Errors as Predictors of Algebra Learning

• In Event: Bridging Research and Practice: Findings From the National Center on Cognition and Mathematics Instruction

Abstract

Errors in mathematics classrooms, while common, are often discouraged. These errors can indicate certain misunderstandings that students have about mathematical concepts. Prior research demonstrates that certain types of errors are related to math achievement difficulties (Booth, Barbieri, Eyer, & Paré-Blagoev, 2014). However, some researchers suggest the use of errors as a mechanism for learning within specific types of instruction. The current in-depth analyses focus on the types and frequency of errors middle school students (N = 140) make while learning to solve systems of equations and whether making certain types of errors is indicative of learning struggles. Students’ problem-solving across the worksheets used within the unit was coded for errors. Through the use of correlations and conceptual similarities, the 23 specific errors found were collapsed into five error categories. These categories included terms errors, operation errors, equal sign errors, graphing errors, and mechanical errors. Operation errors, or errors involving incorrectly performing operations or performing the wrong operation, were most frequent (M = 3.03, SD = 3.66). Terms errors, or errors involving incorrectly working with variables, constants, and coefficients, were also frequent (M = 2.03, SD = 2.61). Multiple regressions were run to determine whether certain types of errors were predictive of learning as indicated at post-test after controlling for pretest as well as number of problems attempted overall. The relationships between specific types of errors and learning are discussed. For example, the number of terms errors made across the unit predicted a small but significant amount of overall learning (β = -.16, p = .028). Students’ errors as potential representations of algebraic misconceptions, as well as implications for education, are discussed.

Authors

• Christina Barbieri, University of Delaware

• Kelly McGinn, Temple University

• Julie L. Booth, Temple University