Effort, Mindset, and Motivation: Comparing Traditional and Machine Learning Regression Models in Predicting Math Performance

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Using secondary data from 4,552 students, five models—multiple regression, Random Forest, Gradient Boosting, XGBoost, and LightGBM—were evaluated for predictive accuracy and feature importance. The results demonstrate that machine learning models, particularly XGBoost, significantly outperform traditional regression, with XGBoost achieving the lowest Mean Squared Error (MSE = 7186.49) and the highest R-squared (0.1571). Effort emerged as the strongest predictor, followed by growth mindset, while motivation had a smaller but notable influence. These findings reinforce the applicability of Self-Regulation Theory and Growth Mindset Theory, highlighting the potential of machine learning to enhance educational research. Practical implications emphasize the importance of fostering effort and growth mindset through targeted interventions and leveraging predictive analytics for data-driven decision-making in education. Educational Psychology Cognitive Neuroscience Artificial Intelligence and Machine Learning mathematics performance machine learning predictive analytics Figures Figure 1 Introduction Mathematics proficiency stands as a cornerstone of academic and professional success, particularly in science, technology, engineering, and mathematics (STEM) fields (National Academy of Sciences, 2007 ). As students continue to face challenges in mastering mathematical concepts, understanding the factors that influence mathematics performance becomes increasingly crucial for developing effective educational interventions. Recent research has highlighted the significance of psychological constructs, specifically effort, mindset, and motivation, in shaping mathematics achievement (Murayama et al., 2013 ). The role of effort, characterized by persistence and determination in learning, has been established as fundamental to self-regulated learning and academic success (Zimmerman, 2002 ). Growth mindset—the belief that intelligence can be developed through effort and learning—has emerged as a significant factor in fostering academic resilience and persistence (Dweck, 2006 ). Additionally, motivation, encompassing both intrinsic drives like curiosity and extrinsic factors such as rewards, plays a crucial role in sustaining engagement with mathematical tasks (Deci & Ryan, 1985 ). Together, these psychological constructs provide a theoretical framework for examining the predictors of mathematics performance. While traditional regression models have historically been employed to investigate relationships among these variables, their ability to capture complex, non-linear interactions remains limited. The emergence of machine learning techniques, including Random Forest, Gradient Boosting, XGBoost, and LightGBM, offers promising alternatives for analyzing these relationships. These advanced approaches enhance predictive accuracy and also provide deeper insights into the relative importance of variables in determining mathematics performance (Breiman, 2001 ; Chen & Guestrin, 2016 ). This study bridges the gap between theoretical frameworks and advanced predictive modeling by examining how effort, mindset, and motivation contribute to mathematics achievement through both traditional and machine learning regression approaches. Our investigation serves two primary objectives: (1) to evaluate the relative contributions of effort, growth mindset, and motivation to mathematics performance, and (2) to compare the predictive accuracy of traditional regression models with advanced machine learning methods. Literature Review The challenge of improving mathematics performance continues to drive educational research, with increasing attention focused on psychological constructs such as effort, mindset, and motivation as key determinants of academic achievement (Murayama et al., 2013 ). Understanding these relationships requires both theoretical grounding and sophisticated analytical approaches to capture their complex interactions. Effort and Self-Regulation in Mathematics Learning Effort, characterized by sustained persistence and dedication, has emerged as a crucial predictor of academic success within the framework of Self-Regulation Theory (Zimmerman, 2002 ). Research by Pintrich and De Groot ( 1990 ) demonstrated that students with strong self-regulatory behaviors achieve superior academic outcomes. Building on this work, Duckworth et al. ( 2007 ) introduced the concept of grit, establishing significant correlations between long-term perseverance and mathematics achievement. However, evidence suggests that the relationship between effort and performance may be moderated by other psychological constructs in ways that traditional regression models struggle to capture (Murayama et al., 2013 ). Growth Mindset's Influence on Mathematical Achievement Growth Mindset Theory (Dweck, 2006 ) emphasizes how beliefs about intelligence malleability affect learning approaches. Blackwell, Trzesniewski, and Dweck ( 2007 ) found that students with growth mindsets demonstrated sustained improvement in mathematics grades compared to those with fixed mindsets. More recently, Yeager et al. (2019) showed that mindset interventions enhanced persistence in challenging tasks, leading to improved mathematics performance. However, meta-analyses by Sisk et al. ( 2018 ) suggest that mindset intervention effects are context-dependent, highlighting the need for more sophisticated modeling approaches to understand these complex interactions. Motivation's Multidimensional Role The Expectancy-Value Theory (Wigfield & Eccles, 2000 ) frames motivation as a function of success expectations and task value. Deci and Ryan ( 1985 ) established that intrinsic motivation more strongly predicts academic success than extrinsic motivation, particularly in mathematics. Further research by Murayama, Pekrun, and Lichtenfeld (2013) revealed that while intrinsic motivation directly influences mathematics achievement, extrinsic motivation's effects are mediated through effort. Limitations of Traditional Regression Approaches While traditional regression models have contributed substantially to our understanding of mathematics performance predictors (Hattie, 2009 ; Fan & Chen, 2001), their reliance on linearity and independence assumptions limits their ability to capture complex interactions and non-linear relationships (Breiman, 2001 ). These limitations particularly affect our understanding of how mindset, effort, and motivation interact synergistically. Machine Learning Advancements in Educational Research Recent machine learning applications have demonstrated promising results in educational research. Xu and Jaggars ( 2013 ) successfully employed Random Forest for predicting student retention, while Jordan et al. (2020) used Gradient Boosting to identify STEM success predictors. Notably, Guo et al. ( 2022 ) demonstrated XGBoost's superior performance over traditional regression in predicting academic outcomes through its ability to capture non-linear interactions. Despite these advances, several research gaps persist. First, existing research often examines effort, mindset, and motivation in isolation, overlooking their combined effects. Second, traditional regression approaches continue to dominate despite their limitations in capturing complex relationships. Third, while machine learning shows promise in educational research, its application to psychological predictors of mathematics performance remains limited. Finally, few studies have directly compared traditional regression and machine learning approaches in this context. This study addresses these gaps by integrating psychological theories with machine learning techniques to investigate mathematics performance predictors. Through comparative analysis of traditional and machine learning approaches, we aim to provide new insights into the complex relationships among effort, mindset, motivation, and mathematics achievement, ultimately informing the design of more effective educational interventions. Conceptual framework Our conceptual framework synthesizes three foundational theories to explain the complex relationships between students' mindset, effort, motivation, and mathematics performance. This integration provides a theoretical basis for understanding both direct and mediated pathways to mathematical achievement, while considering the analytical capabilities of traditional and machine learning approaches in modeling these relationships. At the framework's core, Self-Regulation Theory (Zimmerman, 2002 ) positions effort as a central mechanism through which students monitor and control their learning processes. This self-regulatory component serves as a critical mediator, translating students' mindsets and motivational states into observable mathematics performance. The framework incorporates Growth Mindset Theory (Dweck, 2006 ), which posits that students' beliefs about the malleability of their abilities significantly influence their approach to mathematical challenges. This theoretical component explains how students' mindsets shape their willingness to invest sustained effort in mathematical tasks, particularly when faced with difficulties. The framework further draws on Expectancy-Value Theory (Wigfield & Eccles, 2000 ) to conceptualize motivation as a function of success expectations and task valuation. This theoretical element explains how students' motivational orientations, whether intrinsically or extrinsically driven, contribute to their persistence in mathematical tasks and, consequently, their performance outcomes. The proposed relationships among these constructs suggest both direct and indirect pathways to mathematics performance. Growth mindset is hypothesized to influence performance through two routes: a direct pathway and an indirect pathway mediated by effort. Motivation is conceptualized as having both a direct effect on performance and a moderating effect on the relationship between effort and achievement. This moderation suggests that the impact of effort on performance may be amplified under conditions of high motivation. From an analytical perspective, the framework acknowledges the differential capabilities of traditional regression and machine learning approaches in capturing these relationships. While traditional regression models may adequately capture linear relationships, machine learning approaches offer the potential to identify more complex, non-linear interactions, particularly in understanding how motivation might amplify the effects of effort on performance. This integrated framework makes several contributions to educational research and practice. First, it provides a theoretical foundation for investigating the collective influence of mindset, effort, and motivation on mathematics performance. Second, it offers a basis for comparing the explanatory power of different analytical approaches in modeling these relationships. Finally, it identifies potentially actionable factors that could inform the design of educational interventions aimed at improving mathematics performance. The framework suggests that effective educational interventions might focus on fostering growth mindset and supporting sustained effort, while recognizing the important role of motivation in mathematical achievement. This theoretical integration provides a foundation for future empirical work examining how these factors interact to influence mathematics performance and how different analytical approaches might best capture these complex relationships. Method Research Questions and Design This study investigated two primary research questions: 1. How do effort, mindset, and motivation contribute to the prediction of mathematics performance across traditional and machine learning regression models? and 2. Which regression model—traditional or machine learning—provides the most accurate predictions of mathematics performance based on effort, mindset, and motivation? To address these questions, we employed a quantitative research design that enabled a comparative analysis of traditional and machine learning regression approaches in predicting mathematics performance. Sample and Data Collection The study utilized secondary data from PISA 2022 Student Questionnaire Database, comprising responses from 4,552 students across various U.S. schools. The sample included students ranging from ages 15 to 17, with demographic variables encompassing gender, socioeconomic status, and language of assessment. All data were obtained from publicly available sources and anonymized datasets, ensuring adherence to ethical research standards. Variables and Measurement The analysis incorporated three predictor variables: effort, growth mindset, and motivation. Effort was measured using the "Effort and Persistence in Math" scale, while growth mindset was assessed through the "Growth Mindset WLE" measure. Motivation was operationalized through responses indicating interest or motivation related to mathematics tasks. The outcome variable, mathematics performance, was measured using students' mean scores in mathematics (PV_Math_Mean – mean of all plausible values in Math scores 1–10). Analytical Approach Our analysis employed a comparative modeling strategy utilizing both traditional and machine learning regression techniques. Initial analysis began with descriptive statistics to examine means, standard deviations, and correlations among study variables. For the traditional approach, we implemented multiple linear regression to evaluate linear relationships between predictors and mathematics performance. The machine learning component of our analysis incorporated four distinct models: Random Forest, Gradient Boosting, XGBoost, and LightGBM. The Random Forest model was selected for its capability to capture non-linear relationships through tree-based ensemble learning. Gradient Boosting and its enhanced variants, XGBoost and LightGBM, were chosen for their iterative optimization approaches and ability to handle complex patterns in the data. Model Evaluation and Comparison To evaluate model performance, we employed multiple metrics including Mean Squared Error (MSE) and R-squared values. Feature importance scores were calculated to identify the relative contribution of each predictor across models. All analyses were conducted using Python, leveraging scikit-learn for regression and machine learning models, pandas for data preprocessing, and seaborn and matplotlib for visualization. Also, we implemented an 80 − 20 train-test split for machine learning models to assess performance on unseen data. For the traditional regression approach, we verified standard assumptions including linearity, independence, and normality of residuals through diagnostic plots. Two primary hypotheses guided our analysis: (H1) Growth mindset, effort, and motivation significantly predict mathematics performance, and (H2) Machine learning models would demonstrate superior predictive accuracy compared to traditional regression approaches. The comparative analysis framework enabled us to evaluate both the predictive accuracy of different modeling approaches and the relative importance of effort, mindset, and motivation in explaining mathematics performance. This methodological approach provides a comprehensive examination of how different analytical techniques might capture the complexity of factors influencing mathematical achievement. Results The analysis revealed substantial differences in predictive performance across traditional regression and machine learning approaches. We present these findings through model-specific performance metrics and feature importance analyses. Traditional Multiple Regression Analysis The multiple linear regression model demonstrated limited explanatory power, accounting for only 2.7% of the variance in mathematics performance (R² = .027, MSE = 8296.29). Analysis of standardized coefficients revealed unexpected patterns: effort showed a negative association with performance (β = -0.400), while growth mindset demonstrated a weak negative relationship (β = -0.143) that did not reach statistical significance. Motivation exhibited a small positive association (β = 0.749), though this relationship was also not statistically significant. Machine Learning Model Performance Among the machine learning approaches, model performance varied considerably. The Random Forest model showed the poorest performance, with a negative R-squared value (R² = -0.0714, MSE = 9135.17), indicating performance below that of a simple mean prediction model. However, the gradient boosting approaches demonstrated markedly better predictive capability. The Gradient Boosting model explained 14.94% of the variance in mathematics performance (R² = .1494, MSE = 7252.17), with XGBoost emerging as the strongest performer, accounting for 15.71% of the variance (R² = .1571, MSE = 7186.49). LightGBM showed comparable performance, explaining 15.39% of the variance (R² = .1539, MSE = 7214.28). Table 1.0 Model Mean Squared Error (MSE) R-squared Feature Importance (%) Multiple Regression 8296.29 .027 Effort: -0.400ᵃ Growth Mindset: -0.143ᵃ Motivation: 0.749ᵃ Random Forest 9135.17 − .0714 Effort: 76.72 Growth Mindset: 21.32 Motivation: 1.96 Gradient Boosting 7252.17 .1494 Effort: 58.87 Growth Mindset: 39.28 Motivation: 1.85 XGBoost 7186.49 .1571 Effort: 41.29 Growth Mindset: 40.98 Motivation: 17.73 LightGBM 7214.28 .1539 Effort: 46.94 Growth Mindset: 39.94 Motivation: 13.12 Note: We want our readers to understand that feature importance values represent the relative contribution of each predictor to model performance. ᵃStandardized beta coefficients are reported for Multiple Regression instead of feature importance percentages. Feature Importance Analysis Feature importance patterns varied across models, revealing interesting insights into predictor contributions. In the Random Forest model, effort dominated the prediction (76.72%), with growth mindset contributing substantially less (21.32%) and motivation showing minimal importance (1.96%). The Gradient Boosting model showed a more balanced distribution between effort (58.87%) and growth mindset (39.28%), though motivation remained a minor contributor (1.85%). XGBoost, the best-performing model, demonstrated the most balanced distribution of feature importance, with effort (41.29%) and growth mindset (40.98%) contributing almost equally, and motivation showing increased importance (17.73%) compared to other models. LightGBM showed a similar pattern, with effort (46.94%) maintaining the highest importance, followed by growth mindset (39.94%) and motivation (13.12%). Model Comparison Summary The comparative analysis revealed several key findings. First, machine learning approaches, particularly XGBoost and LightGBM, demonstrated superior predictive performance compared to traditional regression, suggesting the presence of complex, non-linear relationships among the variables. Second, while effort consistently emerged as the strongest predictor across models, the more sophisticated machine learning approaches revealed a more nuanced interplay among predictors, particularly in the balanced contributions of effort and growth mindset. The superior performance of XGBoost (MSE = 7186.49, R² = .1571) compared to other models suggests that this approach may better capture the complex relationships between psychological constructs and mathematics performance. These findings highlight the potential advantages of machine learning approaches in educational research, particularly when modeling complex psychological and academic outcomes. Discussion This study investigated how effort, growth mindset, and motivation predict mathematics performance through comparative analysis of traditional and machine learning regression models. Our findings reveal several important insights about the relative importance of these predictors and the effectiveness of different modeling approaches in capturing their relationships with mathematical achievement. The consistent emergence of effort as the strongest predictor across all models aligns with Self-Regulation Theory (Zimmerman, 2002 ), underscoring the critical role of sustained engagement in mathematical learning. Effort demonstrated the highest feature importance in Random Forest (76.72%), Gradient Boosting (58.87%), and XGBoost (41.29%) models, suggesting that students' persistence and self-regulatory behaviors are fundamental to their mathematical success. Growth mindset emerged as a substantial predictor in machine learning models, particularly in XGBoost (40.98%) and LightGBM (39.94%). This finding supports Growth Mindset Theory (Dweck, 2006 ), indicating that students' beliefs about the malleability of their abilities significantly influence their mathematics performance. Notably, traditional regression failed to capture this relationship effectively, showing a weak and statistically insignificant association. This discrepancy suggests that the relationship between growth mindset and performance may be more complex and non-linear than traditional regression can adequately model. Motivation demonstrated a relatively smaller but meaningful contribution to mathematics performance, with its highest importance observed in XGBoost (17.73%). This aligns with Expectancy-Value Theory (Wigfield & Eccles, 2000 ), suggesting that while motivation influences performance, its effects may be mediated by other factors such as effort and mindset. The machine learning models' ability to capture these nuanced relationships provides important insights into how motivational factors interact with other predictors to influence mathematical achievement. The superior performance of machine learning models, particularly XGBoost (R² = .1571, MSE = 7186.49), compared to traditional regression (R² = .027) demonstrates the advantage of these approaches in capturing complex educational relationships. This finding suggests that the interactions between psychological constructs and academic performance are more sophisticated than linear models can effectively represent. These results have important implications for educational practice. The strong influence of effort and growth mindset suggests that interventions should focus on fostering these qualities through strategies such as goal setting, self-monitoring, and targeted mindset development programs. Additionally, the effectiveness of machine learning models suggests their potential utility in educational analytics for predicting student outcomes and identifying at-risk students. Several limitations warrant consideration. The study's predictor set was limited to three variables, excluding potentially important factors such as socioeconomic status, mathematics anxiety, and teacher quality. Furthermore, the use of data from a single country may limit generalizability across different educational contexts. While machine learning models demonstrated superior predictive accuracy, their complexity can present challenges for interpretation, suggesting the need for future research incorporating explainable AI techniques. This study advances our understanding of how psychological factors influence mathematics performance while highlighting the potential of machine learning approaches in educational research. Future investigations should expand the predictor set, explore cross-cultural generalizability, and develop more interpretable machine learning models to better inform educational practice and policy. Conclusion Our investigation into the predictive relationships between psychological factors and mathematics performance yields several significant conclusions and practical implications for educational stakeholders. The study demonstrates that effort, growth mindset, and motivation substantially influence mathematics performance, with effort emerging as the most robust predictor across analytical approaches. The superior performance of machine learning models, particularly XGBoost, compared to traditional regression highlights the complex, non-linear nature of these relationships and suggests the need for more sophisticated analytical approaches in educational research. These findings, grounded in Self-Regulation Theory and Growth Mindset Theory, emphasize the critical importance of fostering self-regulatory behaviors and adaptive beliefs in mathematics education. The results suggest that successful mathematical achievement is not solely determined by inherent ability but is significantly influenced by malleable factors that can be developed through targeted interventions. Based on these findings, we propose several key recommendations for educational stakeholders. For educators, implementing strategies that cultivate effort and persistence, such as structured goal-setting programs and regular feedback mechanisms, should be prioritized. Additionally, fostering a growth mindset through classroom practices that emphasize the malleability of intelligence and the value of challenge in learning is crucial. Policymakers should consider investing in teacher training programs that focus on promoting self-regulated learning and adaptive belief systems in mathematics education. Furthermore, the development of data-driven policies that utilize predictive analytics could enhance the identification of at-risk students and improve resource allocation. For researchers, future investigations should expand the predictor set to include variables such as mathematics anxiety, socioeconomic status, and instructional quality to enhance model explanatory power. Cross-cultural validation studies would help establish the generalizability of these findings across diverse educational contexts. Educational institutions should consider integrating machine learning models into their academic analytics platforms to enable more personalized student support systems. These predictive insights could inform the design of targeted interventions, particularly for students demonstrating lower levels of effort and growth mindset. In conclusion, this study advances our understanding of the complex relationships between psychological factors and mathematics performance while highlighting the potential of machine learning approaches in educational research. By leveraging these insights, educators and policymakers can develop more effective strategies to support student success in mathematics education. References Blackwell L, Trzesniewski K, Dweck CS (2007) Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Dev 78(1):246–263. https://doi.org/10.1111/j.1467-8624.2007.00995.x Breiman L (2001) Random forests. Mach Learn 45(1):5–32. https://doi.org/10.1023/A:1010933404324 Chen T, Guestrin C (2016) XGBoost: A scalable tree boosting system. Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining , 785–794. https://doi.org/10.1145/2939672.2939785 Deci EL, Ryan RM (1985) Intrinsic motivation and self-determination in human behavior. Springer Duckworth AL, Peterson C, Matthews MD, Kelly DR (2007) Grit: Perseverance and passion for long-term goals. J Personal Soc Psychol 92(6):1087–1101. https://doi.org/10.1037/0022-3514.92.6.1087 Dweck CS (2006) Mindset: The new psychology of success. Random House Guo Y, Liu X, Zhang J (2022) Machine learning models for predicting student performance: A systematic review. Educational Data Min 14(2):15–32 Hattie J (2009) Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge Murayama K, Pekrun R, Lichtenfeld S, vom Hofe R (2013) Predicting long-term growth in students’ mathematics achievement: The unique contributions of motivation and cognitive strategies. Child Dev 84(4):1475–1490. https://doi.org/10.1111/cdev.12036 National Academy of Sciences (2007) Rising above the gathering storm: Energizing and employing America for a brighter economic future. National Academies Pintrich PR, De Groot EV (1990) Motivational and self-regulated learning components of classroom academic performance. J Educ Psychol 82(1):33–40. https://doi.org/10.1037/0022-0663.82.1.33 Sisk VF, Burgoyne AP, Sun J, Butler JL, Macnamara BN (2018) To what extent and under which circumstances are growth mind-sets important to academic achievement? Two meta-analyses. Psychol Sci 29(4):549–571. https://doi.org/10.1177/0956797617739704 Wigfield A, Eccles JS (2000) Expectancy-value theory of achievement motivation. Contemp Educ Psychol 25(1):68–81. https://doi.org/10.1006/ceps.1999.1015 Xu D, Jaggars SS (2013) The impact of online learning on academic performance: Evidence from a large community college system. Econ Educ Rev 37:46–57. https://doi.org/10.1016/j.econedurev.2013.08.001 Zimmerman BJ (2002) Becoming a self-regulated learner: An overview. Theory into Pract 41(2):64–70. https://doi.org/10.1207/s15430421tip4102_2 Additional Declarations The authors declare no competing interests. Supplementary Files MultipleRegressionCode.docx 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-5744169","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":396303759,"identity":"536273b0-3429-4c94-a688-bb6879a27460","order_by":0,"name":"Adedayo Olatunde Afolabi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAu0lEQVRIiWNgGAWjYFCCBAYJBhsGGX4Ij5lYLWkMPJJtzKRqMThGrBb+9uSDN34k2PAY3+8/JsFQYZ3YQEiLxJlnyZY9CWk8ZseY2SQYzqQT1sJwI8dMgvfHYYgWxrbDhLXI38j/Jvkn4TCPcRtIyz8itBjcyGGT5gFqMWADaWkgQovhmWfG1jJAv0gcSza2SDiWbkxQi9zx5Ic33yTYyPE3H3x440ONtSxBLagggTTlo2AUjIJRMApwAQDO8zksWslCPgAAAABJRU5ErkJggg==","orcid":"","institution":"Texas Tech University","correspondingAuthor":true,"prefix":"","firstName":"Adedayo","middleName":"Olatunde","lastName":"Afolabi","suffix":""},{"id":396303760,"identity":"bc781fab-1b23-4119-a081-5016fd339c90","order_by":1,"name":"Oluwatosin Damilola Daramola","email":"","orcid":"","institution":"Responsive Education Solutions","correspondingAuthor":false,"prefix":"","firstName":"Oluwatosin","middleName":"Damilola","lastName":"Daramola","suffix":""}],"badges":[],"createdAt":"2025-01-01 02:01:47","currentVersionCode":1,"declarations":{"humanSubjects":true,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":true,"humanSubjectConsent":true,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-5744169/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5744169/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":72866100,"identity":"3bcf76df-c9ec-4007-b52a-0aa1e68ca0af","added_by":"auto","created_at":"2025-01-03 05:42:05","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":82525,"visible":true,"origin":"","legend":"\u003cp\u003eUnnumbered image in the Conceptual framework section.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5744169/v1/78195261f7c4fa4e51965f9a.png"},{"id":72866423,"identity":"82646ab5-28c7-4040-8596-bdb3bd760dfe","added_by":"auto","created_at":"2025-01-03 05:58:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":377211,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5744169/v1/10ccf785-d114-48a1-b9ae-70a2c53acc4f.pdf"},{"id":72866101,"identity":"b7a630ae-d56f-4648-b2ea-5b7da97a03f9","added_by":"auto","created_at":"2025-01-03 05:42:05","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":16238,"visible":true,"origin":"","legend":"","description":"","filename":"MultipleRegressionCode.docx","url":"https://assets-eu.researchsquare.com/files/rs-5744169/v1/f1d72990a2017673fedf1566.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eEffort, Mindset, and Motivation: Comparing Traditional and Machine Learning Regression Models in Predicting Math Performance\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eMathematics proficiency stands as a cornerstone of academic and professional success, particularly in science, technology, engineering, and mathematics (STEM) fields (National Academy of Sciences, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). As students continue to face challenges in mastering mathematical concepts, understanding the factors that influence mathematics performance becomes increasingly crucial for developing effective educational interventions. Recent research has highlighted the significance of psychological constructs, specifically effort, mindset, and motivation, in shaping mathematics achievement (Murayama et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe role of effort, characterized by persistence and determination in learning, has been established as fundamental to self-regulated learning and academic success (Zimmerman, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Growth mindset\u0026mdash;the belief that intelligence can be developed through effort and learning\u0026mdash;has emerged as a significant factor in fostering academic resilience and persistence (Dweck, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Additionally, motivation, encompassing both intrinsic drives like curiosity and extrinsic factors such as rewards, plays a crucial role in sustaining engagement with mathematical tasks (Deci \u0026amp; Ryan, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1985\u003c/span\u003e). Together, these psychological constructs provide a theoretical framework for examining the predictors of mathematics performance.\u003c/p\u003e \u003cp\u003eWhile traditional regression models have historically been employed to investigate relationships among these variables, their ability to capture complex, non-linear interactions remains limited. The emergence of machine learning techniques, including Random Forest, Gradient Boosting, XGBoost, and LightGBM, offers promising alternatives for analyzing these relationships. These advanced approaches enhance predictive accuracy and also provide deeper insights into the relative importance of variables in determining mathematics performance (Breiman, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Chen \u0026amp; Guestrin, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2016\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis study bridges the gap between theoretical frameworks and advanced predictive modeling by examining how effort, mindset, and motivation contribute to mathematics achievement through both traditional and machine learning regression approaches. Our investigation serves two primary objectives: (1) to evaluate the relative contributions of effort, growth mindset, and motivation to mathematics performance, and (2) to compare the predictive accuracy of traditional regression models with advanced machine learning methods.\u003c/p\u003e"},{"header":"Literature Review","content":"\u003cp\u003eThe challenge of improving mathematics performance continues to drive educational research, with increasing attention focused on psychological constructs such as effort, mindset, and motivation as key determinants of academic achievement (Murayama et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). Understanding these relationships requires both theoretical grounding and sophisticated analytical approaches to capture their complex interactions.\u003c/p\u003e \u003cp\u003eEffort and Self-Regulation in Mathematics Learning\u003c/p\u003e \u003cp\u003eEffort, characterized by sustained persistence and dedication, has emerged as a crucial predictor of academic success within the framework of Self-Regulation Theory (Zimmerman, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). Research by Pintrich and De Groot (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1990\u003c/span\u003e) demonstrated that students with strong self-regulatory behaviors achieve superior academic outcomes. Building on this work, Duckworth et al. (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) introduced the concept of grit, establishing significant correlations between long-term perseverance and mathematics achievement. However, evidence suggests that the relationship between effort and performance may be moderated by other psychological constructs in ways that traditional regression models struggle to capture (Murayama et al., \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eGrowth Mindset's Influence on Mathematical Achievement\u003c/p\u003e \u003cp\u003eGrowth Mindset Theory (Dweck, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) emphasizes how beliefs about intelligence malleability affect learning approaches. Blackwell, Trzesniewski, and Dweck (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) found that students with growth mindsets demonstrated sustained improvement in mathematics grades compared to those with fixed mindsets. More recently, Yeager et al. (2019) showed that mindset interventions enhanced persistence in challenging tasks, leading to improved mathematics performance. However, meta-analyses by Sisk et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) suggest that mindset intervention effects are context-dependent, highlighting the need for more sophisticated modeling approaches to understand these complex interactions.\u003c/p\u003e \u003cp\u003eMotivation's Multidimensional Role\u003c/p\u003e \u003cp\u003eThe Expectancy-Value Theory (Wigfield \u0026amp; Eccles, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) frames motivation as a function of success expectations and task value. Deci and Ryan (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1985\u003c/span\u003e) established that intrinsic motivation more strongly predicts academic success than extrinsic motivation, particularly in mathematics. Further research by Murayama, Pekrun, and Lichtenfeld (2013) revealed that while intrinsic motivation directly influences mathematics achievement, extrinsic motivation's effects are mediated through effort.\u003c/p\u003e \u003cp\u003eLimitations of Traditional Regression Approaches\u003c/p\u003e \u003cp\u003eWhile traditional regression models have contributed substantially to our understanding of mathematics performance predictors (Hattie, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Fan \u0026amp; Chen, 2001), their reliance on linearity and independence assumptions limits their ability to capture complex interactions and non-linear relationships (Breiman, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). These limitations particularly affect our understanding of how mindset, effort, and motivation interact synergistically.\u003c/p\u003e \u003cp\u003eMachine Learning Advancements in Educational Research\u003c/p\u003e \u003cp\u003eRecent machine learning applications have demonstrated promising results in educational research. Xu and Jaggars (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) successfully employed Random Forest for predicting student retention, while Jordan et al. (2020) used Gradient Boosting to identify STEM success predictors. Notably, Guo et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) demonstrated XGBoost's superior performance over traditional regression in predicting academic outcomes through its ability to capture non-linear interactions.\u003c/p\u003e \u003cp\u003eDespite these advances, several research gaps persist. First, existing research often examines effort, mindset, and motivation in isolation, overlooking their combined effects. Second, traditional regression approaches continue to dominate despite their limitations in capturing complex relationships. Third, while machine learning shows promise in educational research, its application to psychological predictors of mathematics performance remains limited. Finally, few studies have directly compared traditional regression and machine learning approaches in this context.\u003c/p\u003e \u003cp\u003eThis study addresses these gaps by integrating psychological theories with machine learning techniques to investigate mathematics performance predictors. Through comparative analysis of traditional and machine learning approaches, we aim to provide new insights into the complex relationships among effort, mindset, motivation, and mathematics achievement, ultimately informing the design of more effective educational interventions.\u003c/p\u003e "},{"header":"Conceptual framework","content":"\u003cp\u003eOur conceptual framework synthesizes three foundational theories to explain the complex relationships between students' mindset, effort, motivation, and mathematics performance. This integration provides a theoretical basis for understanding both direct and mediated pathways to mathematical achievement, while considering the analytical capabilities of traditional and machine learning approaches in modeling these relationships.\u003c/p\u003e\u003cp\u003eAt the framework's core, Self-Regulation Theory (Zimmerman, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2002\u003c/span\u003e) positions effort as a central mechanism through which students monitor and control their learning processes. This self-regulatory component serves as a critical mediator, translating students' mindsets and motivational states into observable mathematics performance. The framework incorporates Growth Mindset Theory (Dweck, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), which posits that students' beliefs about the malleability of their abilities significantly influence their approach to mathematical challenges. This theoretical component explains how students' mindsets shape their willingness to invest sustained effort in mathematical tasks, particularly when faced with difficulties.\u003c/p\u003e\u003cp\u003eThe framework further draws on Expectancy-Value Theory (Wigfield \u0026amp; Eccles, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) to conceptualize motivation as a function of success expectations and task valuation. This theoretical element explains how students' motivational orientations, whether intrinsically or extrinsically driven, contribute to their persistence in mathematical tasks and, consequently, their performance outcomes.\u003c/p\u003e\u003cp\u003eThe proposed relationships among these constructs suggest both direct and indirect pathways to mathematics performance. Growth mindset is hypothesized to influence performance through two routes: a direct pathway and an indirect pathway mediated by effort. Motivation is conceptualized as having both a direct effect on performance and a moderating effect on the relationship between effort and achievement. This moderation suggests that the impact of effort on performance may be amplified under conditions of high motivation.\u003c/p\u003e\u003cp\u003e \u003c/p\u003e\u003cp\u003eFrom an analytical perspective, the framework acknowledges the differential capabilities of traditional regression and machine learning approaches in capturing these relationships. While traditional regression models may adequately capture linear relationships, machine learning approaches offer the potential to identify more complex, non-linear interactions, particularly in understanding how motivation might amplify the effects of effort on performance.\u003c/p\u003e\u003cp\u003eThis integrated framework makes several contributions to educational research and practice. First, it provides a theoretical foundation for investigating the collective influence of mindset, effort, and motivation on mathematics performance. Second, it offers a basis for comparing the explanatory power of different analytical approaches in modeling these relationships. Finally, it identifies potentially actionable factors that could inform the design of educational interventions aimed at improving mathematics performance.\u003c/p\u003e\u003cp\u003eThe framework suggests that effective educational interventions might focus on fostering growth mindset and supporting sustained effort, while recognizing the important role of motivation in mathematical achievement. This theoretical integration provides a foundation for future empirical work examining how these factors interact to influence mathematics performance and how different analytical approaches might best capture these complex relationships.\u003c/p\u003e"},{"header":"Method","content":"\u003cp\u003eResearch Questions and Design\u003c/p\u003e \u003cp\u003eThis study investigated two primary research questions: 1. How do effort, mindset, and motivation contribute to the prediction of mathematics performance across traditional and machine learning regression models? and 2. Which regression model\u0026mdash;traditional or machine learning\u0026mdash;provides the most accurate predictions of mathematics performance based on effort, mindset, and motivation? To address these questions, we employed a quantitative research design that enabled a comparative analysis of traditional and machine learning regression approaches in predicting mathematics performance.\u003c/p\u003e \u003cp\u003eSample and Data Collection\u003c/p\u003e \u003cp\u003eThe study utilized secondary data from PISA 2022 Student Questionnaire Database, comprising responses from 4,552 students across various U.S. schools. The sample included students ranging from ages 15 to 17, with demographic variables encompassing gender, socioeconomic status, and language of assessment. All data were obtained from publicly available sources and anonymized datasets, ensuring adherence to ethical research standards.\u003c/p\u003e \u003cp\u003eVariables and Measurement\u003c/p\u003e \u003cp\u003eThe analysis incorporated three predictor variables: effort, growth mindset, and motivation. Effort was measured using the \"Effort and Persistence in Math\" scale, while growth mindset was assessed through the \"Growth Mindset WLE\" measure. Motivation was operationalized through responses indicating interest or motivation related to mathematics tasks. The outcome variable, mathematics performance, was measured using students' mean scores in mathematics (PV_Math_Mean \u0026ndash; mean of all plausible values in Math scores 1\u0026ndash;10).\u003c/p\u003e \u003cp\u003eAnalytical Approach\u003c/p\u003e \u003cp\u003eOur analysis employed a comparative modeling strategy utilizing both traditional and machine learning regression techniques. Initial analysis began with descriptive statistics to examine means, standard deviations, and correlations among study variables. For the traditional approach, we implemented multiple linear regression to evaluate linear relationships between predictors and mathematics performance.\u003c/p\u003e \u003cp\u003eThe machine learning component of our analysis incorporated four distinct models: Random Forest, Gradient Boosting, XGBoost, and LightGBM. The Random Forest model was selected for its capability to capture non-linear relationships through tree-based ensemble learning. Gradient Boosting and its enhanced variants, XGBoost and LightGBM, were chosen for their iterative optimization approaches and ability to handle complex patterns in the data.\u003c/p\u003e \u003cp\u003eModel Evaluation and Comparison\u003c/p\u003e \u003cp\u003eTo evaluate model performance, we employed multiple metrics including Mean Squared Error (MSE) and R-squared values. Feature importance scores were calculated to identify the relative contribution of each predictor across models. All analyses were conducted using Python, leveraging scikit-learn for regression and machine learning models, pandas for data preprocessing, and seaborn and matplotlib for visualization. Also, we implemented an 80\u0026thinsp;\u0026minus;\u0026thinsp;20 train-test split for machine learning models to assess performance on unseen data. For the traditional regression approach, we verified standard assumptions including linearity, independence, and normality of residuals through diagnostic plots.\u003c/p\u003e \u003cp\u003eTwo primary hypotheses guided our analysis: (H1) Growth mindset, effort, and motivation significantly predict mathematics performance, and (H2) Machine learning models would demonstrate superior predictive accuracy compared to traditional regression approaches.\u003c/p\u003e \u003cp\u003eThe comparative analysis framework enabled us to evaluate both the predictive accuracy of different modeling approaches and the relative importance of effort, mindset, and motivation in explaining mathematics performance. This methodological approach provides a comprehensive examination of how different analytical techniques might capture the complexity of factors influencing mathematical achievement.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eThe analysis revealed substantial differences in predictive performance across traditional regression and machine learning approaches. We present these findings through model-specific performance metrics and feature importance analyses.\u003c/p\u003e \u003cp\u003eTraditional Multiple Regression Analysis\u003c/p\u003e \u003cp\u003eThe multiple linear regression model demonstrated limited explanatory power, accounting for only 2.7% of the variance in mathematics performance (R\u0026sup2; = .027, MSE\u0026thinsp;=\u0026thinsp;8296.29). Analysis of standardized coefficients revealed unexpected patterns: effort showed a negative association with performance (β = -0.400), while growth mindset demonstrated a weak negative relationship (β = -0.143) that did not reach statistical significance. Motivation exhibited a small positive association (β\u0026thinsp;=\u0026thinsp;0.749), though this relationship was also not statistically significant.\u003c/p\u003e \u003cp\u003eMachine Learning Model Performance\u003c/p\u003e \u003cp\u003eAmong the machine learning approaches, model performance varied considerably. The Random Forest model showed the poorest performance, with a negative R-squared value (R\u0026sup2; = -0.0714, MSE\u0026thinsp;=\u0026thinsp;9135.17), indicating performance below that of a simple mean prediction model. However, the gradient boosting approaches demonstrated markedly better predictive capability.\u003c/p\u003e \u003cp\u003eThe Gradient Boosting model explained 14.94% of the variance in mathematics performance (R\u0026sup2; = .1494, MSE\u0026thinsp;=\u0026thinsp;7252.17), with XGBoost emerging as the strongest performer, accounting for 15.71% of the variance (R\u0026sup2; = .1571, MSE\u0026thinsp;=\u0026thinsp;7186.49). LightGBM showed comparable performance, explaining 15.39% of the variance (R\u0026sup2; = .1539, MSE\u0026thinsp;=\u0026thinsp;7214.28).\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 1.0\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e\u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMean Squared Error (MSE)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR-squared\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFeature Importance (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMultiple Regression\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8296.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.027\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEffort: -0.400ᵃ\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eGrowth Mindset: -0.143ᵃ\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eMotivation: 0.749ᵃ\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRandom Forest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e9135.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;.0714\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEffort: 76.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eGrowth Mindset: 21.32\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eMotivation: 1.96\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGradient Boosting\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7252.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.1494\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEffort: 58.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eGrowth Mindset: 39.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eMotivation: 1.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eXGBoost\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7186.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.1571\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEffort: 41.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eGrowth Mindset: 40.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eMotivation: 17.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLightGBM\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7214.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.1539\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eEffort: 46.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eGrowth Mindset: 39.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\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=\"left\" colname=\"c4\"\u003e \u003cp\u003eMotivation: 13.12\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 \u003cem\u003eNote: We want our readers to understand that feature importance values represent the relative contribution of each predictor to model performance. ᵃStandardized beta coefficients are reported for Multiple Regression instead of feature importance percentages.\u003c/em\u003e \u003c/p\u003e \u003cp\u003eFeature Importance Analysis\u003c/p\u003e \u003cp\u003eFeature importance patterns varied across models, revealing interesting insights into predictor contributions. In the Random Forest model, effort dominated the prediction (76.72%), with growth mindset contributing substantially less (21.32%) and motivation showing minimal importance (1.96%). The Gradient Boosting model showed a more balanced distribution between effort (58.87%) and growth mindset (39.28%), though motivation remained a minor contributor (1.85%).\u003c/p\u003e \u003cp\u003eXGBoost, the best-performing model, demonstrated the most balanced distribution of feature importance, with effort (41.29%) and growth mindset (40.98%) contributing almost equally, and motivation showing increased importance (17.73%) compared to other models. LightGBM showed a similar pattern, with effort (46.94%) maintaining the highest importance, followed by growth mindset (39.94%) and motivation (13.12%).\u003c/p\u003e \u003cp\u003eModel Comparison Summary\u003c/p\u003e \u003cp\u003eThe comparative analysis revealed several key findings. First, machine learning approaches, particularly XGBoost and LightGBM, demonstrated superior predictive performance compared to traditional regression, suggesting the presence of complex, non-linear relationships among the variables. Second, while effort consistently emerged as the strongest predictor across models, the more sophisticated machine learning approaches revealed a more nuanced interplay among predictors, particularly in the balanced contributions of effort and growth mindset.\u003c/p\u003e \u003cp\u003eThe superior performance of XGBoost (MSE\u0026thinsp;=\u0026thinsp;7186.49, R\u0026sup2; = .1571) compared to other models suggests that this approach may better capture the complex relationships between psychological constructs and mathematics performance. These findings highlight the potential advantages of machine learning approaches in educational research, particularly when modeling complex psychological and academic outcomes.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study investigated how effort, growth mindset, and motivation predict mathematics performance through comparative analysis of traditional and machine learning regression models. Our findings reveal several important insights about the relative importance of these predictors and the effectiveness of different modeling approaches in capturing their relationships with mathematical achievement.\u003c/p\u003e \u003cp\u003eThe consistent emergence of effort as the strongest predictor across all models aligns with Self-Regulation Theory (Zimmerman, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2002\u003c/span\u003e), underscoring the critical role of sustained engagement in mathematical learning. Effort demonstrated the highest feature importance in Random Forest (76.72%), Gradient Boosting (58.87%), and XGBoost (41.29%) models, suggesting that students' persistence and self-regulatory behaviors are fundamental to their mathematical success.\u003c/p\u003e \u003cp\u003eGrowth mindset emerged as a substantial predictor in machine learning models, particularly in XGBoost (40.98%) and LightGBM (39.94%). This finding supports Growth Mindset Theory (Dweck, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2006\u003c/span\u003e), indicating that students' beliefs about the malleability of their abilities significantly influence their mathematics performance. Notably, traditional regression failed to capture this relationship effectively, showing a weak and statistically insignificant association. This discrepancy suggests that the relationship between growth mindset and performance may be more complex and non-linear than traditional regression can adequately model.\u003c/p\u003e \u003cp\u003eMotivation demonstrated a relatively smaller but meaningful contribution to mathematics performance, with its highest importance observed in XGBoost (17.73%). This aligns with Expectancy-Value Theory (Wigfield \u0026amp; Eccles, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2000\u003c/span\u003e), suggesting that while motivation influences performance, its effects may be mediated by other factors such as effort and mindset. The machine learning models' ability to capture these nuanced relationships provides important insights into how motivational factors interact with other predictors to influence mathematical achievement.\u003c/p\u003e \u003cp\u003eThe superior performance of machine learning models, particularly XGBoost (R\u0026sup2; = .1571, MSE\u0026thinsp;=\u0026thinsp;7186.49), compared to traditional regression (R\u0026sup2; = .027) demonstrates the advantage of these approaches in capturing complex educational relationships. This finding suggests that the interactions between psychological constructs and academic performance are more sophisticated than linear models can effectively represent.\u003c/p\u003e \u003cp\u003eThese results have important implications for educational practice. The strong influence of effort and growth mindset suggests that interventions should focus on fostering these qualities through strategies such as goal setting, self-monitoring, and targeted mindset development programs. Additionally, the effectiveness of machine learning models suggests their potential utility in educational analytics for predicting student outcomes and identifying at-risk students.\u003c/p\u003e \u003cp\u003eSeveral limitations warrant consideration. The study's predictor set was limited to three variables, excluding potentially important factors such as socioeconomic status, mathematics anxiety, and teacher quality. Furthermore, the use of data from a single country may limit generalizability across different educational contexts. While machine learning models demonstrated superior predictive accuracy, their complexity can present challenges for interpretation, suggesting the need for future research incorporating explainable AI techniques.\u003c/p\u003e \u003cp\u003eThis study advances our understanding of how psychological factors influence mathematics performance while highlighting the potential of machine learning approaches in educational research. Future investigations should expand the predictor set, explore cross-cultural generalizability, and develop more interpretable machine learning models to better inform educational practice and policy.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eOur investigation into the predictive relationships between psychological factors and mathematics performance yields several significant conclusions and practical implications for educational stakeholders. The study demonstrates that effort, growth mindset, and motivation substantially influence mathematics performance, with effort emerging as the most robust predictor across analytical approaches. The superior performance of machine learning models, particularly XGBoost, compared to traditional regression highlights the complex, non-linear nature of these relationships and suggests the need for more sophisticated analytical approaches in educational research.\u003c/p\u003e \u003cp\u003eThese findings, grounded in Self-Regulation Theory and Growth Mindset Theory, emphasize the critical importance of fostering self-regulatory behaviors and adaptive beliefs in mathematics education. The results suggest that successful mathematical achievement is not solely determined by inherent ability but is significantly influenced by malleable factors that can be developed through targeted interventions.\u003c/p\u003e \u003cp\u003eBased on these findings, we propose several key recommendations for educational stakeholders. For educators, implementing strategies that cultivate effort and persistence, such as structured goal-setting programs and regular feedback mechanisms, should be prioritized. Additionally, fostering a growth mindset through classroom practices that emphasize the malleability of intelligence and the value of challenge in learning is crucial.\u003c/p\u003e \u003cp\u003ePolicymakers should consider investing in teacher training programs that focus on promoting self-regulated learning and adaptive belief systems in mathematics education. Furthermore, the development of data-driven policies that utilize predictive analytics could enhance the identification of at-risk students and improve resource allocation.\u003c/p\u003e \u003cp\u003eFor researchers, future investigations should expand the predictor set to include variables such as mathematics anxiety, socioeconomic status, and instructional quality to enhance model explanatory power. Cross-cultural validation studies would help establish the generalizability of these findings across diverse educational contexts.\u003c/p\u003e \u003cp\u003eEducational institutions should consider integrating machine learning models into their academic analytics platforms to enable more personalized student support systems. These predictive insights could inform the design of targeted interventions, particularly for students demonstrating lower levels of effort and growth mindset.\u003c/p\u003e \u003cp\u003eIn conclusion, this study advances our understanding of the complex relationships between psychological factors and mathematics performance while highlighting the potential of machine learning approaches in educational research. By leveraging these insights, educators and policymakers can develop more effective strategies to support student success in mathematics education.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBlackwell L, Trzesniewski K, Dweck CS (2007) Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. 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Theory into Pract 41(2):64\u0026ndash;70. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1207/s15430421tip4102_2\u003c/span\u003e\u003cspan address=\"10.1207/s15430421tip4102_2\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":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":"mathematics performance, machine learning, predictive analytics","lastPublishedDoi":"10.21203/rs.3.rs-5744169/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5744169/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study examines the influence of effort, growth mindset, and motivation on mathematics performance, comparing the effectiveness of traditional and machine learning regression models. Using secondary data from 4,552 students, five models\u0026mdash;multiple regression, Random Forest, Gradient Boosting, XGBoost, and LightGBM\u0026mdash;were evaluated for predictive accuracy and feature importance. The results demonstrate that machine learning models, particularly XGBoost, significantly outperform traditional regression, with XGBoost achieving the lowest Mean Squared Error (MSE\u0026thinsp;=\u0026thinsp;7186.49) and the highest R-squared (0.1571). Effort emerged as the strongest predictor, followed by growth mindset, while motivation had a smaller but notable influence. These findings reinforce the applicability of Self-Regulation Theory and Growth Mindset Theory, highlighting the potential of machine learning to enhance educational research. Practical implications emphasize the importance of fostering effort and growth mindset through targeted interventions and leveraging predictive analytics for data-driven decision-making in education.\u003c/p\u003e","manuscriptTitle":"Effort, Mindset, and Motivation: Comparing Traditional and Machine Learning Regression Models in Predicting Math Performance","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-03 05:42:01","doi":"10.21203/rs.3.rs-5744169/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":"f2bc108c-bdac-4b6b-a5e0-982935146c66","owner":[],"postedDate":"January 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":42222008,"name":"Educational Psychology"},{"id":42222009,"name":"Cognitive Neuroscience"},{"id":42222010,"name":"Artificial Intelligence and Machine Learning"}],"tags":[],"updatedAt":"2025-01-03T05:42:01+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-03 05:42:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5744169","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5744169","identity":"rs-5744169","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}