Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction

Abstract

Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level.

Fraction Symbols and their Relation to Conceptual Knowledge

“…To accurately place fractions on a fraction number line, students need to integrate information from the numerator and the denominator to determine the fraction magnitude, then they need to locate the magnitude on a number line (Schneider et al, 2018). Consistent with this view, we found that a conceptual understanding of fraction symbols (Hansen et al, 2015) and strong whole number line estimation skills (Jordan et al, 2017;Liu, 2018;Resnick et al, 2016) were related to fraction number line accuracy. Specifically, relational estimators had stronger fraction mapping skills and more precise whole number line estimation skills than whole-component estimators.…”

“…As shown in Figure 6.3, the whole number estimators and denominator estimators more accurately placed 1 4 than 1 2 on the number line. This finding was unexpected because we anticipated students would accurately estimate both 1 4 and 1 2 because they are familiar fractions (Liu, 2018). As expected, the students in the relational profile were very accurate at placing ½.…”

“…Researchers have used qualitative analyses to describe students' misconceptions about fraction magnitudes (Deringöl, 2019;D. Zhang et al, 2017) whereas quantitative researchers have primarily focused on overall task performance (Liu, 2018;Resnick et al, 2016;Siegler et al, 2011;Torbeyns et al, 2015) and its relation to later math skills (Rodrigues et al, 2019;Siegler & Pyke, 2013;Torbeyns et al, 2015). Thus, the goals of the present research were to better understand the strategies students use to place fractions on the number line and determine what mathematical skills differentiate students based on their estimation strategies.…”

“…Segmentation examples included dividing the number line into equal sections based on common fractions such as halves and quarters, or defining segments based on the denominator (e.g., dividing the number line into seven segments to place changing the fraction into a more convenient number through rounding, reducing, or converting the fraction to a decimal or percentage (e.g., a student might "round" because it is a more familiar proportion. Students in grade 8 reported using a transformation strategy more frequently than those in grade 6 indicating that strategy selection changes as students' fraction skills develop (Braithwaite & Siegler, 2018;Liu, 2018;Siegler et al, 2011).…”

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

“…Fraction magnitude understanding is known to be an important component of overall fraction competence (Fazio, Bailey, Thompson, & Siegler, 2014b;Fazio et al, 2016;Hamdan & Gunderson, 2017;Liu, 2018). In order to assess whether relational reasoning predicts fraction knowledge above and beyond what is predicted by fraction magnitude awareness, we included two measures of fraction magnitude awareness as predictors.…”