Uses the modern development of mathematics education in the United States as background for the analysis of the influence of mathematics philosophy on mathematics education. Discusses the problem of how to develop the subject of philosophy of mathematics education, regarded as an impetus from mathematics education, to the further development of…

Examines the impact of the recent shift towards calculating and computing tools on the nature of learning in traditionally difficult curriculum area. Focuses on the use of graphic calculators by undergraduates taking an innovative new mathematics course at Open University. Indicates that graphic calculator technology acted as a critical mediator…

Presents scores teachers assigned to samples of actual students' problem-solving work and rationales teachers provided for these scores which may reflect teachers' values relative to aspects of mathematical problem solving. Concludes that when teachers can express rationales for scoring students' work, they are able to justify their evaluation of…

Describes some real-life problem situations and the mathematical applications used to solve the situations in order to promote an inquiring and problem-posing approach. (MKR)

Poses several questions about problem solving and provides six reasons that support how problem solving enhances the development of numeracy and mathematical thinking. (ASK)

Offers a tangible suggestion for how dot paper can be used to implement an exploratory approach to problem solving in middle school geometry. Presents some intriguing mathematical tasks that demonstrate the elegance of mathematics, the usefulness of dot paper as a teaching tool, and the value of divergent thinking approaches to problem solving.…

Discusses ways of using six literature books to study mathematics in which students read about mathematics in the context of literature to explore problems embedded in the context of a story. (ASK)

Focuses on the use of different strategies for solving sequences of interrelated problems. Discusses some useful techniques a teacher could employ to design problem chains. (Contains 20 references.) (ASK)

Presents some results of a study on teaching negative numbers. Focuses on the identification of addition and subtraction, the use of the number line, additive problem solving, and the possibility of following several sequences of numerical extensions. Indicates the importance of previous ideas on positive numbers and how these ideas influence the…

Knowledge in academic disciplines is being challenged by the instrumentality of workplace learning. However, the way math is taught in vocational education is often irrelevant or infantilized. To satisfy the need for a creative, problem-solving work force, mathematical disciplinarity is needed. (Contains 68 references.) (SK)

Three sample physics problems are presented in this article. The solutions to the three problems addresses a major student difficulty in problem solving--knowing where to begin. The first suggested step is to begin by stating what is asked for. Step 2 is identifying the fundamental physics that underlies the problem situation. Step 3 is isolating…

Students should be given an opportunity to explore and conjecture with the help of new technology to become good problem solver. Ron Mclister, while using the Geometer's Sketchpad to explore the Pythagorean theorem, came upon a nice result about the relationship of some geometrical patterns.

Students solve a geometric problem of measuring polygons with the help of proportional reasoning. Thus the importance of conceptual reasoning is emphasized as a highly efficient technique for teaching and strengthening mathematical content.

A Mandelbrot mathematical set is an object with endless borders, and in the present exercise a graphing calculator is used to identify and examine the set points. The significance and power of technology is also displayed in the understanding and solving of problems.

The way in which a mathematical problem was used as a vehicle to introduce the joy of mathematical research to a high school student is demonstrated. The student was interested in learning about other classical problems delighting an eager high school student.