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)…

Useful for small groups or one-on-one instruction, this book offers successful math interventions and response to intervention (RTI) connections. Teachers will learn to target math instruction to struggling students by: (1) Diagnosing weaknesses; (2) Providing specific, differentiated instruction; (3) Using formative assessments; (4) Offering…

Background: Although it is believed that children with cerebral palsy are at high risk for learning difficulties and arithmetic difficulties in particular, few studies have investigated this issue. Methods: Arithmetic ability was longitudinally assessed in children with cerebral palsy in special (n = 41) and mainstream education (n = 16) and…

In the article we compare the approaches of 3 in-service teachers and 3 student teachers when they tried to solve a verbal arithmetic problem in the classroom. Each interaction was studied using a System of Analysis that takes into account the cognitive processes involved in the solution of a mathematic problem and describes the interaction at…

Teachers must be prepared to recognize valid alternative representations of arithmetic problems. Challenging examples involving mixed fractions and division are presented along with teacher's discussion from a professional development workshop. (Contains 6 figures and 1 table.)

In the late seventies, Guy Brousseau set himself the goal of verifying experimentally a theory he had been building up for a number of years. The theory, consistent with what was later named (non-radical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics. The experiment,…

This article communicates findings from a year-long constructivist teaching experiment about the relationship between four sixth-grade students' multiplicative structures and their construction of improper fractions. Students' multiplicative structures are the units coordinations that they can take as given prior to activity--i.e., the units…

This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

The aims of this study were to investigate whether the executive functions, inhibition, shifting, and updating, are distinguishable as latent variables (common factors) in children aged 9 to 12, and to examine the relations between these executive functions and reading, arithmetic, and (non)verbal reasoning. Confirmatory factor analysis was used…

History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and…

The addition and subtraction of integers is the first major avenue, and roadblock, to student success in learning algebra. This article describes a hands-on activity using a regular deck of playing cards that facilitates class discussion and helps students overcome this initial roadblock. (Contains 14 figures.)

This article describes one way to introduce fraction, decimal, and percent equivalents by linking student-created Op Art with examples of twentieth-century abstract painting. (Contains 7 figures.)