Causal pathways from fractions to algebra: Integrating psychology and math education perspectives

Abstract

Algebra knowledge is an important gatekeeper to educational and economic opportunity. Both math education researchers and psychologists have shown that fractions may be a key to this gate (e.g., Hackenberg, 2013; Siegler et al., 2012). However, psychological and educational research on the fractions-algebra association has been disconnected, with separate frameworks, definitions, and designs. This integrative review synthesizes evidence from both disciplines about how and why fractions knowledge leads to stronger algebra knowledge. I suggest that the strength of causal evidence is limited by idiosyncratic measurement, limited longitudinal research, and imprecise definitions. I also review six plausible fractions-to-algebra mechanisms, which future research should empirically test. Throughout, I argue that more nuanced understanding of the fractions-algebra association will require interdisciplinary teams. Finally, I propose an integrative conceptual model of how fractions knowledge may lead to success in algebra and suggest new directions for collaborative investigation to inform developmental theory and educational practice.

Math anxiety differentially impairs symbolic, but not nonsymbolic, fraction skills across development

“…However, less attention has been given to the differential effects of MA on specific domains of mathematics. Recent work has started to address this gap by investigating the effects of MA on domains such as fractions and algebra 18,19 . For example, Sidney et al 18 .…”

“…Despite the evidence that MA may negatively affect performance in symbolic fraction tasks in adults, previous studies remain unclear how MA impacts children's fraction skills. Learning about fractions may be one of the first places that children encounter serious difficulties with math, and they may develop negative attitudes toward mathematics in general as a result 19 . Students who were not previously math anxious could begin to experience MA due to the difficulties of learning about fractions, which would then persist into later, more advanced domains of mathematics.…”