The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…

There exists a substantial number of studies that have identified a subset of low-achieving mathematics students who do not develop a reliance on retrieval for simple addition but who continue to use a counting strategy to solve these problems. There are few studies, however, that have focused on how retrieval of simple addition facts may be…

Introduction: Moved by our interest in the curricular proposal of integrating algebraic thinking in elementary mathematics, we analyse the understanding of number sentences of a group of elementary students and its evolution when working on solving open and true/false number sentences. Method: We developed a teaching experiment with a group of…

Background: Working memory is linked to learning outcomes and there is emerging evidence that training working memory can yield gains in working memory and fluid intelligence. Aims: The aim of the present study was to investigate whether interactive working memory training would transfer to acquired cognitive skills, such as vocabulary and…

The mixed method sequential nested study examines whether and how the cognitive type of teachers' content knowledge is associated with student achievement, and correlated with teaching practice. In the context of this study, the "cognitive type" refers to the kind of teacher content knowledge and thinking processes required to accomplish…

In a longitudinal intervention study, the effects of three intervention strategies on the reading skills of children with reading disabilities in Grade 2 were analyzed. The interventions consisted of computerized training programs: One bottom-up intervention aimed at improving word decoding skills and phonological abilities, the second…

The purpose of this technical report is to describe a research study exploring students' cognitive processing while solving problems related to division of fractions. Four students were interviewed using verbal protocol techniques with the intention of better understanding their cognitive processing when dividing fractions. Information gained from…

The manipulation of numbers required during calculation is known to rely on working memory (WM) resources. Here, we investigated the respective contributions of verbal and/or spatial WM manipulation brain networks during the addition of four numbers performed by adults, using functional magnetic resonance imaging (fMRI). Both manipulation and…

This article reports on 20 children's learning in arithmetic after teaching was adjusted to their conceptual development. The report covers periods from three months up to three terms in an ongoing intervention study of teachers and children in schools for the intellectually disabled and of remedial teaching in regular schools. The researcher…

This article is the third in a series of articles describing a research project entitled "Entering into Symbols" (EIS) on the use of mathematical applets at key stages 2 and 3. The first two articles, in "MT200" and "MT203", described applets designed to teach place value ("Tuckshop subtraction") and basic algebra ("Matchbox algebra"). In this…

With the introduction of arithmetic as a compulsory part of the elementary school curriculum in late eighteenth- and early nineteenth-century Germany, textbooks and pedagogical methods were wanted. Relying on the traditions of the Rechenbucher and informed by the demand for method found in Wolffian style advanced textbooks, the first generation of…

Previous work has investigated adults' knowledge of principles for arithmetic with positive numbers (Dixon, Deets, & Bangert, 2001). The current study extends this past work to address adults' knowledge of principles of arithmetic with a negative number, and also investigates links between knowledge of principles and problem representation.…

The cognitive underpinnings of arithmetic calculation in children are noted to involve working memory; however, cognitive processes related to arithmetic calculation and working memory suggest that this relationship is more complex than stated previously. The purpose of this investigation was to examine the relative contributions of processing…

A variety of experimental evidence indicates that the memory representation for multiplication facts (e.g., 6 [times] 9 = 54) incorporates bidirectional links with a forward association from factors to product and a reverse association from product to factors. Surprisingly, the authors did not find evidence in Experiment 1 of facilitative…

This manual is collection of examinations. The first part contains 150 examination papers, the questions for which have been selected mainly from the English, French, and German collections of problems. These papers may be divided into three groups. The first 50 papers are confined to the simple rules, fractions, and weights and measures; the next…