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Arnon, Ilana; Nesher, Pearla; Nirenburg, Renata

doi:10.1023/a:1017998922475

Cited by 39 publications

(4 citation statements)

References 9 publications

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“…Equivalent fractions were not understood by the majority of children (Kamii and Clark, 1995; Arnon et al, 2001). For example, performance was poor when they were asked to place 2/3 on a number line when the references were 0 and 1/6.…”

Section: Discussionmentioning

confidence: 99%

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A componential view of children's difficulties in learning fractions

et al. 2013

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Fractions are well known to be difficult to learn. Various hypotheses have been proposed in order to explain those difficulties: fractions can denote different concepts; their understanding requires a conceptual reorganization with regard to natural numbers; and using fractions involves the articulation of conceptual knowledge with complex manipulation of procedures. In order to encompass the major aspects of knowledge about fractions, we propose to distinguish between conceptual and procedural knowledge. We designed a test aimed at assessing the main components of fraction knowledge. The test was carried out by fourth-, fifth- and sixth-graders from the French Community of Belgium. The results showed large differences between categories. Pupils seemed to master the part-whole concept, whereas numbers and operations posed problems. Moreover, pupils seemed to apply procedures they do not fully understand. Our results offer further directions to explain why fractions are amongst the most difficult mathematical topics in primary education. This study offers a number of recommendations on how to teach fractions.

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Section: Discussionmentioning

confidence: 99%

“…Teaching children concrete activities could help them develop the corresponding abstract concepts (Arnon et al, 2001; Gabriel et al, 2012). For example, most primary school children consider fractions as being entities smaller than one (Behr et al, 1992; Stafylidou and Vosniadou, 2004).…”

Section: Discussionmentioning

confidence: 99%

A componential view of children's difficulties in learning fractions

et al. 2013

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“…How might students experience 1:2 and 2:4 as sensuously identical? Ideally, I reflected, this sensuous identity should be instantiated in forms that are readily conducive to numerical quantification via measurement, so as Several inspirational prior designs satisfy some of my own design specifications [94,57,95,96]. However either these designs introduce symbols too early, do not leverage NUI (Natural User Interfaces), or do not offer proportional equivalence as sensuous identity.…”

Section: Action-based Designmentioning

confidence: 99%

Building educational activities for understanding: An elaboration on the embodied-design framework and its epistemic grounds

Abrahamson

2014

International Journal of Child-Computer Interaction

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“…Concrete activities and their teaching can help primary school pupils develop the necessary abstract concepts [32].…”

Section: Discussionmentioning

confidence: 99%

Knowledge of Fractions of Learners in Slovakia

2022

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In this research, we set two main goals: to provide empirical data that point to the knowledge of fractions among fifth-grade primary school pupils on a national scale; and to determine the level of knowledge about fractions among university students, including future primary school teachers. We used two tests—the national-wide test T5 for the fifth-graders (a research sample of approximately 45,000 pupils), and the modified fraction test based on Sfard’s theory of reification, for the university students (162 students). At the end of the study, we focused on a content analysis of the university students’ solutions. We identified persistent difficulties with concepts of fractions not only by fifth graders but also by future primary school teachers.

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Cited by 39 publications

References 9 publications

A componential view of children's difficulties in learning fractions

A componential view of children's difficulties in learning fractions

Building educational activities for understanding: An elaboration on the embodied-design framework and its epistemic grounds

Knowledge of Fractions of Learners in Slovakia

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