Does initial learning about the meaning of fractions present similar challenges for students with and without adequate whole-number skill?

Abstract

The purposes of this study were to (a) explore whether early fractions understanding at 4th grade is differentially challenging for students with versus without adequate whole-number competence and (b) identify specific whole-number skill associated with difficulty in fractions understanding. Based on initial whole-number competence, 1,108 4th graders were classified as having (a) adequate whole-number competence (n = 775), (b) less severe whole-number difficulty (n = 201), and (c) severe whole-number difficulty (n = 132). At the end of 4th grade, they were assessed on fractions understanding and further classified as with versus without difficulty in fractions understanding. Multi-level logistic regression indicated that compared to students with adequate whole-number competence, those with less severe whole-number difficulty were almost 5 times as likely to experience difficulty with fractions understanding whereas those with severe whole-number difficulty were about 32 times as likely to experience difficulty with fractions understanding. Students with severe whole-number difficulty were about 7 times as likely to experience difficulty with fractions understanding compared to those with less severe whole-number difficulty. Among students with adequate whole-number competence, the pretest whole-number skill distinguishing those with versus without difficulty in fractions understanding was basic division facts (i.e., 2-digit dividend ÷ 1-digit divisor) and simple multiplication (i.e., 3-digit × 1-digit without regrouping). The role of whole-number competence in developing initial fractions understanding and implications for instruction are discussed.

Embedding Self-Regulation Instruction Within Fractions Intervention for Third Graders With Mathematics Difficulties

“…We adopted the approach used in prior research at fourth grade, demonstrating the efficacy of focusing on magnitude understanding (Fuchs et al, 2013, 2014; Fuchs, Malone, et al, 2016; Fuchs, Schumacher, et al, 2016). While examining effects of the base fraction magnitude program, we explored the added value of a SR component, operationalized in terms of a growth mindset with active goal setting and perseverance through the challenging tasks, as required for this domain for third-grade students with histories of poor learning with whole numbers (Namkung et al, 2018). We hypothesized that embedding an SR component into a demanding mathematics intervention may hold added value for this population of learners.…”

“…At the same time, because fractions represent a major hurdle for students with histories of whole-number difficulty (Namkung et al, 2018), our second purpose was to examine whether embedding a self-regulation (SR) component within third-grade fractions intervention provides added value on student outcomes. In the context of academic learning, SR is viewed in multiple ways.…”

“…The present study expanded SR further to build a growth mindset and encourage goal setting, self-monitoring, and perseverance through challenging tasks, with tutor-led discussions prompted via a series of stories featuring individuals who have faced school and other life hurdles. Because fractions is a challenging topic for many students, especially those with a history of poor learning with whole numbers (Namkung et al, 2018) and in this age group when a strong emphasis of fractions understanding is introduced, we hypothesized that embedding SR into a demanding fractions intervention provides added value for this population of learners.…”

“…Competence with fractions is foundational for algebra, success with more advanced mathematics, and competing in the American workforce (Booth & Newton, 2012; Geary Hoard, Nugent, & Bailey, 2012; National Mathematics Advisory Panel [NMAP], 2008; Siegler et al, 2012). For this reason and because many students have difficulty understanding and operating with fractions (Namkung, Fuchs, & Koziol, 2018), the NMAP assigned high priority to improving fractions performance. As randomized controlled trials demonstrate (Fuchs et al, 2013, 2014; Fuchs, Malone, et al, 2016; Fuchs, Schumacher, et al, 2016), small-group intervention that focuses on fraction magnitude understanding with explicit strategy development improves understanding of and the capacity to work productively with fractions for fourth graders at risk for mathematics learning disabilities.…”

Addressing Challenging Mathematics Standards With At-Risk Learners: A Randomized Controlled Trial on the Effects of Fractions Intervention at Third Grade

“…Many students experience difficulty understanding and operating with fractions (Namkung et al, 2018; National Mathematics Advisory Panel [NMAP], 2008). This is problematic because competence with fractions predicts high school algebra and overall math achievement (Siegler et al, 2012).…”