A Fraction Sense Intervention for Sixth Graders With or At Risk for Mathematics Difficulties

Abstract

<jats:p> The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties ( N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was centered on a visual number line in the meaningful context of a color run race. Students were randomly assigned to the fraction sense intervention ( n = 25) or a business-as-usual control group ( n = 27). Students in the intervention condition received 21 lessons in small groups (45 min each) during their regular mathematics intervention period. Students in the intervention group performed significantly better than those in the control group on a measure of fraction number line estimation and a more general measure of fraction concepts, both at immediate posttest and delayed posttest, with large effect sizes; lesser effects were shown for fraction arithmetic. </jats:p>

Putting fractions together.

“…This prediction has been supported by studies showing strong correlations between understanding of whole number magnitudes and whole number arithmetic (Booth & Siegler, 2008; Fuchs et al, 2010) and between understanding of fraction magnitudes and fraction arithmetic (Byrnes & Wasik, 1991; Siegler et al, 2011). It has also been supported by experimental studies in which interventions emphasizing accurate representation of numerical magnitudes yielded improved arithmetic learning, again for both whole numbers (Booth & Siegler, 2008; Siegler & Ramani, 2009) and fractions (Dyson, Jordan, Rodrigues, Barbieri, & Rinne, 2018; Fuchs et al, 2013).…”

“…Further evaluation of the importance of PFT will require assessing the added value of incorporating PFT into more comprehensive interventions, ideally ones that share PFT’s emphasis on magnitudes and its use of the number line as a central conceptual structure. Several such interventions have been developed recently, and each of them has yielded better learning outcomes than control interventions lacking the aforementioned characteristics (Dyson et al, 2018; Fuchs et al, 2013; Saxe, Diakow, & Gearhart, 2013). However, none of these interventions emphasized the idea of representing fraction sums by putting unit fractions together, whereas this idea is central in PFT.…”

Fraction ball: Playful and physically active fraction and decimal learning.

“…for 4 th -6 th graders who struggled with fraction concepts (Barbieri et al, 2020;Dyson et al, 2020;Fuchs et al, 2013; as well as students with disabilities in grades 6 th -8 th (Bottge et al, 2014). While the above studies vary in many other components where each study integrates differing and sometimes overlapping principles stemming from the science of learning (e.g., selfexplanation prompts; Barbieri et al, 2020) the visual representation of the number line is common to all of these interventions that showed improvements on rational number skills.…”

Understanding development requires assessing the relevant environment: Examples from mathematics learning

“…Providing children with a foundation for understanding fraction arithmetic, analogous to the foundation that counting provides for whole number arithmetic, could greatly improve their ability to learn fraction arithmetic procedures. Several recent studies have tested experimental interventions designed with these goals in mind and have shown promising results (Braithwaite & Siegler, 2020; Dyson, Jordan, Rodrigues, Barbieri, & Rinne, 2018; Fuchs et al., 2013). Below, one of these interventions is described in detail.…”