Guided by Shulman, 1986 and Shulman, 1987 tripartate model of teacher expertise [subject matter knowledge (SMK), pedagogical content knowledge (PCK), and general pedagogical knowledge (GPK)], the present study examined 162 U.S. and Chinese 3rd grade mathematics teachers' expertise in teaching fractions. Results show that U.S. teachers lag…

The purpose of this study was to examine the effects of actively categorizing math problems on the math problem solving performance of students with and without attention deficit disorder (ADD). To this purpose, 52 fifth and sixth grade students were involved in actively categorizing or noncategorizing (control) tasks followed by two problem…

From a very young age, shoes for boys tend to be wider than shoes for girls. Is this because boys have wider feet, or because it is assumed that girls are willing to sacrifice comfort for fashion, even in elementary school? To assess the former, a statistician measures kids' feet. (Contains 2 tables and 3 figures.)

The overall purpose of this paper is to describe a practical and useful approach to mathematics assessment that is meaningful to teachers, students and families. The format is highly flexible, yet specifically designed to provide detailed information as to the performance characteristics of the student and a variety of curricula and instructional…

Math in a Cultural Context (MCC) is based in traditional Yup'ik cultural values and ways of knowing and representing the world, which provide access to math concepts through hands-on exploration and active problem solving. This case illustrates how a novice and outsider teacher successfully implemented MCC in a classroom with predominantly…

EQUALS is a teacher advisory program that helps elementary and secondary educators acquire methods and materials to attract minority and female students to mathematics. The program supports a problem-solving approach to mathematics, including having students working in groups, using active assessment methods, and incorporating a broad mathematics…

This manual presents instructional design strategies and sample student activities for creative problem solving. The ideas and suggestions are intended to support both students' mathematical attainment and their development of creative ability. The book begins with an introduction followed by discussions of unit design strategies and activity…

There are selected philosophies in the teaching of mathematics which can provide guidance to the teacher in developing the curriculum and also a framework for teaching and learning. This paper discusses four such philosophies of teaching mathematics: Idealism, Realism, Experimentalism, and Existentialism. Idealism stresses that students live in an…

A study on sampling errors of variance components was conducted within the framework of generalizability theory by P. L. Smith (1978). The study used an intuitive approach for solving the problem of how to allocate the number of conditions to different facets in order to produce the most stable estimate of the universe score variance. Optimization…

This book is designed to provide middle-grade mathematics teachers with ideas for enlivening instruction to help students acquire a sense about numbers. Guided classroom discussions for writing opportunities centered on the theme of problem solving are provided. Following an introduction, chapters include the following: Counterintuitive Problems;…

This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 4-6, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, whole numbers, number theory, fractions, decimals, geometry, ratio, proportion, percent, probability, sets, and…

Brief mystery stories such as the three presented here can be used to help students develop critical reading and thinking skills, as well as to introduce the notion of indirect proof. (SD)

Students were given the problem: Given a deck of cards in a certain order, after how many shuffles will it return to its original order? They worked with small decks of cards to develop a general formula, but were unhappy with the results. (SD)

A series of problems involving number theory, the law of cosines, and geometric interpretations of solutions to equations is discussed. (SD)

Four problems in which elementary mathematics can be used in constructing models are described. (SD)