An algorithm is first defined by an example of making pancakes and then through discussion of how computers operate. The understanding that human beings bring to a task is contrasted with this algorithmic processing. In the second section, the question of understanding is related to learning algorithmic performance, with counting used as the…

The purpose of this project was to determine if the method of subtraction of integers taught to seventh grade students affected their mathematics achievement or retention. Computation, concept, and problem-solving sections of the California Achievement Test were given as pretests and posttests. An investigator-constructed test of the addition and…

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…

This issue contains abstracts and critical comments for 11 articles. Three articles focus on problem solving; the remainder concern understanding of the equals sign, mathematical structure, mathematical abilities, the role of language in tasks involving sets, sex differences in mathematical errors, subtraction, algorithms as schemes, and…

The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented:…