This article discusses two sequences of activities that were developed to support middle school students' and preservice teachers' construction of algorithms for dividing fractions. One sequence is intended to promote understanding of the common-denominator algorithm; the other sequence is intended to promote understanding of the…

Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…

This article describes the process of design and implementation of a hands-on unit on fractions in the sixth grade. The fraction unit, taught by a classroom teacher with the aid of a university professor, uses pattern blocks to help students develop conceptual understanding of fractions. Student misunderstandings and outcomes are presented, as…

This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and…

We conducted this study to determine the relationship between math preference and mastery for five middle school students with autism spectrum disorders. We randomly presented several math addition and subtraction problem formats to determine the students' preferences. Results indicated that preference was idiosyncratic across students. In…

It is not often that one can introduce primary school students to a problem at the forefront of mathematics research, and have any expectation of understanding; but with magic squares, one can do exactly that. Magic squares are an ideal tool for the effective illustration of many mathematical concepts. This paper assumes little prior knowledge on…

This paper reports the results of four dual-task experiments that were designed to determine the extent of domain-specificity of the verbal working memory resources used in linguistic integrations. To address this question, syntactic complexity was crossed in a 2x2 design with the complexity of a secondary task, which involved either (1)…

The aim of the study was to analyze the development of children's adaptive expertise in computing sums and differences up to 100. We defined the adaptive nature of children's strategy choices on the basis of problem (addition, subtraction), achievement, and strategy performance (accuracy, speed). Sixty-nine 2nd graders of high, above-average, or…

In teaching primary teacher trainees, an awareness of the characteristic features, especially commutativity and associativity of basic operations play an important role. Owing to a deeply set automatism rooted in their primary and secondary education, teacher trainees think that such characteristics of addition are so trivial that they do not need…

The effects of using homework guides, and homework logs on students' abilities to solve word problems involving basic addition and subtraction facts were studied. Students received one of three versions of addition and subtraction timed tests once per week--every Thursday--that focused on measuring automaticity of basic addition and subtraction…

"Singapore Math: Place Value, Computation & Number Sense" is a six-part presentation on CD-ROM that can be used by individual teachers or an entire school. The author takes primary to upper elementary grade teachers through place value skills with each of the computational operations: addition, subtraction, multiplication, and division. She gives…

The present study focuses on math and related skills among 32 girls with fragile X (n = 14) or Turner (n = 18) syndrome during late elementary school. Performance in each syndrome group was assessed relative to Full Scale IQ-matched comparison groups of girls from the general population (n = 32 and n = 89 for fragile X syndrome and Turner…

Background: The study was conducted in an attempt to further our understanding of how working memory contributes to written arithmetical skills in children. Aim: The aim was to pinpoint the contribution of different central executive functions and to examine the contribution of the two subcomponents of children's written arithmetical skills.…

Previous research stresses the importance of seriation, classification, and counting abilities that should be assessed in kindergarten, when looking for crucial predictors of mathematical learning disabilities in Grade 1. This study examines (n = 158) two-year-long predictive relationships between children's seriation, classification, procedural…

How can teachers learn what they need to know? Every community of educators, regardless of field or specialization, can benefit from being well informed about current research findings. A considerable amount of mathematics education research exists to inform teachers and administrators about teaching and learning mathematics. Research can show…