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…

Pattern recognition is a critical component of success in mathematics. Students at all levels should be provided with opportunities to investigate and uncover patterns throughout their mathematical careers. Further, they should be allowed to explore situations in which pattern recognition plays a vital role in the construction of important…

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…

"Learning by doing" in pursuit of real-world goals has received much attention from education researchers but has been unevenly supported by mathematics education software at the elementary level, particularly as it involves arithmetic word problems. In this article, we give examples of doing-oriented tools that might promote children's ability to…

In the first part of this article, we briefly present the context of mathematics education in Italy and its specific programs, teaching and assessment methods, use of psychological concepts, and policies in favor of pupils with difficulties. We illustrate the importance and the role of mathematics teachers' associations. In the second part, we…

The purpose of this paper is to provide researchers with a shared framework, terminology and tool to improve the coherence of research into learning mathematics with CAS and to assist its findings to accumulate into a significant body of knowledge. Experience with calculators in arithmetic led to a framework for number sense. There is an obvious…

Groups of first-grade (mean age = 82 months), third-grade (mean age = 107 months), and fifth-grade (mean age = 131 months) children with a learning disability in mathematics (MD, n=58) and their normally achieving peers (n = 91) were administered tasks that assessed their knowledge of counting principles, working memory, and the strategies used to…

An alternating treatments design was used to compare the effects of baseline, interspersed brief problems, and interspersed brief problems plus token reinforcement on students' endurance while completing math worksheets. By pairing the completion of brief problems with token reinforcement, the role of problem completion as a conditioned reinforcer…

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…

Math is about the relationship between numbers. Right answers are not the only thing to look for when examining students' work in mathematics. Looking at how children solve computation problems can give teachers insight into their thinking and help determine what math skills they already know and what they still need to learn. The author contends…

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,…

Through her work as a consultant, Burns has found that a handful of students in all classes lack an adequate foundation in basic math concepts and lag far behind their peers in both understanding and skills. Students who lack a foundation on which to build new learning are generally not well served even by well-planned, differentiated instruction;…

Can the salience of gender identity affect the math performance of 7-8 year old girls? Third-grade girls and boys were required to solve arithmetical problems of varied difficulty. Prior to the test, one half of the participants had their gender identity activated. Results showed that activation of gender identity affected girls' performance but…

The paper discusses the results of a research project based on the field testing of a course aimed at developing arithmetic problem solving skills in primary school pupils. The course was designed to incorporate e-learning techniques, including the use of ARI@ITALES authoring tools. These tools allowed the integration in the course of…