Markus W. H. Spitzer, Lisa Bardach, Eileen Richter, Younes Strittmatter, Korbinian Moeller
{"title":"智能辅导系统中分数与代数子题相互依存关系的心理网络分析","authors":"Markus W. H. Spitzer, Lisa Bardach, Eileen Richter, Younes Strittmatter, Korbinian Moeller","doi":"10.1111/jcal.70093","DOIUrl":null,"url":null,"abstract":"<div>\n \n \n <section>\n \n <h3> Background</h3>\n \n <p>Many students face difficulties with algebra. At the same time, it has been observed that fraction understanding predicts achievements in algebra; hence, gaining a better understanding of how algebra understanding builds on fraction understanding is an important goal for research and educational practice.</p>\n </section>\n \n <section>\n \n <h3> Objectives</h3>\n \n <p>However, a wide range of algebra subtopics (e.g., <i>Using formulas</i> and <i>Simplifying products in formulas</i>) and fraction subtopics (e.g., <i>Adding and subtracting fractions</i>, <i>Multiplying and dividing fractions</i>) exist, and little is known about which specific fraction subtopics matter most for (i.e., best predict) which specific algebra subtopics. In addition to addressing across-topic subtopic correlations, a comprehensive understanding of within-topic subtopic correlations (i.e., among fraction subtopics and algebra topics, respectively) has not yet been achieved.</p>\n </section>\n \n <section>\n \n <h3> Methods</h3>\n \n <p>Here, we leveraged a large data set (3158 students; 257,321 problem sets) from an intelligent tutoring system (ITS) and employed state-of-the-art psychological network analysis to visualise and quantify interdependencies between students' performance on different fractions and algebra subtopics.</p>\n </section>\n \n <section>\n \n <h3> Results and Conclusions</h3>\n \n <p>We observed one robust correlation between a specific fraction and a specific algebra subtopic (<i>Fractions and the order of operations</i> and <i>Using formulas</i>). In addition, a larger number of within-topic subtopic correlations were observed. Importantly, cross-topic correlations and most within-topic correlations seemed to be driven by shared mathematical components (e.g., multiplication, operating rules or reading comprehension). Our findings advance the current understanding of mathematics learning and have implications for the design and improvement of ITSs, such as for developing automatic suggestions on which other subtopics to work on when a student encounters difficulties with a specific subtopic. Moreover, our study highlights the potential of psychological network analysis for analysing learning data from ITSs.</p>\n </section>\n </div>","PeriodicalId":48071,"journal":{"name":"Journal of Computer Assisted Learning","volume":"41 4","pages":""},"PeriodicalIF":5.1000,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/jcal.70093","citationCount":"0","resultStr":"{\"title\":\"A Psychological Network Analysis to Examine Interdependencies Between Fraction and Algebra Subtopics in an Intelligent Tutoring System\",\"authors\":\"Markus W. H. Spitzer, Lisa Bardach, Eileen Richter, Younes Strittmatter, Korbinian Moeller\",\"doi\":\"10.1111/jcal.70093\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n \\n <section>\\n \\n <h3> Background</h3>\\n \\n <p>Many students face difficulties with algebra. At the same time, it has been observed that fraction understanding predicts achievements in algebra; hence, gaining a better understanding of how algebra understanding builds on fraction understanding is an important goal for research and educational practice.</p>\\n </section>\\n \\n <section>\\n \\n <h3> Objectives</h3>\\n \\n <p>However, a wide range of algebra subtopics (e.g., <i>Using formulas</i> and <i>Simplifying products in formulas</i>) and fraction subtopics (e.g., <i>Adding and subtracting fractions</i>, <i>Multiplying and dividing fractions</i>) exist, and little is known about which specific fraction subtopics matter most for (i.e., best predict) which specific algebra subtopics. In addition to addressing across-topic subtopic correlations, a comprehensive understanding of within-topic subtopic correlations (i.e., among fraction subtopics and algebra topics, respectively) has not yet been achieved.</p>\\n </section>\\n \\n <section>\\n \\n <h3> Methods</h3>\\n \\n <p>Here, we leveraged a large data set (3158 students; 257,321 problem sets) from an intelligent tutoring system (ITS) and employed state-of-the-art psychological network analysis to visualise and quantify interdependencies between students' performance on different fractions and algebra subtopics.</p>\\n </section>\\n \\n <section>\\n \\n <h3> Results and Conclusions</h3>\\n \\n <p>We observed one robust correlation between a specific fraction and a specific algebra subtopic (<i>Fractions and the order of operations</i> and <i>Using formulas</i>). In addition, a larger number of within-topic subtopic correlations were observed. Importantly, cross-topic correlations and most within-topic correlations seemed to be driven by shared mathematical components (e.g., multiplication, operating rules or reading comprehension). Our findings advance the current understanding of mathematics learning and have implications for the design and improvement of ITSs, such as for developing automatic suggestions on which other subtopics to work on when a student encounters difficulties with a specific subtopic. 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A Psychological Network Analysis to Examine Interdependencies Between Fraction and Algebra Subtopics in an Intelligent Tutoring System
Background
Many students face difficulties with algebra. At the same time, it has been observed that fraction understanding predicts achievements in algebra; hence, gaining a better understanding of how algebra understanding builds on fraction understanding is an important goal for research and educational practice.
Objectives
However, a wide range of algebra subtopics (e.g., Using formulas and Simplifying products in formulas) and fraction subtopics (e.g., Adding and subtracting fractions, Multiplying and dividing fractions) exist, and little is known about which specific fraction subtopics matter most for (i.e., best predict) which specific algebra subtopics. In addition to addressing across-topic subtopic correlations, a comprehensive understanding of within-topic subtopic correlations (i.e., among fraction subtopics and algebra topics, respectively) has not yet been achieved.
Methods
Here, we leveraged a large data set (3158 students; 257,321 problem sets) from an intelligent tutoring system (ITS) and employed state-of-the-art psychological network analysis to visualise and quantify interdependencies between students' performance on different fractions and algebra subtopics.
Results and Conclusions
We observed one robust correlation between a specific fraction and a specific algebra subtopic (Fractions and the order of operations and Using formulas). In addition, a larger number of within-topic subtopic correlations were observed. Importantly, cross-topic correlations and most within-topic correlations seemed to be driven by shared mathematical components (e.g., multiplication, operating rules or reading comprehension). Our findings advance the current understanding of mathematics learning and have implications for the design and improvement of ITSs, such as for developing automatic suggestions on which other subtopics to work on when a student encounters difficulties with a specific subtopic. Moreover, our study highlights the potential of psychological network analysis for analysing learning data from ITSs.
期刊介绍：
The Journal of Computer Assisted Learning is an international peer-reviewed journal which covers the whole range of uses of information and communication technology to support learning and knowledge exchange. It aims to provide a medium for communication among researchers as well as a channel linking researchers, practitioners, and policy makers. JCAL is also a rich source of material for master and PhD students in areas such as educational psychology, the learning sciences, instructional technology, instructional design, collaborative learning, intelligent learning systems, learning analytics, open, distance and networked learning, and educational evaluation and assessment. This is the case for formal (e.g., schools), non-formal (e.g., workplace learning) and informal learning (e.g., museums and libraries) situations and environments. Volumes often include one Special Issue which these provides readers with a broad and in-depth perspective on a specific topic. First published in 1985, JCAL continues to have the aim of making the outcomes of contemporary research and experience accessible. During this period there have been major technological advances offering new opportunities and approaches in the use of a wide range of technologies to support learning and knowledge transfer more generally. There is currently much emphasis on the use of network functionality and the challenges its appropriate uses pose to teachers/tutors working with students locally and at a distance. JCAL welcomes: -Empirical reports, single studies or programmatic series of studies on the use of computers and information technologies in learning and assessment -Critical and original meta-reviews of literature on the use of computers for learning -Empirical studies on the design and development of innovative technology-based systems for learning -Conceptual articles on issues relating to the Aims and Scope
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