Why is learning fraction and decimal arithmetic so difficult?

Lortie‐Forgues, Hugues; Jing, Tian; Siegler, Robert S.

doi:10.1016/j.dr.2015.07.008

Cited by 195 publications

(152 citation statements)

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“…Unfortunately these problems tend to persist over time, particularly among students who exhibit low mathematics achievement to begin with, or who have a mathematics learning disability (Lortie‐Forgues, Tian, & Siegler, ; Mazzocco, Myers, Lewis, Hanich, & Murphy, ). This performance is consistent with a survey of Algebra I teachers, who reported that students have poor foundational skills in rational numbers including fractions and decimals (NMAP, ).…”

Section: Introductionmentioning

confidence: 99%

“…However, the studies reviewed in both Misquitta () and Shin and Bryant () included primarily secondary students, leaving a gap in the literature on what instructional components are most effective for students at the elementary level. Given that students’ difficulties in fractions begin early and persist throughout schooling (Lortie‐Forgues et al, ; Mazzocco et al, ), identifying the common and effective approaches to address students’ early fraction knowledge is needed. Additionally, Shin and Bryant () found that the majority of studies focused on a limited scope of fraction learning aligned with the CCSSM and none addressed how to represent fractions on a number line to build a conceptual to procedural link for students.…”

Section: Introductionmentioning

confidence: 99%

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Fraction interventions for struggling elementary math learners: A review of the literature

Roesslein¹,

Codding²

2018

Psychology in the Schools

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Understanding fractions has been a pervasively difficult skill for struggling math learners, yet it is essential for success in secondary level mathematics skills. The present systematic review examined the evidence base of fraction interventions for elementary level students identified as struggling math learners. Twelve studies met inclusion criteria and were reviewed for (a) instructional focus (b) instructional components, and (c) effectiveness of the intervention on fraction performance. The majority of studies had a primary instructional focus on conceptual knowledge of fraction learning. Results of the study also indicated that all interventions included multiple evidence-based instructional components (e.g., concrete and visual representations, range and sequence of examples, etc.). These multicomponent interventions improved performance on a variety of proximal fraction outcome measures. Intervention effects were mixed for generalized outcome measures and minimal for distal outcome measures. Limitations, implications for practice, and future research directions are discussed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fraction interventions for struggling elementary math learners: A review of the literature

Roesslein¹,

Codding²

2018

Psychology in the Schools

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“…We consider the concept of fraction and the symbol "a/b" as a case from school mathematics. The research (e.g., [8][9][10][11]) shows that fractions are one of the most challenging areas in school mathematics. Pupils, prospective class and subject teachers, and sometimes even experienced teachers, have trouble with fractions, especially understanding fractions as numbers that extend the whole number system to rational numbers (e.g., [12,13]).…”

Section: A Case: Fractions and Meanings Of Symbol "A/b"mentioning

confidence: 99%

Sustainability Development in Mathematics Education—A Case Study of What Kind of Meanings Do Prospective Class Teachers Find for the Mathematical Symbol “23”?

Joutsenlahti

Perkkilä

2019

Sustainability

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In this article, our focus is on sustainable development in mathematics education from the point of view of teacher training. The aim was to develop prospective teachers' content knowledge and pedagogical content knowledge of school mathematics. As a case study, we chose the mathematical symbol "a/b", and examined how prospective class teachers in Finland connect it to the concepts of fraction, ratio, division, rational number or probability. Mathematics textbooks often have a central role in lessons, and they affect strongly how pupils understand concepts and the relationships between them. We chose languaging as a multi-semiotic approach to interpreting what kind of meanings the prospective class teachers gave the mathematical symbol "a/b". The results show that some of these concepts are difficult to see at the same time from the given mathematical symbol. The concept of ratio is particularly difficult for prospective class teachers to interpret. Pictorial presentation supported the interpretations. Mathematics learning materials and teacher education should develop in accordance with the results of the study.

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“…Despite the importance of fractions and the several years children spend studying them, many children fail to master them. Fraction arithmetic presents a particular challenge (Byrnes & Wasik, 1991;Fuchs et al, 2014;Hecht & Vagi, 2010;Jordan et al, 2013;Lortie-Forgues, Tian, & Siegler, 2015;Newton, Willard, & Teufel, 2014). For example, percent correct on fraction arithmetic problems involving all four operations was only 46% among sixth graders and 57% among eighth graders in Siegler and Pyke (2013), and it was only 32% among sixth graders and 60% among eighth graders in Siegler, Thompson, and Schneider (2011).…”

Section: Introductionmentioning

confidence: 99%

Do children understand fraction addition?

Braithwaite

Jing

Siegler

2017

Developmental Science

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Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining fourth to eighth graders' estimates of fraction sums. We found that roughly half of estimates of sums were smaller than the same child's estimate of one of the two addends in the problem. Moreover, children's estimates of fraction sums were no more accurate than if they had estimated each sum as the average of the smallest and largest possible response. This weak performance could not be attributed to poor mastery of arithmetic procedures, poor knowledge of individual fraction magnitudes, or general inability to estimate sums. These results suggest that a major source of difficulty in this domain is that many children's learning of fraction arithmetic procedures develops unconstrained by conceptual understanding of the procedures. Implications for education are discussed.

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Why is learning fraction and decimal arithmetic so difficult?

Cited by 195 publications

References 65 publications

Fraction interventions for struggling elementary math learners: A review of the literature

Fraction interventions for struggling elementary math learners: A review of the literature

Sustainability Development in Mathematics Education—A Case Study of What Kind of Meanings Do Prospective Class Teachers Find for the Mathematical Symbol “23”?

Do children understand fraction addition?

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