A systematic investigation of the link between rational number processing and algebra ability

Abstract

Recent research suggests that fraction understanding is predictive of algebra ability; however, the relative contributions of various aspects of rational number knowledge are unclear. Furthermore, whether this relationship is notation-dependent or rather relies upon a general understanding of rational numbers (independent of notation) is an open question. In this study, college students completed a rational number magnitude task, procedural arithmetic tasks in fraction and decimal notation, and an algebra assessment. Using these tasks, we measured three different aspects of rational number ability in both fraction and decimal notation: (1) acuity of underlying magnitude representations, (2) fluency with which symbols are mapped to the underlying magnitudes, and (3) fluency with arithmetic procedures. Analyses reveal that when looking at the measures of magnitude understanding, the relationship between adults' rational number magnitude performance and algebra ability is dependent upon notation. However, once performance on arithmetic measures is included in the relationship, individual measures of magnitude understanding are no longer unique predictors of algebra performance. Furthermore, when including all measures simultaneously, results revealed that arithmetic fluency in both fraction and decimal notation each uniquely predicted algebra ability. Findings are the first to demonstrate a relationship between rational number understanding and algebra ability in adults while providing a clearer picture of the nature of this relationship.

Taking the relational structure of fractions seriously: Relational reasoning predicts fraction knowledge in elementary school children

“…Despite this complexity, considerable recent work in psychology has emphasized the importance of a single interpretation: the unidimensional magnitude of a fraction (for example, its position on number line) (Siegler, 2016). These studies demonstrate that understanding of fraction magnitudes (particularly with fraction number lines) is an important predictor of fraction knowledge and overall mathematical competence (Fazio, Bailey, Thompson, & Siegler, 2014a;Hansen et al, 2017;Hurst & Cordes, 2018a, 2018bYoshida & Shinmachi, 1999) and suggest that this subconstruct should be emphasized in instruction (Fazio, Kennedy, & Siegler, 2016;Siegler, 2016). While fraction magnitude understanding is clearly important, additional relation-based approaches to fractions could complement the work done on fraction magnitudes.…”

University students' misconceptions about rational numbers: Implications for developmental mathematics and instruction of younger students

“…Educators of younger students could use this information to help students who are struggling to learn and master rational number concepts or procedures as they bridge the gap to algebra. Understanding university‐level misconceptions could also inform university‐level instruction in mathematics courses (i.e., developmental courses) for students experiencing difficulty with the foundations of algebra, as researchers have demonstrated a significant connection between rational numbers performance and success with algebra (DeWolf et al, 2016; Hurst & Cordes, 2018).…”

“…Understanding university-level misconceptions could also inform university-level instruction in mathematics courses (i.e., developmental courses) for students experiencing difficulty with the foundations of algebra, as researchers have demonstrated a significant connection between rational numbers performance and success with algebra (DeWolf et al, 2016;Hurst & Cordes, 2018).…”

Fraction Symbols and their Relation to Conceptual Knowledge

“…These difficulties start in elementary school and persist into high school and beyond (Siegler & Lortie-Forgues, 2017;Siegler & Pyke, 2013). Educators are concerned about students' difficulties with fractions because fraction knowledge is a foundation for later success in algebra and for more advanced math learning (Booth & Newton, 2012;Hurst & Cordes, 2018a;Siegler et al, 2012). Moreover, people need fraction knowledge to successfully participate in STEM fields (i.e., science, technology, engineering and mathematics; .…”