Solving Linear Equations: Identifying Common Errors in a Digital Learning Platform

• In Event: Identifying and Harnessing Students’ Math Errors for Intervention and Instruction

Abstract

1. Purpose
The current study explored the frequency of students’ errors made in the context of solving linear equations in a digital math learning platform. This can help gain better insight into how students' understandings and misunderstandings around linear equations develop, which could eventually inform instruction.
2. Perspective
One important algebraic skill is solving linear equations (i.e., solving for x in 5 = 2x - 2). This skill requires understanding concepts and procedures first introduced in elementary and middle school, like multiplication and the equal sign (Booth & Davenport, 2013). Unfortunately, sometimes students do not master earlier foundational topics, which can lead to systematic errors in more advanced topics like solving linear equations (e.g., Knuth et al., 2006). While past research has found a relation between misunderstanding the equal sign, and solving linear equations, we know less about how this error specifically manifests. Directly addressing these errors improves student learning (Barbieri et al., 2019). Thus, we focused on three errors in linear equation solving that may be the result of misunderstanding the equal sign (Booth et al., 2014; Knuth et al., 2006).
3. Methods
Students who completed learning sessions solving linear equations were identified (n = 7728). In order to be part of the analysis, students had to have completed at least 3 problems that could elicit a particular error (n = 3406). See Table 1. This decision allowed us to draw conclusions about patterns of errors.
4. Data sources
We conducted secondary data analysis using data from a digital learning platform. The digital learning platform is used by 9 to 14 year olds in the United Kingdom. We identified 64 questions that elicit these errors, with certain multiple choice responses indicating an error of interest. Students were presented with an average of 5.5 relevant questions (SD = 3.1).
5. Results
Overall, students answered about half of the questions incorrectly, with 49% indicating a specific error of interest. Some students repeated their errors, with 30% making a particular error two or more times. See Figure 1 for more on the frequency of error types. A subset of students completed problems that could elicit two or three errors of interest (12%). Of these students, 60% made at least two types of errors.
6. Significance
Past work demonstrates that equal sign understanding affects accuracy in solving linear equations (Booth & Davenport, 2013; Knuth et al., 2006). The current study adds to this literature by specifically examining what errors students make while solving linear equations (see also Booth et al., 2014). Most often, students unequally multiplied terms, and many made multiple types of errors. Moreover, we found that while about half of the students made an error of interest only once, another third made the same error two or more times. Thus, it seems that for some students, these errors reflect a slip, while for others, there may be a deeper misunderstanding of how to solve linear equations. The more instructors and digital learning platforms know about students’ errors, the better instruction can be tailored.

Authors

• Rebecca Adler, Vanderbilt University

• Kelley Durkin, Vanderbilt University

• Bethany Rittle-Johnson, Vanderbilt University