The processes and procedures used by expert mental calculators are identified from a literature review. Experts are characterized by knowledge of a variety of methods, ability to recall numerical equivalents, and ability to remember the numbers involved in various stages of calculations. (MNS)

The role of mental discipline theory in the history of mathematics education is considered. The author argues that we now remember mental discipline theory only as a caricature of what it was; moreover, it persists among both teachers and researchers. (MNS)

This bulletin concerns the role of memorization in mathematics instruction. Sections of the bulletin are devoted to discussions of: old math vs. new math; the importance of memorization ability on mathematics learning; misconceptions about memory; how to enhance the memory, including short-term vs. long-term memory systems, attention, interest,…

Previous studies indicate that many early elementary school children have the misconception that whole number subtraction is a commutative operation. The degree and character of this subtraction error was investigated in this longitudinal study. Results obtained from three groups of students with different number abilities provided further…

Provides examples which suggest the importance of giving children opportunities to create their own arguments and of allowing them the opportunity to verbalize these arguments in clinical interviews. Also indicates that if time is spent interviewing children individually, instruction can be matched to the way they think. (JN)

This monograph presents research findings from a series of 11 studies conducted in grades 5 through 10 on the role of games in learning mathematics. The first chapter considers "What is learning from a game?" and includes two examples of mathematical instructional games, with a definition of such games, cognitive effects, game-related…

How the author moved from concern about research to development of prescriptive models of heuristic problem solving and the exploration of metacognition and belief systems is discussed. Student beliefs about problem solving, and their corollaries, are included. (MNS)

Twenty-nine students in grades four, six, and eight were asked to find solutions to fraction equivalence problems and to verify their solutions using discrete material. Discontinuities were observed between strategies students used for producing solutions and supporting knowledge grounded in physical reality. (Author/MNS)

An awareness of negative effects of mind set is promoted, and ways to minimize harmful sets are suggested. Visual perception, Eistelung effect, and functional fixedness are discussed as categories of potentially negative mind sets, with several examples given of each. Fixation combinations are noted as well. (MP)

This monograph provides teachers with a wide range of articles on the teaching of problem solving in the mathematics classroom. The first section, on Understanding the Problem, includes articles which provide a sense of the "problem" of teaching problem solving. The second section, on Devising a Plan, provides suggested plans for…

Examines principles which can be applied to determine how hints can be used effectively in problem-solving. Conscious and unconscious hints, timing of hints, expected functions, and teaching are discussed. Conscious hints are explained in detail with suggestions and references. Charts are included for types, timing, and expected functions. (DH)

Indicates how thinking strategies help children learn the basic facts for whole numbers, listing several strategies involved in addition, subtraction, multiplication, and division. Also lists books and articles for illustrations of the strategies and how to teach them, and two sources for research findings on thinking strategies for basic facts.…

Some central issues relating to the nature of mathematical activity in schools are explored. Motives for including multicultural mathematics topics are discussed, as are using mathematics to educate, culture-based cognitive problems, and the sociopsychological impact of learning mathematics. (MNS)

This book details the findings from a research team that used cognitive principles and a large range of experiments to devise a variety of instructional designs. Their recommendations are based on 20 years of objective, published research. Although the program focused on technical subjects, the findings can easily be applied to a range of…

How mathematics subject matter can be enhanced through the scientific reasoning method, how this integration can be achieved, adaptations needed for a modified approach, and resulting attainments are all considered. Prime numbers using the Sieve of Erastosthenes are the vehicle through which the approach is described. (MNS)