In this article, the author describes a 200-year-old ladder problem that can carry learners to high levels of mathematical thinking and activity. This problem requires learners to go from a word problem to an equation to a graph and from there to a solution. As this problem of specifics is turned into a problem using variables, technology,…

Mathematics is both a beautiful language and the simplest systematic discipline men ever created. The simplicity of mathematical concepts almost guarantees that the facts it establishes about those concepts will also be elemental. Despite this simplicity, most people complain about the difficulty of mastering the subject and shun the study of…

High school students in the United States have been taking more challenging courses in recent years, but academic achievement has been stagnant. At the heart of the matter is the quality of curriculum, instruction, and assessment. Some courses tend to be more challenging in name than in practice. High schools also have a history of autonomy that…

In this study, I present an analysis of high school geometry curricula regarding mathematical proof opportunities. I examined eight U.S. high school level geometry textbooks, which were categorized into three main groups: technology-intensive, standards-based, and traditional curricula. I conceptualized "ideal" proving activity combining…

Presents 13 examples in which the intuitive approach to solve the problem is often misleading. Presents analysis of these problems for five different sources of misleading intuitive generators: lack of analysis, unbalanced perception, improper analogy, improper generalization, and misuse of symmetry. (MDH)

Because of the educational importance of mathematics and science, IEA's (International Association for the Evaluation of Educational Achievement) Trends in International Mathematics and Science Study, widely known as TIMSS, is dedicated to providing countries with information to improve teaching and learning in these curriculum areas. Conducted…

This paper was prepared in response to the Conference Board of Mathematical Sciences recommendations for the preparation of secondary teachers. It shows how using trigonometry as a conceptual tool in spreadsheet-based applications enables one to develop mathematical understanding in the context of constructing geometric representations of unit…

Presented are practical activities relevant to teaching mathematics in the American Indian culture that can be used in the non-Indian classroom. Discussed are tessellations, exercises that allow for artistic creativity and geometric exploration. The use of Pascal's triangle is included. (KR)

Describes a geometry course that integrates transformation geometry into traditional high school geometry. Discussion of the scope and sequence of the course includes the topics of proof, congruence, translations, rotations, reflections, dilations, quadrilaterals, parallel lines, and similarity. (MDH)

The purpose of this book is to introduce the geoboard as an effective tool that can help young children understand geometry as they develop spatial sense and mathematical thinking. Activities are clustered into three main sections: beginning geoboard explorations, exploring polygons, and coordinates. Blackline masters are included. (MKR)

This book contains materials to present mathematics concepts using cooperative learning activities. The first section explains how to make cooperative learning part of the mathematics curriculum. It includes an overview, instructions, activities for introducing cooperative learning to students and parents, guidelines for setting up groups, ideas…

This investigation is part of a combined research/curriculum development project in which children's learning is being examined in the context of developing and testing instructional units on 3-D geometry in grades 3, 4, and 5. There are two components to the article. First, the strategies and cognitive constructions that students utilize to…

Several approaches to the teaching of vectors are discussed, and a particular model is advocated. (SD)

Theorems about the hyperbola which are ordinarily introduced in calculus courses can be proved without using the calculus. (SD)

Common strategies for teaching proofs are discussed. Prerequisite behaviors, components of a learning hierarchy, are expressed in behavioral terms. The six categories are knowledge about logic, knowledge about the components of a deductive system, knowledge about proof strategies, knowledge of proof formats, proof completion, and generalization.…