Although the average, or arithmetic mean, has a rich conceptual meaning, it is often defined simply as the outcome of a procedure. The purpose of this study was to compare the nature and extent of the procedural and conceptual understandings developed by two groups of students who received different forms of instruction, one based on the…

Compares the development of two students' understanding of addition and subtraction. One student's understanding is based on memorized rules and the other's on understanding the concept of place value. Discusses the effects of different goals for instruction and the importance of understanding place value. (MDH)