Poster #32 - Grade of Acquisition of Understanding Mathematical Equivalence Predicts Algebra Readiness

• In Event: 1-115 - Poster Session 03
  In Poster Session: PS 03 Section - Cognitive Processes

Integrative Statement

Mathematical equivalence is widely regarded as an important concept for promoting children’s algebra readiness. Unfortunately, many elementary school children in the U.S. struggle to understand this concept, especially when presented in symbolic form (e.g., 3 + 4 = 5 + 2). Historically, children’s difficulties were attributed to age-related limitations in memory and reasoning, but researchers now generally agree that difficulties are due, at least in part, to the way arithmetic is traditionally taught in school. Despite progress in understanding why children struggle to understand mathematical equivalence, no research to date has examined if there are long-term benefits to gaining an understanding in elementary school. This has potential implications for whether teachers should integrate pre-algebraic content into elementary mathematics lessons. Researchers have assumed that an early understanding of mathematical equivalence begets greater algebra readiness, but this has not been tested. We predicted that an earlier understanding of mathematical equivalence would be associated with greater algebra readiness, even after controlling for gender, SES, IQ, and calculation fluency.
We tested this hypothesis in a longitudinal study with elementary school children (n = 84 [37 girls, 47 boys]; M age at T1 = 8;1). Children’s understanding of mathematical equivalence was tested in second grade and then every year through sixth grade using a measure consisting of solving mathematical equivalence problems (e.g., 3 + 4 + 5 = 3 + __), encoding mathematical equivalence problems, and defining the equal sign (McNeil & Alibali, 2005). A grade-of-acquisition variable was created to index the grade at which children began showing understanding. We defined this a priori as the first grade level in which the child solved at least one problem correctly, encoded at least one correctly, and either explicitly defined the equal sign relationally (e.g., “it means ‘the same as’”), or rated relational definitions as “smart” (or both). Additionally, we required that children continue to display that understanding (or better) in subsequent grades. We captured individual differences at the endpoints based on children’s performance in 2nd and 6th grade, so scores of 1.5 (demonstrates mastery), 6.5 (one component only), and 7 (never acquired) were possible; however, conclusions are unchanged when only whole numbers are considered. In sixth grade, children completed the Iowa Algebra Aptitude Test, a standardized measure of algebra readiness, and answered the research-based Transition from Arithmetic to Algebraic Reasoning interview items. A composite measure was created by summing the z-scores of the two measures.
As predicted, the earlier children exhibited understanding of mathematical equivalence, the more algebra readiness they exhibited in sixth grade (Figure 1). The grade-of-acquisition variable had a significant zero-order correlation with algebra readiness and a significant partial effect in the full model (Table 1). Grade-of-acquisition of understanding of mathematical equivalence accounted for 12.87% of unique variance and 5.84% of the variability in algebra readiness overall. We also demonstrated discriminant validity, as the grade-of-acquisition variable did not predict reading fluency. These findings suggest that earlier may be better when it comes to the learning of foundational pre-algebraic concepts.

Authors

• Brianna Devlin, University of Delaware
  Presenting Author

• Caroline Byrd Hornburg, Purdue University
  Non-Presenting Author

• Nicole McNeil, University of Notre Dame
  Non-Presenting Author