Heterogeneity in Middle-School Students' Encoding of Algebraic Equations

The current study examines subgroup differences in middle schoolers' (N = 306) representation, or encoding, of problem features in algebraic equations at the start and end of an academic year. We use latent profile analysis to examine the heterogeneity within middle school students' encoding errors at the start of the academic year (SOY) and end of the academic year (EOY) and determine the predictors of the likelihood of displaying each encoding profile at EOY. We also compare EOY algebra and fraction performance of students who displayed different encoding profiles. Across all grades (6-8), students displayed three profiles that differed in nature based on the amount and particular types of errors made; the frequency of each profile varied between SOY and EOY, and the likelihood of displaying a certain encoding profile at EOY varied based on the profile shown at SOY. Profile membership was predicted by SOY fraction computation skills and was subsequently predictive of EOY fraction and algebra skills. These findings emphasize the need for investigation into methods for supporting the development of encoding accuracy. Findings illuminate potential leverage points that could be intervened upon to lessen students' struggles learning algebra.