Describes an exploratory geometry course in which students were challenged to develop their own axiomatic system instead of using a textbook. They developed a Euclidean system and learned to write proofs as a natural consequence of building the system. (13 references) (MKR)

Presents an activity to analyze the data from the Challenger explosion to help students understand the critical role of statistics in decision making and the importance of considering all available data. (MKR)

Two teachers compared eighth graders who solved math story problems using a strategies approach (several strategies), a strategies and traditional approach, or a traditional approach. Achievement test results improved with the strategies approach. Students who learned strategies considered themselves good problem solvers who liked challenge and…

Described are classroom strategies chosen to elicit greater involvement by students in the learning process and to furnish opportunities for practice in critical thinking. The advantages and disadvantages of this teaching approach are discussed. (CW)

Compared are the van Hiele levels of geometric thinking and the geometry curriculum recommended by the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics. Activities which illustrate the various levels are provided by grade level with procedures. (CW)

The relationship between mathematics and music has been investigated for thousands of years. Presented are the mathematical features of music through a study of melody, harmony, and rhythm, and the musical features of mathematics through a study of pattern, ratio, modular arithmetic, Pythagorean triples, and number sequences. (MDH)

Students (n=105) enrolled in a college remedial mathematics course participated in a one-semester experiment to determine whether cooperative learning would help students increase their problem-solving skills in mathematics. Results indicated significant differences in favor of students using cooperative learning in solving word problems in…

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

Analyzes how practice in mathematics education might be reformed toward a professional practice. Argues that conventional school mathematics be replaced by a constructivist school mathematics based on children's use of their schemes of actions and operations in learning situations as illustrated through examples of the numerical schemes of…

Discusses an activity-based, exploratory-centered model of instruction based on the Piagetian theory of developmental learning that bridges the gap between the expected and actual levels of student reasoning. Applies the method to learning the mathematical concepts of circumference, area and volume, and division by zero. (22 references) (MDH)

Presents a method for demonstrating addition and subtraction of integers on the number line in a way that distinguishes between subtraction and negative numbers. The model depicts the sign of the number by forward or backward movement on the number line. Subtraction is illustrated by a turning around movement. (MDH)

Discusses a classroom presentation using a Tonka toy truck's forward and backward motion that (1) develops a graphical representation of the truck's one-dimensional motion; (2) creates graphs representing constant velocity; (3) leads students to a definition of average velocity; and (4) introduces the concept of instantaneous velocity. (MDH)

Proposes the use of humor and the personalization of word problems by inserting students' names in the problem statement as methods of gaining students' attention. Illustrates their use in a mixture problem and the Tower of Hanoi problem. (MDH)

Presents three problems that help students develop a repertoire of heuristics and persistence in problem solving: the water-jug problem; the missionaries-and-cannibals problem; and the census-taker problem. Discusses methods to encourage students to persist. (MDH)

Presents five activities for multiple grade levels and family use that connect mathematics and football by using the Super Bowl. Mathematical concepts involved in the activities include number sense, geometry, measurement, statistics, estimation, and problem solving. Includes reproducible worksheets. (MDH)