The Role of Fraction Magnitude Understanding in the Development of Encoding of Algebraic Equations

• In Event: Poster Session 04
  In Poster Session: PS 04 Topic - Education, Schooling

Abstract

Encoding, or the break down and perceptual processing of important problem features, is crucial for successful equation-solving (e.g., McNeil & Alibali, 2004). Encoding accuracy predicts problem solving (Alibali et al., 2009; Rittle-Johnson & Alibali, 1999), algebraic equation-solving success (Booth & Davenport, 2013), and algebraic feature knowledge (AUTHORS, under review). Yet, not much is known regarding the development of this skill. We consider encoding development by first examining individual differences in middle schoolers’ representation of problem features in algebraic equations at the start and end of an academic year. We then examine whether encoding skills change or remain the same over the school year, as well as predictors of different transitional probabilities.
Participants included (N = 306) middle schoolers from four public schools serving ethnically and racially diverse populations in the Northeast U.S. Encoding skills were assessed at the start (SOY) and end (EOY) of the academic year using a reconstruction task (e.g., McNeil & Alibali, 2004). We coded item responses based on the number and types of encoding errors (i.e. addition, subtraction, equals sign, negative sign, variable, fraction, and number). Additional tests were administered at both time points to assess students’ fraction (i.e. fraction number line estimation, fraction comparisons, and fraction arithmetic) and algebra (i.e. equation encoding, algebra feature knowledge, and algebra equation-solving) skills. Students’ received business-as-usual mathematics instruction between time points.
We assessed individual differences in the latent structure of students’ encoding performance using latent profile analysis (LPA). A two-profile solution was accepted at both SOY and EOY based on model fit and interpretability. For SOY, Profile 1 (Low Errors, 46.7%) was characterized by a low number of encoding errors, whereas Profile 2 (High Errors, 53.3%) was characterized by a high number of encoding errors across the board. For EOY, Profile 1 (Low Errors, 65.4%) and Profile 2 (High Errors, 34.6%), were similarly characterized by an overall small and large number of encoding errors, respectively. Means are displayed in Figure 1. Latent transition analysis (LTA) and multinomial logistic regression were subsequently used to examine the relationship between students’ SOY mathematics skills and probability of transitioning latent profiles over the school year. Results (Table 1) indicated grade level and fraction number line estimation performance (percent absolute error, PAE) were significant predictors of specific transitions students made between profiles. Students in Grades 7 and 8 (compared to Grade 6) as well as those with more accurate performance on the number line estimation task were more likely to transition from Profile 2 (High Errors) to Profile 1 (Low Errors) across the school year.
Results indicate that there are subgroups of students who display strong and weak encoding performance (i.e. low and high errors) at the middle school level. These profiles are not static over the course of a school year. Proficiency in fraction NLE predicting transitions from less to more optimal profiles of encoding. Future research is needed to examine whether improvements in fraction NLE corresponds to more optional transitional paths, as well as the effects of these transitions on distal outcomes.

Authors

• Kelly-Ann Gesuelli, University of Delaware
  Presenting Author

• Christina Areizaga Barbieri, University of Delaware
  Non-Presenting Author

• Julie L Booth, Temple University
  Non-Presenting Author