General and math-specific predictors of sixth-graders’ knowledge of fractions

Hansen, Nicole; Jordan, Nancy C.; Fernandez, Edmund P.; Siegler, Robert S.; Fuchs, Lynn S.; Gersten, Russell; Micklos, Deborah

doi:10.1016/j.cogdev.2015.02.001

Cited by 140 publications

(189 citation statements)

References 40 publications

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“…ESs ranged from 0.63 to In these ways, each intervention condition produced superior fraction learning for at-risk fourth graders compared to the business-as-usual at-risk control group. These results echo earlier randomized control trials suggesting the importance of supplemental explicit fraction intervention (Fuchs et al, 2015) that incorporates a strong emphasis on the measurement interpretation of fractions , 2014. Finding that the measurement interpretation of fractions is a key instructional target is also in line with the perspective expressed in the NMAP report (2008).…”

Section: Effects Of the Multi-component Fraction Interventionsupporting

confidence: 77%

“…Also, both tasks involve language comprehension because teachers use language to convey new ideas/procedures, because students use language when self-explaining, and because word problems are presented linguistically. In longitudinal studies aimed at predicting children's development of fraction and word-problem knowledge, roles have been demonstrated for reasoning Seethaler et al, 2011), working memory , 2014Hansen et al, 2015;Jordan et al, 2013;Seethaler et al, 2011), and language comprehension Jordan et al, 2013). …”

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confidence: 99%

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Supported self-explaining during fraction intervention.

Fuchs¹,

Malone²,

Schumacher³

et al. 2016

Journal of Educational Psychology

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100

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The main purposes of this study were to test the effects of teaching at-risk 4 th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3conditions: a control group and 2 variants of a multi-component fraction intervention. Both intervention conditions included 36 sessions, each lasting 35 min. All but 7 min of each session were identical. In the 7-min component, students were taught to provide high quality explanations when comparing fraction magnitudes or to solve fraction word problems. Children were pretested on cognitive variables and pre/posttested on fraction knowledge. On accuracy of magnitude comparisons and quality of explanations, children who received the explaining intervention outperformed those in the word-problem condition. On word problems, children who received the word-problem intervention outperformed those in the explaining condition.Moderator analyses indicated that the explaining intervention was more effective for students with weaker working memory, while the word-problem intervention was more effective for students with stronger reasoning ability.Key words: supported self-explaining, fractions, intervention, moderator, working memory, reasoning EXPLAINING WHY FRACTION MAGNITUDES DIFFER-4 Supported Self-Explaining during Fraction InterventionCompetence with fractions is important for advanced mathematics learning and success in the American workforce (National Mathematics Advisory Panel [NMAP], 2008;Geary Hoard, Nugent, & Bailey, 2012;Siegler et al., 2012). Yet understanding about fractions and skill in operating with fractions are difficult for many students (National Council of Teachers of Mathematics, 2007; NMAP;Ni, 2001). The NMAP therefore assigned high priority to improving fraction instruction. The focus of the present study was on the effects of intervention to enhance at-risk learners' performance on fractions at fourth grade. Our main purposes were to isolate the effects of intervention focused on teaching children to explain why fractions differ in magnitude and to examine whether effects accrue by compensating for limitations in cognitive processes.In this introduction, we describe why teaching children to provide high quality explanations may enhance understanding of the explained content and provide a rationale for the supported self-explaining approach we took. We also discuss how self-explaining without such scaffolding can be cognitively demanding and why the approach we took may compensate for limitations in the cognitive resources many children with histories of poor mathematics learning experience. Finally, we describe the theoretical orientation of the multi-component intervention program in which our explaining intervention component was embedded. Explaining Why Fractions Differ in MagnitudeA major purpose of the present study was to isolate the effects of intervention teaching children to provide sound explanations regard...

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Section: Effects Of the Multi-component Fraction Interventionsupporting

confidence: 77%

mentioning

confidence: 99%

Supported self-explaining during fraction intervention.

Fuchs¹,

Malone²,

Schumacher³

et al. 2016

Journal of Educational Psychology

Self Cite

100

View full text Add to dashboard Cite

show abstract

“…Bailey et al (2014) found that simple multi-digit whole-number calculation skill at first grade predicts fractions calculation competence in middle school. Hansen et al (2015) showed that simple whole-number addition and number line estimation at third grade make unique contributions to fractions calculations and conceptual understanding at fifth grade. Vukovic et al (2014) found that second-grade whole-number addition, subtraction, multiplication, and division competence contributes to the prediction of fractions calculations at fourth grade.…”

Section: Role Of Whole-number Knowledge In Understanding Fractionsmentioning

confidence: 99%

“…Yet, with the exception of Hansen et al (2015), the latter set of studies, in which whole-number calculations predict fractions outcomes, differ from the former set of studies by focusing on fraction calculations outcomes, rather than fractions understanding. They also relied on simple whole-number calculation skill as the predictor.…”

Section: Role Of Whole-number Knowledge In Understanding Fractionsmentioning

confidence: 99%

“…Hansen et al (2015) showed that fifth-grade whole-number long division predicts knowledge of fractions concepts at sixth grade, and Siegler and Pyke (2012) showed that whole-number long division concurrently predicts fractions calculation competence among sixth and eighth graders. Together, these studies suggest that whole-number long division predicts fractions understanding as well as fractions calculation skill.…”

Section: Role Of Whole-number Knowledge In Understanding Fractionsmentioning

confidence: 99%

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

Namkung

Fuchs

Koziol

2018

Learning and Individual Differences

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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.

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Number line estimation and standardized test performance: The left digit effect does not predict SAT math score

et al. 2020

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Introduction: Recent work reveals a new source of error in number line estimation (NLE), the left digit effect (Lai, Zax, et al., 2018), whereby numerals with different leftmost digits but similar magnitudes (e.g., 399, 401) are placed farther apart on a number line (e.g., 0 to 1,000) than is warranted. The goals of the present study were to: (1) replicate the left digit effect, and (2) assess whether it is related to mathematical achievement. Method: Participants were all individuals (adult college students) who completed the NLE task in the laboratory between 2014 and 2019 for whom SAT scores were available (n = 227). Results: We replicated the left digit effect but found its size was not correlated with SAT math score, although it was negatively correlated with SAT verbal score for one NLE task version. Conclusions: These findings provide further evidence that individual digits strongly influence estimation performance and suggest that this effect may have different cognitive contributors, and predict different complex skills, than overall NLE accuracy.

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General and math-specific predictors of sixth-graders’ knowledge of fractions

Cited by 140 publications

References 40 publications

Supported self-explaining during fraction intervention.

Supported self-explaining during fraction intervention.

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

Number line estimation and standardized test performance: The left digit effect does not predict SAT math score

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