This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform--which was eventually itself replaced in the longer term--provides some keys to understanding the influence of mathematical theories on…

The transition from natural to rational numbers is difficult for most elementary school children. A major cause for these difficulties is assumed to be the "conceptual change" they need to undergo in order to see that several natural number properties do not apply to rational numbers. To appropriately handle pupils' difficulties,…

A cognitive schema is a mechanism which allows an individual to organize her/his experiences in such a way that a new similar experience can easily be recognised and dealt with successfully. Well-structured schemas provide for the knowledge base for subsequent mathematical activities. A new experience can be assimilated into a previously existing…

In this paper, we analyze and compare two didactical designs for introducing primary school pupils to proportional reasoning in the context of plane polygons. One of them is well-documented in the literature; the other one is based on our own data and is accordingly presented and discussed in more detail in this paper. The two designs come from…

In this article we consider how elementary education students' views of mathematics changed during their mathematics methods course. We focus on four female students: two started the course with mainly positive views of mathematics and a task orientation, two with negative views of the subject and an ego-defensive orientation. The biggest change…

This article presents a Vygotsky-inspired analysis of how a teacher mediated a "thinking aloud" whole-group discussion in a 6th grade mathematics classroom. This discussion centered on finding patterns in a triangular array of consecutive numbers as a phase towards building recursive and direct algebraic formulas. By a "thinking aloud" discussion…

This paper draws on data from the development of annual national mathematics assessment materials for 7-year-old pupils in Wales for use during the period 2000-2002. The materials were developed in both English and Welsh and were designed to be matched. The paper reports on item analyses which sought items that exhibited differential performance…

Trainee teachers, new and non-specialist teachers of elementary mathematics have a tendency to avoid thought about reasons in mathematics. Instead, they tend to favour the development of computational skill through the rote application of procedures, routines and algorithms. Could elementary mathematics textbooks serve as models of practice and…

This paper examines 6th grade children's local conceptual development and mathematization processes as they worked a comprehensive mathematical modeling problem (creating a consumer guide for deciding the best snack chip) over several class periods. The children and their teachers were participating in a 3-year longitudinal teaching experiment in…

The value of including a unit on graph theory in the elementary school mathematics curriculum is discussed. A module for use in teaching graph theory to elementary school teachers is presented. (SD)

The author's theories concerning the learning of mathematical concepts are outlined. (SD)

This paper proposes a semantic analysis in which meanings of word problems are structures that include class and order relations, and suggests a hypothesis of developmental levels that can account for children's performance of these problems at various ages. The different kinds of problems vary in the complexity of semantic structures and the…

Two experiments on the translation of verbal expressions into mathematical expressions are described. The author concludes that the usual way of training students to solve arithmetic word problems is inadequate. (SD)

The author interprets several mathematical concepts as groupings using Piaget's definition. He also discusses (briefly) the implications for primary education. (SD)

Four geoboard activities for elementary school students are described. (SD)