The topic of teaching troubleshooting is examined as an example of the teaching of cognitive strategies for technical problem solving. The traditional behavioral approach to teaching troubleshooting has essentially been algorithmic. Recent cognitive research suggests an approach founded first on task analysis and characterized by: (1) analysis of…

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

The concept of an algorithm derives from the physical sciences, but it has often been misunderstood and misapplied in the social sciences and in education. The theoretical and practical significance of algorithms stems from their applicability to problems of learning, instruction, and instructional design, and they may potentially provide the…

Forty-five children aged four-and-a-half to five-and-a-half years old were given number conservation tasks in three conditions: (1) a count condition in which children were helped to count each set after the transformation; (2) a match condition in which children were helped to connect by a string each animal with its peanut; and (3) the standard…

This study was designed to follow up earlier work on mapping instruction. The two main goals were to: (1) test the effectiveness of mapping instruction as a general cure for "buggy" subtraction algorithms, and (2) explore two alternative explanations of how this new form of instruction works. It was hypothesized that mapping cures bugs…

The use of counting for subtraction was investigated. Counting for subtraction is related to counting-on for addition and to four skills: the ability to use the subtrahend cardinality to gain entry into the count sequence, the ability to use the minuend cardinality to gain entry into the count sequence, the ability to use the count sequence to…

The results of an investigation of the development of children's knowledge of addition and subtraction concepts before they start school are detailed. The purpose of the study was to test the predictions of the three-stage model about the distinctions between the last two stages. Twenty-four children participated in the investigation. None of…