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…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

The effects of problem size on judgments of commutativity by 51 moderately and mildly retarded students were investigated. Results indicated that many retarded students who are given computational practice recognize the general principle that addend order does not affect the sum. (Author/DB)

Examined effects of problem size in mental addition among elementary children in China (n=104) and Missouri (n=105) and among undergraduates in China (n=26) and Missouri (n=35). For all Missouri subjects and Chinese through first grade, larger-valued numbers took longer and induced more errors. (Author/NBI)

Investigates the effect of mental schemes corresponding to additive and multiplicative situations in the process of interpreting and solving problems. Classifies relative difficulties of problems according to their situations which are considered through a written test administered to pupils in grades 2, 3, and 4. Supports the assumption that…

This book is a compilation of recent research on the development of multiplicative concepts. The sections and chapters are: (1) Theoretical Approaches: "Children's Multiplying Schemes" (L. Steffe), "Multiplicative Conceptual Field: What and Why?" (G. Vergnaud), "Extending the Meaning of Multiplication and Division" (B. Greer); (2) The Role of the…

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…

This paper considers whether or not curriculum initiatives within England are in fact leading to qualitatively improved levels of thinking among children identified as lower achievers in arithmetic. Revisiting data from two earlier studies and introducing current data, the paper draws comparisons in the strategies that 8-year-old children use to…

A study asked 24 first grade children from 3 different classes to write number sentences and select appropriate alternative number sentences for addition and subtraction word problems. Results indicated that children could be characterized into five clusters according to their flexibility in accepting alternative number sentences and that…

Examined the performance of kindergartners from middle- and low-income families on arithmetic calculations presented in a nonverbal format and in three verbal formats. Children from middle-income families performed better than those from low-income families on verbal calculation tasks but not on the nonverbal task. (BC)

Compares two experimental programs for teaching mental addition and subtraction in the Dutch second grade (N=275). Discusses realistic program design (RPD) and gradual program design (GPD). Concludes that RPD pupils show a more varied use of solution procedures than GPD pupils. Contains 46 references. (Author/ASK)

This report describes a simulation of adults' retrieval of arithmetic facts from a network-based memory representation. The goals of the simulation project are to: demonstrate in specific form the nature of a spreading activation model of mental arithmetic; account for three important reaction time effects observed in laboratory investigations;…

In the foreword to this book, Inhelder states that its essential contribution is that "it transposed to actual reality Piaget's central epistemological thesis according to which mathematical thought is, from its most elementary manifestations, the product of the subject's activity that he characterized by the term 'reflective…

Students in grades 1, 3, 4, 5, 6, and college were timed as they produced the answers to simple addition problems or verified a given problem as true or false. First graders clearly relied on a counting process for their performance, as advanced by the Groen and Parkman "min" (for minimum addend) model. Third grade appears to be a…

The purpose of this study was to identify the working memory capacity (M-space) for a group of 139 children (4 to 8 years of age) enrolled at Sandy Bay Infant School in Hobart, Tasmania, Australia. Four M-space tests -- The Counting Span Test (Case and Kurland, 1978), Mr. Cucui Test (DeAvila and Havassy, 1974), the Digit Placement Test (Case,…