Developmental mathematics students are generally students who are at risk of dropping out of school because of various factors. Many are nontraditional students who have jobs and families; others are traditional students who lack the skills needed to succeed in the college environment. Math anxiety, fear, and intimidation often affect…

Using Kazemi's and Stipek's (2001) framework of classroom practice, the discourse between students enrolled in a mathematics-for-teachers course and their instructor is examined. The teacher's practice is in transition from a focus on having students share multiple strategies toward a practice that additionally includes the mathematical…

In this paper we consider geometrical construction problems and their role in mathematical education. Owing to the main features of construction problems (accuracy in making conclusions, strict structure, rigorous language and constructivistic nature), they can be fruitfully used in teaching mathematics and computer science. We shall try to shed…

Background: The implementation of the nine-year integrated curriculum in the primary and secondary schools of Taiwan represented, in practice, a great change to the nature of school teaching. This was mainly due to the fact that the new scheme for the curriculum required teachers to collaborate with one another, when they had been teaching…

The study describes teachers' collective work in which they developed deeper understanding of their own students' mathematical thinking. Teachers at one school met in monthly workgroups throughout the year. Prior to each workgroup, they posed a similar mathematical problem to their students. The workgroup discussions centered on the student work…

In the context of U.S. and world wide educational reforms that require teachers to understand and respond to student thinking about mathematics in new ways, ongoing learning from practice is a necessity. In this paper we report on this process for one teacher in one especially productive year of learning. This case study documents how Ms. Statz's…

We describe an urban school initiative aimed at teachers' professional development with the goal of increasing their mathematics content knowledge and helping them improve their practice. In the lowest performing schools, mathematics specialists were employed to teach only mathematics in upper-elementary grades (ages 9-12). One aspect of this…

Many students enter mathematics courses with a poor attitude toward mathematics (Gal & Ginsburg, 1994), making attitude as important a consideration as achievement in mathematics (Cognition and Technology Group at Vanderbilt (CTGV), 1992; Marsh, Cairns, Relich, Barnes, & Debus, 1984; Sedighian & Sedighian, 1996). Pedagogical agents are often…

Negative numbers extend our number line and greatly simplify our calculations, but sometimes students struggle with the concepts. These fun activities will help kids to make sense of the "other half" of our number system.

This article addresses the issue of helping students who work collaboratively on mathematical problems with the aim of raising the level of their mathematical understanding and competence. We investigated two kinds of teacher interventions aimed at helping students. The rationale of these interventions was based on a process model for interaction…

In this paper, we use the theory of didactic situations to characterize a mathematics teaching practice, currently used in secondary schools in France, which we have called "interactive synthesis discussion." We have studied this practice in ordinary classes, i.e. classes where the researcher intervenes neither in the preparation nor in…

When we consider the gap between mathematics at elementary and secondary levels, and given the logical nature of mathematics at the latter level, it can be seen as important that the aspects of children's logical development in the upper grades in elementary school be clarified. In this study we focus on the teaching and learning of "division with…

In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's own representations (in particular "diagrams") of mathematical problems. As a paradigmatic…

Explaining new ideas to oneself can promote transfer, but how and when such self-explanation is effective is unclear. This study evaluated whether self-explanation leads to lasting improvements in transfer success and whether it is more effective in combination with direct instruction or invention. Third- through fifth-grade children (ages 8-11;…

Good early mathematics is broader and deeper than early practice on "school skills." High-quality mathematics should be a joy--not a pressure. It can emerge from children's play, their curiosity, and their natural ability to think. This article describes the areas of mathematics that young children can learn, and encourages elementary teachers to…