If the goal is to promote mathematical thinking and help children become flexible problem solvers, then it is important to show students multiple representations of a problem. Because it is important to help students develop both counting-based and collections-based conceptions of number, teachers should be showing students both number line…

Recent studies using a violation-of-expectation task suggest that preverbal infants are capable of recognizing basic arithmetical operations involving visual objects. There is still debate, however, over whether their performance is based on any expectation of the arithmetical operations, or on a general perceptual tendency to prefer visually…

The hypothesis investigated is that children with a reading disability understand and use sound-spelling correspondence rules less frequently in spelling than children with other learning disabilities (arithmetic disability) and normally achieving children. Results showed that subtypes of learning-disabled children use spelling strategies that are…

Working from Carolyn Kieran's categorization of "arithmetic" and "algebraic" thinkers, the article describes one eighth-grade "arithmetic" thinker's progress as she attempts to solve one- and two-step equations.

In this article, the author describes his experiences when he decided to teach university-level mathematics to Year 8. Handling a particularly able class who had investigated the isoperimetric problem, he was confident that the class was more than up to the challenge and adequately motivated. Using a Powerpoint, he delivered the lessons to the…

In this study, we investigated the development of basic effects that have been found in single-digit multiplication arithmetic: the problem size, five, and tie effects. Participants (9-,10-, and 11-year-olds and adults) performed a production task on simple multiplication. The procedure replicated Campbell and Graham's (1985) study ["Canadian…

Factors affecting performance on base-10 tasks were investigated in a series of four studies with a total of 453 children aged 5-7 years. Training in counting-on was found to enhance child performance on base-10 tasks (Studies 2, 3, and 4), while prior knowledge of counting-on (Study 1), trading (Studies 1 and 3), and partitioning (Studies 1 and…

This article describes how third-grade students developed an understanding of the equals sign and began to use relational thinking as they discussed true/false and open-number sentences. The sequence of instructional activities and children's responses to them are provided.

Background: In this study, 2 main hypotheses have been put forward to explain the variation in childhood intelligence or school performance by season of birth. In the first hypothesis, it is suggested that it is due to school policy concerning school entry, whereas the second suggests that a seasonally patterned exposure such as temperature,…

This submission contains the Proceedings of the 2007 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of New Brunswick in Fredricton, New Brunswick. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning.…

This document plus diskette product provides nine interactive puzzles and games that both teach and provide practice with simple addition and subtraction concepts. The activities address these skills through carrying in addition and regrouping in subtraction. The activities address cognitive skills such as problem solving, planning, visual pattern…

Mathematics research has discovered two elements that are consistently linked to student achievement: parental involvement and manipulative materials. This book offers a rich assortment of spinner, matrix, and card learning games which can be used in the classroom or at home. The concepts and skills range from whole number operations to geometry.…

This paper presents research conducted as part of the field test of the University of Chicago School Mathematics Project's (UCSMP) curriculum, Fifth Grade Everyday Mathematics. The UCSMP curriculum is one of the current reform programs funded by the National Science Foundation to implement the Standards of the National Council of Teachers of…

This computer software program helps to make classroom worksheets, take home assignments, and school mathematics tests easy to design and manufacture. The accompanying printed teaching guide provides technical information for setting up and using the program, along with sample worksheets and instructions on how to create them using the software.…

The objective of this pilot study was to directly compare operationalizations of Piagetian and behavioristic learning theories in terms of acquired skills and transferability of knowledge acquired. It was hypothesized that, in a population of kindergarten children, (1) Piagetian and behavioristic methods would be equally effective in teaching…