This document contains informal geometry explorations that provide students with opportunities to investigate the environment from a geometric perspective, construct connections between related mathematics and other content areas, and solve problems in a geometric context. The activities provide experiences that develop curiosity, understanding,…

This paper describes the use of radical constructivism as a basis for curriculum reform in university mathematics courses and reports on research conducted on two of the courses developed, one in geometry and one in problem solving. The theoretical underpinnings of the project are described along with the implications for course design and…

This simple example demonstrates the physical significance of similarity solutions and the utility of dimensional and asymptotic analysis of partial differential equations. A procedure to determine the existence of similarity solutions is proposed and subsequently applied to transient constant-flux heat transfer. Short-time expressions follow from…

This is unit eleven of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include coordinate geometry and problem analysis. (MP)

The research reported in this paper was designed to analyze the incidence of use of higher-order rules by students solving geometric construction problems. A carefully selected set of construction problems was subjected to rigorous a priori analysis by mathematics educators to determine what basic and second-order rules might be used by able high…

This article examines the Pythagorean Theorem from a geometric point of view by suggesting some natural extensions of the theorem. The use of a more general theorem to prove a difficult one is suggested, where possible. The article includes figures and proofs. (Author/MA)

This paper describes the nature and use of a computer-assisted sequence of instruction in college-level mathematics. Units in differential and integral calculus and geometry are described. The authors claim that students acquire increased confidence in their knowledge and problem-solving ability. (SD)

Four stages of problem solving are believed to occur in programing. Spirolaterals are discussed as specific examples of programing activity that have mathematical and programing interest. The BASIC programing language is used on the Apple II computer to provide examples of possible solutions to the problems posed. (MP)

The following ideas are included: (1) solving a quadratic equation geometrically by completing the square, which helped a class of secondary physics students understand the formulas; and (2) a way of teaching factoring of quadratic trinomials that is based on the behavior of odd and even numerals under addition and multiplication. (MP)

Adults' geometric analogy solution was investigated as a function of systematic variations in the information structure of items. Latency data from verification of true and false items were recorded. A model incorporating assumptions about the form of item representation, working memory factors, and processing components and strategies was…

The process that Hippasus of Metapontum (ca. 470 B.C.) may have used to discover irrational numbers is reconstructed. (MP)

A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)