Classrooms that used different instructional approaches to mathematics were observed, contrasting instruction that aimed to promote conceptual understanding rather than algorithmic skill with more conventional instruction. Results with 6 second-grade classrooms (135 students) suggest that relationships between teaching and learning are a function…

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)