A psychological network analysis to examine interdependencies between fraction and algebra subtopics in an intelligent tutoring system

Abstract

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.