This article focuses on spontaneous knowledge-building in the field of "the arithmetic "of" the child." The aim is to investigate the conceptual progress of fifteen children during their early school years in the compulsory school. The study is based on the epistemology of radical constructivism and the methodology of…

Number sense has been recognised as central to young children's development of mathematics for a number of decades. A student with a "good" sense of number normally has a thorough understanding of relationships among numbers and operations--being able flexibly to partition and combine numbers in convenient ways to allow appropriate…

The present study was carried out to examine physiological arousal modulation (heart activity and skin conductance), across baseline and cognitive tasks, in females with fragile X or Turner syndrome and a comparison group of females with neither syndrome. Relative to the comparison group, for whom a greater increase in skin conductance was…

Using differentiated instruction in the classroom can be a challenge, especially when teaching mathematics. This book cuts through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Specific strategies and examples for grades Kindergarten - 8 are organized…

The purpose of this paper is to share the results of a fourteen-week study that focused on the effects of teaching mathematics instruction with the implementation of manipulatives in an elementary classroom. Students that fill our classrooms deserve the opportunity to use manipulatives to help them grasp all the different concepts that are taught…

The purpose of this paper is to present a summary of selected facets of geometry and measurement in elementary school programs and to describe curricula content options designed to demonstrate the feasibility of seeking high level outcomes and meanings for students with learning disabilities. While there are a multitude of published papers…

Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…

Five to seven percent of children experience severe difficulties in learning mathematics and/or reading. Current trials that are focused on identifying biological markers suggest that these learning disabilities, known as Developmental Dyscalculia (DD) and Dyslexia (for reading), are due to underlying brain dysfunctions. One ongoing controversy…

A paucity of research has directly compared empirically supported interventions to examine their effectiveness among students with different mathematics fluency skills. The purpose of this study was to compare the effects of two empirically supported interventions and a control condition on the mathematics fluency of 98 second and third grade…

The juxtaposition of articles by Ian Thompson and Ian Sugarman in "MT202" on addition and subtraction respectively engendered some bemused thoughts in this author, who for some years has been sheltered from controversy by retirement. In this article, Fielker shares some thoughts on addition and subtraction raised by Thompson and Sugarman in their…

Everyday, people face situations that call for adding, subtracting, multiplying, or dividing, and at least half of the time, these calculations are accomplished without the use of pen, paper, or calculators. Because figuring "in your head" is such an important life skill, it should have a regular role in classroom math teaching. This article…

We discuss mathematical tasks used in a first mathematics content course for elementary teachers at our university to foster a deep conceptual understanding of early arithmetic, including basic concepts of number, number relationships and strategies, and coordinating units of different rank. Our approach is to immerse our students in a base 8…

The purpose of this paper is to offer three alternatives to patterns or visualization used to justify division of fraction "algorithm" invert and multiply". The three main approaches are historical, similar denominators and algebraic, that teachers could use to justify the standard algorithm of division of fraction. The historical approach uses…

Introduction: For decades birth order and gender differences have attracted research attention. Method: Birth order, family size and gender, and the relationship with arithmetic achievement is studied among 1152 elementary school children (540 girls, 612 boys) in Flanders. Children were matched on socioeconomic status of the parents and…

Introducing an approach to detailed assessment involving videotaping clinical interviews, the authors highlight strengths of this approach for understanding children's thinking, informing instruction, and furthering professional learning. (Contains 4 figures.)