Solving Equations in Grade 4: Common Errors and Implications

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

Abstract

​​1. Objectives or purposes
In this study, we determined common errors made by Grade 4 students when solving for an unknown in an equation (i.e., solving an open equation). Our research questions were as follows:
How do students identified with mathematics difficulty (MD) perform on a task of solving open equations as compared to students without MD?
How does operation type within an open equation (i.e., addition, subtraction, multiplication, or division) impact students’ success with solving open equations?
How does position of the unknown impact students’ success with solving open equations?
2. Perspective(s) or theoretical framework
Students’ mathematical errors provide insight into their misconceptions and procedural challenges (Nelson & Powell, 2018; Ralston & Li, 2022). This insight is useful in designing and implementing mathematics instruction and intervention (Powell et al., 2022). Error analysis of solving open equations (e.g., 3 + ___ = 5; 10 – 8 = ___) is warranted, because solving these equations requires (a) computational skill and (b) conceptual understanding of the equal sign. Proficiency in these areas is essential in advanced mathematics.
3. Methods, techniques, or modes of inquiry
The sample for this study included 1,380 Grade 4 students, 339 (31.8%) of whom experienced MD based on performance at or belowthe 25th percentile on a screening assessment (Author, 2020). All students completed the Open Equations Expanded assessment. Responses were coded as correct or incorrect, and incorrect responses were coded for error type (e.g., incorrect operation applied). We first calculated error rates for students with vs. without MD. Next, we determined students’ accuracy on items by which operation(s) was involved in the problem. Last, we analyzed how position of the unknown impacted students’ error rates (e.g., 4 + 3 = ___ vs. 4 + ___ = 7).
4. Data sources, evidence, objects, or materials
The data source for this study was student performance on the Open Equations Expanded assessment (Author, 2020). Problems in this assessment had 1 unknown and 1 or 2 operation symbols (e.g., ___ = 2 + 6; 24 6 = ___ 3).
5. Results and/or substantiated conclusions or warrants for arguments/point of view
Preliminary analyses have revealed several themes. First, students with MD have lower overall accuracy rates in solving open equations than students without MD. Across the sample, problems involving division had the lowest accuracy rates. Last, students most frequently responded correctly to problems with an isolated unknown on the right side of the equal sign (e.g., 6 5 = ___).
6. Scientific or scholarly significance of the study or work
Student performance on solving open equations highlights skills and concepts to address in instruction and intervention. Students with MD are especially likely to require support in solving open equations. Students with and without MD may benefit from increased emphasis on (a) solving problems involving division, and (b) understanding the equal sign as a relational symbol.

Authors

• Danielle Lariviere, University of Texas at Austin

• Sarah R. Powell, University of Texas at Austin