The author describes several physical problems whose solutions involve a helix. He argues that students remember "offbeat" approaches to important mathematical concepts. (SD)

In this article the reader will be able to download four spreadsheet tools that interactively relate symbolic and graphical representations of four different functions and learn how to create tools for other functions. These tools uniquely display the symbolic functional representation exactly as found in textbooks. Five complete lesson activities…

The authors provide a list of calculators which have a capacity for handling programs, and a list of programs for such calculators which are available at cost. They argue that the use of these materials at many levels of mathematics instruction enhances both motivation and understanding. (SD)

Instruments have been used for centuries in mathematical experience and in the teaching tradition as well. One example is cultural instruments inherited from tradition (e.g., rulers, abaci, compasses, curve-drawing devices) that have followed or anticipated the theoretical development of mathematics. In this article, the authors analyze two cases…

Analogical reasoning is frequently used in acquisition of mathematical concepts. Concrete representations used to teach mathematics are essentially analogs of mathematical concepts, and it is argued that analogies enter into mathematical concept acquisition in numerous other ways as well. According to Gentner's theory, analogies entail a…

This book contains 15 essays written between 1969 through 1983. The essays included are: (1) "Semantic Analysis of Verbs in Terms of Conceptual Situations"; (2) "'Because' and the Concepts of Causation"; (3) "The Development of Language as Purposive Behavior"; (4) "Adaptation and Viability"; (5) "On the…

The primary objective of this study was to provide an experimental model of children's representations of addition and subtraction concepts viewed as constructed schemes. How children with different counting schemes differ in their addition and subtraction concepts and how the types of problems children solve correlate with the addition and…

This monograph is one of a series describing goals, student outcomes, and instructional techniques for mathematics in the elementary and middle grades. Sections included are: (1) "Introduction"; (2) "Overview of the Kindergarten Mathematics Program"; (3) "Kindergarten Teaching Considerations" (considering variability, learning characteristics,…

This book introduces children to the numbers 1 through 16 (and some basic mathematical concepts) using the petals of a variety of flowers. The first part of the book contains 16 full-color photographs, each photograph showing a flower with 1 to 16 petals, with the number printed below the photograph. These pages can be used to introduce or…

This paper proposes an hypothsis describing how some college students incorrectly view semantically laden letters and provides both clinical and written data that supports that hypothesis. Several word problems were given to nine college math students. These students were then interviewed as they attempted to solve these problems. In addition to…

Structuring the algebra course to provide a link between a student's existing knowledge and the new topic being presented is discussed. Developing relationships among topics is suggested through examples describing a mathematical problem and effective teaching approaches. Stress is placed on teachers reflecting on mistakes pupils are likely to…

"More" and "less" were analyzed into two meaning dimensions, "occurence" and "quantity", which were hypothesized to be developmentally related to acts of addition and subtraction. (SBT)

The value and technique of pre-geometry and geometry instruction in the primary grades are discussed. Geometric concepts such as open and closed figures, connectedness, similarity, congruence, straightness, and angle are presented through suggested activities, lesson plans, and evaluation procedures. (SD)

Activities related to content areas important to the primary mathematics program, but outside the scope of arithmetic, geometry and measurement, are presented. Topics include relations, number sentences, solving sentences, logic, probability, statistics, number theory, and the system of integers, Inclusion of these topics is justified and…

Reports on the second place win in the sixteenth international mathematics olympiad by the eight member United States team. The competitors reported that they gained their mathematical competence in spite of their schools. (GS)