Semantic Domains of Rational Numbers and the Acquisition of Fraction Equivalence

Ni, Yujing

doi:10.1006/ceps.2000.1072

Cited by 68 publications

(73 citation statements)

References 11 publications

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“…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.…”

Section: Supported Self-explaining During Fraction Interventionmentioning

confidence: 99%

Supported self-explaining during fraction intervention.

Fuchs¹,

Malone²,

Schumacher³

et al. 2016

Journal of Educational Psychology

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: Supported Self-explaining During Fraction Interventionmentioning

confidence: 99%

Supported self-explaining during fraction intervention.

Fuchs¹,

Malone²,

Schumacher³

et al. 2016

Journal of Educational Psychology

100

View full text Add to dashboard Cite

show abstract

“…Seven of these tasks (41-45 and 48-49) examined students' procedural fluency in these operations, whereas the remaining ten were related to the conceptual understanding of these operations (e.g., estimating the result of different operations on fractions). Similar tasks were employed in several previous studies (Kyriakides and Charalambous, 2002;Ni, 2001;Philippou and Christou, 1994). It should be noted here that, due to the vagueness of the term "problem solving" used in the theoretical model under consideration, we opted not to include separate tasks to measure this construct.…”

Section: The Development Of the Testmentioning

confidence: 99%

Drawing on a Theoretical Model to Study Students’ Understandings of Fractions

2006

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Teaching and learning fractions has traditionally been one of the most problematic areas in primary school mathematics. Several studies have suggested that one of the main factors contributing to this complexity is that fractions comprise a multifaceted notion encompassing five interrelated subconstructs (i.e., part-whole, ratio, operator, quotient, and measure). Kieren was the first to establish that the concept of fractions is not a single construct, but consists of several interrelated subconstructs. Later on, in the early 1980s, Behr et al. built on Kieren's conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence, and problem solving. In the present study we used this theoretical model as a reference point to investigate students' constructions of the different subconstructs of fractions. In particular, using structural equation modeling techniques to analyze data of 646 fifth and sixth graders' performance on fractions, we examined the associations among the different subconstructs of fractions as well as the extent to which these subconstructs explain students' performance on fraction operations and fraction equivalence. To a great extent, the data provided support to the associations included in the model, although, they also suggested some additional associations between the notions of the model. We discuss these findings taking into consideration the context in which the study was conducted and we provide implications for the teaching of fractions and suggestions for further research.

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“…This limitation in children's use of representations results in difficulties in relating fractions to other representations such as locating them on a number line such as shown in Figure 7 (Baturo and Cooper 1999;Hannula 2003). In relation to the above point, this reliance also results in difficulties in understanding the ordering and equivalence of fractions (Behr et al 1984;Hart 1981;Kamii and Clark 1995;Kerslake 1986;Ni 2001).…”

Section: (Insertmentioning

confidence: 99%

Developing the use of diagrammatic representations in primary mathematics through professional development

Barmby

Bolden

Raine

et al. 2013

Educational Research

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Conclusions: Implications for the development of professional development programmes to facilitate the transfer of research into practice were identified.Recommendations for the use of diagrammatic representations are also put forward.

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Semantic Domains of Rational Numbers and the Acquisition of Fraction Equivalence

Cited by 68 publications

References 11 publications

Supported self-explaining during fraction intervention.

Supported self-explaining during fraction intervention.

Drawing on a Theoretical Model to Study Students’ Understandings of Fractions

Developing the use of diagrammatic representations in primary mathematics through professional development

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