Some Issues in the Psychology of Mathematics Instruction

Given a large proportion of students failing to learn basic skills in mathematics, the problem of improving mathematics learning may be illuminated by an examination of contemporary learning research and theory. Three major phases can be seen in the performance of a mathematical task: translating from a verbal problem statement to a mathematical expression, carrying out an operation on the expression, and validating the solution. Less attention in instruction and research should be given to the classification of tasks as abstract or concrete, and more attention to the deliberate teaching of correct rules and the advantages of making computational operations automatic. Each performance phase has its implications for instruction, and all could be more fully addressed by research.