influence on achievement. The study explored perception and knowledge regarding learning related rates of change problems. According to Engelke (2008), to solve related rates of change problems successfully students are required to possess strong mathematical problem-solving skills. Mkhatshwa (2019) argues that a few studies are available on students' perception and reasoning when solving related rates of change problems. Calculus is a first-year mandatory course for all STEM majors (Sadler \u0026amp; Sonnert, 2018; Schraeder et al., 2019). Students learn the concept of related rates of change, which involves solving problems that connect at least two quantities through an equation, function, or formula. These problems are often challenging for many students in differential calculus (Infante, 2021; Mkhatshwa, 2020). Moreover, researchers have identified that students often struggle with related rates of change problems due to challenges in developing a solid conceptual understanding of the underlying mathematics (Mkhatshwa, 2020; Engelke, 2004).\u003c/p\u003e \u003cp\u003eThe findings of this study indicate a strong association between perception and knowledge regarding learning related rates of change problems which align with the previous study indicating that students can gain better knowledge about the main concepts of calculus when have a better perception about them (Caltson et al., 2010). Similarly, another study done by Martin (2000) found that 48% of the students could not solve the related rates of change problems due to lower perception about the concept.\u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe research highlights that students' perceptions about their learning experiences significantly influence their academic knowledge and outcomes. Positive attitudes and beliefs about their capabilities can lead to better performance in understanding related rates of change problems. The study's demographic analysis indicates that the majority of participants were first-year students, predominantly male, which may affect their engagement and learning experiences. This demographic distribution suggests that early academic experiences are crucial for shaping students' perceptions and knowledge. Utilizing a cross-sectional survey design allowed for a comprehensive assessment of students' perceptions and knowledge levels. The study employed self-structured questionnaires and statistical analyses, such as the Kruskal-Wallis Test and Spearman's correlation, to evaluate the relationships between demographic features and knowledge levels. The findings suggest that understanding the relationship between perception and knowledge can inform the development of effective instructional strategies. By creating supportive learning environments that address students' perceptions, educators can enhance comprehension and mastery of calculus concepts, particularly related rates. The study contributes to the broader discourse on mathematics education by emphasizing the need to consider students' perceptions in instructional design. This approach can lead to improved academic success and a deeper understanding of complex mathematical concepts. In summary, the study underscores the critical role of students' perceptions in their learning processes and outcomes, particularly in the context of calculus education. By addressing these perceptions, educators can foster better learning environments and improve student performance in related rates of change problems.\u003c/p\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003eScope and Limitations\u003c/h2\u003e \u003cp\u003eThe research is primarily concerned with individuals pursuing engineering disciplines at the University. This particular population may restrict the applicability of the results to other academic areas or institutions, as the experiences and viewpoints of engineering students may substantially diverge from those in alternative fields. A total of 218 individuals engaged in the survey, predominantly comprising first-year students, with a notable male predominance (87.2%). This demographic configuration may sway the outcomes, as the perceptions and levels of knowledge among students across various academic years or genders could differ markedly. The investigation adopts a cross-sectional survey methodology, which captures data at a singular temporal snapshot. This methodological approach constrains the capacity to infer shifts in perceptions and knowledge over time, as it fails to incorporate longitudinal data that might illuminate the evolution of these parameters. The study specifically explores related rates of change problems within the realm of calculus. While this emphasis permits a thorough examination of a pivotal sector in mathematics education, it may not encompass other significant mathematical constructs or broader educational elements that could also impact student learning and perceptions. The research employs self-structured questionnaires to collect information regarding perceptions and knowledge. Although this technique yields valuable insights, it may simultaneously introduce biases contingent upon the manner in which questions are articulated and interpreted by respondents. Furthermore, the dependence on self-reported data can potentially compromise the precision of the findings.\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\u003eThe sociodemographic characteristics of participants\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eCharacteristics\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eFrequency (N)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ePercentage (%)\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eGender\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e102\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e87.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eCurrent Year of Study\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e78.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eDegree Program\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArchitecture\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.8\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBiomedical\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eChemical\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCivil\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eComputer\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCybersecurity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e17.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElectrical\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrial\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMechanical\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSoftware\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003e\u003cb\u003eCurrent CGPA\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1.0\u0026ndash;1.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e33.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2.0\u0026ndash;2.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e18.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3.0\u0026ndash;3.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e39.32\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8.55\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cb\u003eResidence\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDormitory\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHome\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e103\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e88.0\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\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\u003eAssociation of knowledge with gender\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"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\u003e\u003cem\u003eFactors\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eGender\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eMean Rank\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eH Test\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003ep value\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cem\u003eAre you familiar to related rates of change problems?\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.882\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e59.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cem\u003eAre you confident to solve related rates of change problems?\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.986\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.321\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.97\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e66.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cem\u003eIn solving related rates of change problems, we can draw diagram before understanding the statement of the problem?\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e1.128\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.288\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e66.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cem\u003eIn solving related rates of change problems, we can draw diagram after understanding the statement of the problem?\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.396\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.529\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.47\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cem\u003eIntegration is involved in solving related rates of change problems intensively.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e1.156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.282\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60.12\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e51.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cem\u003eDifferentiation is involved in solving related rates of change problems intensively.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.177\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.674\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e61.20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cem\u003eDifferentiation with respect to time is involved in solving related rates of change problems.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e1.309\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.253\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e59.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e52.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cem\u003eImplicit differentiation is involved in solving related rates of change problems intensively.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.070\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e0.791\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60.60\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\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\u003eAssociation of perception with gender\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"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\u003e\u003cem\u003eFactors\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eGender\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eMean Rank\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eH Test\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003ep value\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eIt is easy to understand the statement of Related Rates of Change question.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.175\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.675\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to sketch the diagram when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.222\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.637\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to identify what is given in the question when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.870\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to identify what is required in the question when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.094\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.759\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e61.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eRelated Rates of Change topic has many formulas that make me confuse to use in solving the questions.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e1.456\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.228\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e68.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to develop the required equation when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e1.301\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.254\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e67.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to identify the derivatives rules when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e2.353\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.125\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e70.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cem\u003eI will not able to master the Related Rates of Change topic.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.742\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.389\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFemale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e65.70\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\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAssociation of knowledge with achievement\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\u003e\u003cem\u003eFactors\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eCGPA\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eMean Rank\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eH Test\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003ep value\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eAre you familiar to related rates of change problems?\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e50.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e8.754\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.033\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e67.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e61.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eAre you confident to solve related rates of change problems?\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e46.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e10.872\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.012\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e66.89\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e65.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eIn solving related rates of change problems, we can draw diagram before understanding the statement of the problem?\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e51.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e5.659\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.129\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60.57\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e74.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eIn solving related rates of change problems, we can draw diagram after understanding the statement of the problem?\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e1.712\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.634\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e52.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eIntegration is involved in solving related rates of change problems intensively.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e58.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e2.011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.570\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.57\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e55.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e68.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eDifferentiation is involved in solving related rates of change problems intensively.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e1.336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.721\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e59.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e55.35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eDifferentiation with respect to time is involved in solving related rates of change problems.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e56.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e2.448\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.485\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e64.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e59.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eImplicit differentiation is involved in solving related rates of change problems intensively.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e2.829\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.419\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e56.70\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\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAssociation of perception with achievement\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\u003e\u003cem\u003eFactors\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eCGPA\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eMean Rank\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eH Test\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003ep value\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eIt is easy to understand the statement of Related Rates of Change question.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e70.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e8.156\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.043\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e55.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e51.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e55.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to sketch the diagram when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e50.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e4.540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.209\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e60.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e65.53\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to identify what is given in the question when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e5.881\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.118\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e67.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e42.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to identify what is required in the question when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e51.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e6.724\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e69.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e62.86\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e47.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eRelated Rates of Change topic has many formulas that make me confuse to use in solving the questions.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e49.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e6.435\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.092\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e57.36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e67.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e59.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to develop the required equation when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e46.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e10.002\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.019\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e65.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e66.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e59.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eIt is difficult for me to identify the derivatives rules when solving the Related Rates of Change problem.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e48.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e6.928\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.074\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e64.59\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e65.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e53.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eI will not able to master the Related Rates of Change topic.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e47.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e14.356\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.002\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e71.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e66.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e39.00\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eQuestions related to Related Rates of Change topic are easy to solve.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e70.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e9.721\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.021\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e49.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e66.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cem\u003eI feel that Related Rates of Change topic is interesting.\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e69.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e8.339\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e0.040\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e48.16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e54.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e61.75\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\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCorrelation between knowledge, perception, achievement and gender\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eVariables\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eCorrelation coefficient\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ep value\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ePerception-knowledge\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.662\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eKnowledge-achievement\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.235\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eachievement-gender\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.265\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003eDeclarations This study has been reviewed and approved by the Institutional Review Board for Human Subjects Research (IRB) at Abu Dhabi University, Abu Dhabi, UAE. The IRB has determined that the research complies with all applicable ethical standards and regulations, ensuring the protection of the rights, welfare, and privacy of human subjects involved in the study. The authors have no relevant financial or non-financial interests to disclose. The authors have no competing interests to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article.\u003c/p\u003e\u003cul\u003e\n \u003cli\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/li\u003e\n \u003cli\u003eThe authors have no competing interests to declare that are relevant to the content of this article.\u003c/li\u003e\n \u003cli\u003eAll authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.\u003c/li\u003e\n \u003cli\u003eThe authors have no financial or proprietary interests in any material discussed in this article.\u003c/li\u003e\n\u003c/ul\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAhmed, J. W. (2024). Problem-Based Learning: A Strategy to Foster 21st Century Critical Thinking and Perseverance in Building Technology Students. \u003cem\u003eBIJOTE-BICHI Journal Of Technology Education\u003c/em\u003e,\u003cem\u003e 7\u003c/em\u003e(1), 99-111. \u003c/li\u003e\n\u003cli\u003eBibi, A., Aurangzeb, W., Tabassum, F., \u0026amp; Ahmad, M. (2025). Modelling the relationship among calculus scholars\u0026rsquo; beliefs, critical thinking, elaboration, and problem-solving. \u003cem\u003eInternational Electronic Journal of Mathematics Education\u003c/em\u003e,\u003cem\u003e 20\u003c/em\u003e(1), em0808. \u003c/li\u003e\n\u003cli\u003eCohen, O., \u0026amp; Sukenik, N. (2024). Mathematical proficiency in adolescents with ASD. \u003cem\u003eJournal of Autism and Developmental Disorders\u003c/em\u003e, 1-16. \u003c/li\u003e\n\u003cli\u003eD\u0026iacute;az, B., Luengo‐Aravena, D., Barahona, P., \u0026amp; Felmer, P. (2025). Assessing the impact of online collaborative problem solving on a calculus class for first‐year engineering students: A communities of practice lens. \u003cem\u003eJournal of Engineering Education\u003c/em\u003e,\u003cem\u003e 114\u003c/em\u003e(1), e20622. \u003c/li\u003e\n\u003cli\u003eDomondon, C. S., Pardo, C. G., \u0026amp; Rin, E. T. (2022). Analysis of difficulties of students in learning calculus. \u003cem\u003eScience International (Lahore)\u003c/em\u003e,\u003cem\u003e 34\u003c/em\u003e(6), 1-4. \u003c/li\u003e\n\u003cli\u003eDzaiy, A. H. S., \u0026amp; Abdullah, S. A. (2024). The use of active learning strategies to foster effective teaching in higher education institutions. \u003cem\u003eZanco Journal of Human Sciences\u003c/em\u003e,\u003cem\u003e 28\u003c/em\u003e(4), 328-351. \u003c/li\u003e\n\u003cli\u003eHonrubia-Montesinos, C., \u0026amp; Otero, L. A. (2025). Fostering Intercultural Skills Through Geography: A Proposal for Future Primary Education Teachers. In \u003cem\u003eGeography Education and Explorations on Human Development and Culture\u003c/em\u003e (pp. 243-264). IGI Global Scientific Publishing. \u003c/li\u003e\n\u003cli\u003eJain, S., Bharti, M., \u0026amp; Tripathi, S. (2025). Graphical User Interface for Handwritten Mathematical Expression Employing RNN-based Encoder-decoder Model. \u003cem\u003eRecent Advances in Computer Science and Communications\u003c/em\u003e,\u003cem\u003e 18\u003c/em\u003e(1), E290524230473. \u003c/li\u003e\n\u003cli\u003eKaplan, H. A. (2025). ChatGPT\u0026apos;s Knowledge in Mathematics Teaching: An Example of Rational Numbers. \u003cem\u003ePegem Journal of Education and Instruction\u003c/em\u003e,\u003cem\u003e 15\u003c/em\u003e(2), 63-75. \u003c/li\u003e\n\u003cli\u003eKasa, Y., Areaya, S., \u0026amp; Woldemichael, M. (2024). Mathematics Teachers\u0026apos; Beliefs about Mathematics, Its Teaching, and Learning: The Case of Five Teachers. \u003cem\u003ePedagogical Research\u003c/em\u003e,\u003cem\u003e 9\u003c/em\u003e(2). \u003c/li\u003e\n\u003cli\u003eKidron, I. (2020). Calculus teaching and learning. \u003cem\u003eEncyclopedia of mathematics education\u003c/em\u003e, 87-94. \u003c/li\u003e\n\u003cli\u003eMergendoller, J. R., Markham, T., Ravitz, J., \u0026amp; Larmer, J. (2013). Pervasive management of project-based learning: Teachers as guides and facilitators. In \u003cem\u003eHandbook of classroom management\u003c/em\u003e (pp. 593-626). Routledge. \u003c/li\u003e\n\u003cli\u003eMuldoon Brown, T. (2025). Becoming a More Effective Instructor Using Primary Source Projects. \u003cem\u003eThe Mathematics Enthusiast\u003c/em\u003e,\u003cem\u003e 22\u003c/em\u003e(1), 9-28. \u003c/li\u003e\n\u003cli\u003ePelemeniano, A. P., \u0026amp; Siega, M. H. (2023). Integrating Mathematical Modeling of Real-Life Problems: A Contextualized Approach to Developing Instructional Material in Basic Calculus. \u003cem\u003eInternational Journal\u003c/em\u003e,\u003cem\u003e 10\u003c/em\u003e(3), 149-163. \u003c/li\u003e\n\u003cli\u003eSaha, M., Islam, S., Akhi, A. A., \u0026amp; Saha, G. (2024). Factors affecting success and failure in higher education mathematics: Students\u0026apos; and teachers\u0026rsquo; perspectives. \u003cem\u003eHeliyon\u003c/em\u003e,\u003cem\u003e 10\u003c/em\u003e(7). \u003c/li\u003e\n\u003cli\u003eSantos-Trigo, M., Camacho-Mach\u0026iacute;n, M., \u0026amp; Barrera-Mora, F. (2024). Focusing on foundational Calculus ideas to understand the derivative concept via problem-solving tasks that involve the use of a dynamic geometry system. \u003cem\u003eZDM\u0026ndash;Mathematics Education\u003c/em\u003e, 1-15. \u003c/li\u003e\n\u003cli\u003eSubramaniam, G., \u0026amp; Saleh, Z. M. (2024). Development of GeoExplorer: A Gamification Platform Utilizing Constructivist Approach to Alleviate Mathematical Anxiety. \u003cem\u003eSemarak International Journal of STEM Education\u003c/em\u003e,\u003cem\u003e 3\u003c/em\u003e(1), 1-16. \u003c/li\u003e\n\u003cli\u003eTulis, M., \u0026amp; Fulmer, S. M. (2013). Students\u0026apos; motivational and emotional experiences and their relationship to persistence during academic challenge in mathematics and reading. \u003cem\u003eLearning and Individual Differences\u003c/em\u003e,\u003cem\u003e 27\u003c/em\u003e, 35-46. \u003c/li\u003e\n\u003cli\u003eTurunen, E., \u0026amp; Sepp\u0026auml;l\u0026auml;, U. (2025). How does it feel to be poor? Resources and strength limiting action. \u003cem\u003eNordic Social Work Research\u003c/em\u003e, 1-14. \u003c/li\u003e\n\u003cli\u003eUyen, D. P., Nhu, N. T. H., Nghi, D. D., Khanh, V. H., Vy, H. T., Sa, N. T. H., \u0026amp; Vy, N. T. H. (2024). Optimal pedagogical strategies in research methodology: Insights from student experiences. \u003cem\u003eEnvironment and Social Psychology\u003c/em\u003e,\u003cem\u003e 9\u003c/em\u003e(4). \u003c/li\u003e\n\u003cli\u003eWagner, D., \u0026amp; Tamayo, C. (2024). Invisibilization and Intersectionality in Mathematics Education: A Panoramic View: Invisibiliza\u0026ccedil;\u0026atilde;o e Interseccionalidade na Educa\u0026ccedil;\u0026atilde;o Matem\u0026aacute;tica: Uma Vis\u0026atilde;o Panor\u0026acirc;mica. In \u003cem\u003eFourth International Handbook of Mathematics Education\u003c/em\u003e (pp. 379-411). Springer. \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Related rates of change, student perception, knowledge, calculus, learning outcomes, instructional strategies","lastPublishedDoi":"10.21203/rs.3.rs-6490660/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6490660/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates the relationship between students' perception and knowledge in learning related rates of change problems. Related rates of change are fundamental concepts in calculus, requiring students to grasp the dynamic nature of variables and their interdependencies. However, students' perception and knowledge regarding these problems can significantly determine their learning outcomes. The study is about relationship which is under correlational study (quantitative), incorporating surveys to gauge students' perceptions and knowledge tests to assess their performance. The findings illuminate the complex interplay between students' perceptions of related rates problems and their actual knowledge levels. Understanding this kinetics can inform instructional strategies and interventions aimed at improving students' comprehension and mastery of related rates concepts.\u003c/p\u003e","manuscriptTitle":"The Relationship between Student’s Perception and Knowledge in Learning Related Rates of Change Problems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-23 08:59:59","doi":"10.21203/rs.3.rs-6490660/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":"ae4d03c1-5bf7-4e79-86c5-65980f7d26ea","owner":[],"postedDate":"April 23rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":47416051,"name":"Social science/Education"},{"id":47416052,"name":"Social science/Science technology and society"}],"tags":[],"updatedAt":"2025-05-27T04:53:38+00:00","versionOfRecord":[],"versionCreatedAt":"2025-04-23 08:59:59","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6490660","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6490660","identity":"rs-6490660","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}