Many important human activities involve accomplishing goals without a script. There is no formula for true problem-solving. Heuristic, cognitive "rules of thumb" are the problem-solver's best guide. Learners should understand heuristic tools such as means-end analysis, working backwards, successive approximation, and external representation. Since…

Describes two experiments that investigate how "buggy algorithms" in multi-digit subtraction are used. The first experiment tested third grade students (N=110) and repeated the test two years later. The second experiment tested students in grades 3-6 (N=301). Contains 21 references. (DDR)

Teaching which does not in any significant way address the genesis of mathematical ideas hides the fact that mathematics is created by people; that it involves intuition, exploring, conjecturing, and reasoning; and that it is purposeful. Such teaching can give students appearance that much of mathematics is very arbitrary; it just falls from the…

Data from the 1977-78 mathematics assessment of the National Assessment of Educational Progress (NAEP) on the use of calculators are discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

The main objective of this study is to construct models based on strategies students use to solve chemistry problems and to show that these models form sequences of progressive transitions similar to what Lakatos (1970) in the history of science refers to as progressive 'problemshifts' that increase the explanatory' heuristic power of the models.…

Arguments for and against the use of computers in mathematics classes have centered on whether students benefit from or are merely hindered by practicing computational skills. This paper claims that the true essence of mathematics lies not in computation, basically a mechanical operation, but in problem-solving. Since no amount of computational…

Examples of student-developed methods for dividing fractions and dividing and multiplying whole numbers are presented. Both are selected to show mathematical creativity in general mathematics students which would often be overlooked. (MP)

Defines one approach to problem solving in terms of student use of algorithms to find their solutions and gives examples. Discusses how problems and algorithms relate to each other. Describes strategies for teaching problem solving using algorithms. (CW)

The reasons people most often give for the failures of U.S. schools involve poverty, racial inequality, and a host of social problems. This paper argues that even if all these conditions were remedied, the schools would not produce many more people with the ability to think than they do today. Teachers, who are usually able to think, do not know…

This 1998 yearbook aims to stimulate and answer questions that all educators of mathematics need to consider to adapt school mathematics for the 21st century. The papers included in this book cover a wide variety of topics, including student-invented algorithms, the assessment of such algorithms, algorithms from history and other cultures, ways…

The need for incorporating algorithmics into mathematics instruction is presented. The proliferation of computers is seen to have made the designing of algorithms an essential skill. Examples are given, and the view that mathematics will lose much prestige and importance if algorithmics is not integrated into it is presented. (MP)

Advantages of using flow charts are listed. Flow charts for adding and subtracting fractions and for polynomial division are provided. Rules for constructing flow charts are given. (DT)

Discusses the use of a historical profile for illustrating the significance of the mathematical components of scientific laws. Addresses the need for the purposive use of scientific laws rather than the blind substitutionary procedures characteristic of most problem solvers. Claims the approach has the potential for increasing female participation…

This yearbook provides the mathematics education community with specific perceptions about discrete mathematics concerning its importance, its composition at various grade levels, and ideas about how to teach it. Many practical suggestions with respect to the implementation of a discrete mathematics school program are included. A unifying thread…

About 25 children in each of grades 3, 5, 7, 9, and 11 were tested in their ability to solve linear syllogisms, such as: John is taller than Mary. Mary is taller than Pete. Who is tallest--John, Mary, or Pete? Response latencies and error rates decreased across grade levels and sessions. Component latencies also generally decreased with increasing…