The general purposes of a model are discussed, then seven papers are presented which demonstrate several different facets of the problems associated with constructing and using models of mathematics learning. In the first paper, the task addressed concerns how to incorporate developmental psychology into perceptions of what is happening in the…

A series of maps is presented for coloring with the fewest possible colors. (SD)

Rational points in the plane were defined as points having both coordinated rational. Students solved several problems linking rational points with lines, circles, and other geometric figures. (SD)

An elementary knowledge of geometry is shown to be helpful in problem solving, especially in that the shortest distance between two points is a straight line. (MN)

The technique of organizing data in tables to solve counting problems in geometry is illustrated in the solution of five problems. (MN)

The author has selected a number of episodes that illustrate some of the successes and failures of humanity's attempt to find the area of the circle and presents them as problem studies. (MN)

Discussed is an approach in which algebra and geometry are interwoven in a series of problems that develop one from another. The two main concepts are the algebraic concept of function and the geometric concept of the "family of quadrilaterals." (MNS)

This book is a guide to the development of mathematical talent in students in grades K through 8. The first chapter is on developing mathematical promise and considers characteristics of students who are mathematically promising, the goals of mathematics instruction, how to find and/or create good problems, models for increasing the numbers and…

This study explores students algebraic and geometric approach in solving tasks in functions and the relation of these approaches with complex geometric problem solving. Data were obtained from 95 sophomore pre-service teachers, enrolled in a basic algebra course. Implicative statistical analysis was performed to evaluate the relation between…

The integration of History in the educational practice can lead to the development of a series of activities exploiting genetic "moments" of the history of Mathematics. Utilizing genetic ideas that developed during the 14th century (Merton College, N. Oresme), activities are developed and mathematical models for solving problems related to uniform…

Much has been said on matter of aesthetics and mathematics--perhaps most commonly articulated in relation to properties such as "beauty" and "elegance," which are used to distinguish good from not-so-good mathematical products. Despite its importance in the work of mathematicians, it has been argued that aesthetics cannot be incorporated into…

This video offers an exciting four-part adventure about two teenage sleuths who discover the presence of an alien below New York City. As they try to make contact with the alien, they are confronted with a series of mathematical challenges that test their knowledge of the content strands recommended by the National Council of Teachers of…

This print guide to the "XY Encounter" video offers an exciting four-part adventure about two teenage sleuths who discover the presence of an alien below New York City, and expands upon themes presented in the video. As the students try to make contact with the alien, they are confronted with a series of mathematical challenges that test their…

This report describes a program for improving attitudes towards mathematics and problem solving in order to improve performance in these areas. The targeted population consists of two high school geometry classes. The school is located in a western suburb of a major mid-western city. The problems of negative attitudes towards mathematics and…