How Many<i>Decimals</i>Are There Between Two<i>Fractions</i>? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation

Vamvakoussi, Xenia; Vosniadou, Stella

doi:10.1080/07370001003676603

Cited by 187 publications

(145 citation statements)

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“…To the extent that relations between whole numbers and fractions are posited, the earlier developing understanding of whole numbers is said to interfere with the later developing understanding of fractions. For instance, according to conceptual change theories (DeWolf & Vosniadou, this issue; Stafylidou & Vosniadou, 2004;Vamvakoussi & Vosniadou, 2010), children form an initial theory of number as counting units before they encounter fractions, and draw heavily Running head: FRACTION UNDERSTANDING: THREE CONTINENTS 3 on this initial understanding of number to make sense of fractions. Children's faulty generalization of understanding of number as counting units interferes with their learning about fractions, a phenomenon often referred to as the "whole number bias" (Ni & Zhou, 2005).…”

Section: The Integrated Theory Of Numerical Developmentmentioning

confidence: 99%

Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents

Torbeyns

Schneider

Xin

et al. 2015

Learning and Instruction

151

117

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Section: The Integrated Theory Of Numerical Developmentmentioning

confidence: 99%

Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents

Torbeyns

Schneider

Xin

et al. 2015

Learning and Instruction

151

117

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“…The purpose of the short interview was to shed more understanding on the students' thought process as they completed the items on the test. According to Vamvakoussi and Vosniadou (2010), interviewing students allows researchers to better understand the process of thinking involved in solving mathematical problems and, consequently, better identifying what misconceptions students hold, which lead to mathematical errors in solving problems.…”

Section: Data Collectionmentioning

confidence: 99%

“…Vamvakoussi and Vosniadou (2010) conducted a study to investigate students' understanding of decimals, and concluded that students' understanding and conceptualization of decimals was robust and that students found it difficult to make the connection between decimals and fractions.…”

Section: Introductionmentioning

confidence: 99%

Exploring Common Misconceptions and Errors about Fractions among College Students in Saudi Arabia

Alghazo¹,

Alghazo²

2017

IES

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The purpose of this study was to investigate what common errors and misconceptions about fractions exist among Saudi Arabian college students. Moreover, the study aimed at investigating the possible explanations for the existence of such misconceptions among students. A researcher developed mathematical test aimed at identifying common errors about fractions as well as short interviews, aimed at understanding the thought process while solving problems on the test, were conducted among a total of 107 (n=107) college students. The findings suggested that the majority of college students in Saudi Arabia hold common misconceptions about fractions and mathematical calculations involving fractions, such as thinking that all fractions are always part of 1 and never greater than 1, and using cross multiplication to solve multiplication problems involving fractions.

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“…The rationale for applying the framework theory approach to conceptual change in the number domain was originally described in Vosniadou and Verschaffel (2004) and later further expanded in Vamvakoussi and Vosniadou (2010) as follows: In the domain of number, there is a great deal of evidence that children form a principled understanding of numbers as counting numbers, already at preschool age (Gelman, 2000;Smith, Solomon, & Carey, 2005). This initial understanding enables children to reason about natural numbers, to learn about their properties, and to build strategies in relation to natural number operations.…”

Section: The Framework Theory Approach To Conceptual Changementioning

confidence: 99%

“…Addition and subtraction are conceptualized in terms of counting, multiplication is conceptualized as repeated addition, and division is conceptualized as fair sharing, where the divisor is always smaller that the dividend. Each number is associated with one singular symbol, the unit is explicit and indivisible, there is a least positive number, and the size of a number can be judged by its position in the number sequence or by the number of its digits (see also Smith et al, 2005; Moss, 2005;Ni & Zhou, 2005;Vamvakoussi & Vosniadou, 2010). We stress that it is not assumed that students are aware of these assumptions; rather, these are implicit in nature (see also Fischbein et al, 1985, for a similar idea regarding the intuitive models of multiplication and division).…”

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confidence: 99%

Bridging psychological and educational research on rational number knowledge

2018

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In this paper we focus on the development of rational number knowledge and present three research programs that illustrate the possibility of bridging research between the fields of cognitive developmental psychology and mathematics education. The first is a research program theoretically grounded in the framework theory approach to conceptual change. This program focuses on the interference of prior natural number knowledge in the development of rational number learning. The other two are the research program by Moss and colleagues that uses Case's theory of cognitive development to develop and test a curriculum for learning fractions, and the research program by Siegler and colleagues, who attempt to formulate an integrated theory of numerical development. We will discuss the similarities and differences between these approaches as a means of identifying potential meeting points between psychological and educational research on numerical cognition and in an effort to bridge research between the two fields for the benefit of rational number instruction.Keywords: number cognition, natural number bias, conceptual change, rational number development, educational implications Numerical cognition is a research area that appeals to mathematics education researchers, to cognitivedevelopmental psychologists and to neuroscientists. However, the researchers coming from these different fields approach numerical cognition in different ways in terms of theoretical perspectives, questions asked, methodologies used, and most importantly, of end goals (Berch, 2016). Thus there is great need for dialogue between psychological and educational research, particularly when it comes to implications for instruction. In With this article we contribute to this effort, arguing that some of the research that lies in the intersection of cognitive-developmental psychology and mathematics education can be fruitful for both fields and very relevant for instruction. We focus on the development of rational number knowledge and we present our research jnc.psychopen.eu | 2363-8761 program that is theoretically grounded in the framework theory approach to conceptual change (Vosniadou, Vamvakoussi, & Skopeliti, 2008;Vosniadou & Verschaffel, 2004). This research program focuses on the adverse effects of prior number knowledge in the transition from natural to rational numbers (aka the natural number bias) and the challenges it presents for students' numerical and algebraic reasoning. This phenomenon has been long noticed and studied by mathematics education researchers and has more recently attracted much attention by psychologists and neuroscientists. Apart from being a phenomenon of interest to both fields, research on the natural number bias has many important implications for instruction. We will compare our research program to two other programs that also illustrate the possibility of bridging research between psychology and mathematics education. The first is a program by Moss and colleagues who developed and tested a curriculum fo...

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How ManyDecimalsAre There Between TwoFractions? Aspects of Secondary School Students’ Understanding of Rational Numbers and Their Notation

Cited by 187 publications

References 27 publications

Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents

Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents

Exploring Common Misconceptions and Errors about Fractions among College Students in Saudi Arabia

Bridging psychological and educational research on rational number knowledge

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