This article describes a mathematics unit developed with second-grade students based on the story, "Grandpa's Quilt." The activities encourage students to make connections with a number of areas of mathematics, particularly patterns and relationships, measurement, geometry, and spatial sense as well as multiplication activities. (Contains 7…

This article describes how teachers learn to implement problem solving in their classrooms through participation in an evolving problem-solving class. (Contains 3 figures.)

We present an expository account of the development of the theory of binary quadratic forms. Beginning with the formulation and proof of the Two-Square Theorem, we show how the study of forms of the type x[squared] + ny[squared] led to the discovery of the Quadratic Reciprocity Law, and how this theorem, along with the concept of reduction relates…

Traditionally, primary schools place minimal emphasis upon relations and transformations as objects of study. In their research, the authors have found the young children can engage in conversations about equivalence and equations (Warren & Cooper, 2005a) and functional thinking (Warren & Cooper, 2005b). Fundamental to relations and…

The authors provide activities for overcoming some fraction misconceptions using calculators specially designed for learners in primary years. The writers advocate use of the calculator as a way to engage children in thinking about mathematics. By engaging with a calculator as part of mathematics learning, children are learning about and using the…

This article describes a problem-centered curriculum for grades 9-12, using problem sets developed by a mathematics department and designed to take the place of textbooks. The students discover mathematical concepts in the context of the problems and activities in the materials.

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an…

This paper will describe results concerning the impact of the PD on the three primary study outcomes: teacher knowledge of rational number topics, teacher instructional practices, and student achievement in rational number topics. All analyses are completed. However, the results cannot be shared at this time because the report is currently under…

The research objectives were to identify the middle level mathematics teachers' conceptions of mathematics teaching and learning and ascertain changes in their conceptions and instructional behavior at the end of a three-year professional development (PD) project. These changes were studied through the qualitative analysis of their reflective…

Aligned with recent changes to syllabuses in Australia is an assessment regime requiring teachers to identify what their students "know" and "can do" in terms of the quality of understanding demonstrated. This paper describes the experiences of 25 secondary science and mathematics teachers in rural schools in New South Wales as…

The purpose of this article is to discuss the current shortcomings in science and mathematics education in Malaysia. The use of cooperative learning as an alternative to traditional method is emphasized. Cooperative learning is grounded in the belief that learning is most effective when students are actively involved in sharing ideas and work…

The purpose of this article is to discuss the current shortcomings in science and mathematics education in Malaysia. The use of cooperative learning as an alternative to traditional method is emphasized. Cooperative learning is grounded in the belief that learning is most effective when students are actively involved in sharing ideas and work…

This mixed-methods study assessed the effects of Enhanced Anchored Instruction (EAI) on the math performance of adolescents with learning disabilities in math (MLD). A quasi-experimental pretest-posttest control group design with switching replications was used to measure students' computation and problem-solving skills on EAI compared to control…

This article discusses how math skills, teamwork and higher-level thinking come together when students create strategic board games. In this article, the authors provide a glimpse of what it was like to be part of "To the Sun!," a game designed by students in the fifth-grade class at Olive Martin School in Lake Villa, IL. Students combined a math…

A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…