Instructional Tasks, Classroom Discourse, and Students’ Learning in Second-Grade Arithmetic

To investigate relationships between teaching and learning mathematics, the six second-grade classrooms in one school were observed regularly during the 12 weeks of instruction on place value and multidigit addition and subtraction. Two classrooms implemented an alternative to the more conventional textbook approach. The alternative approach emphasized constructing relationships between place value and computation strategies rather than practicing prescribed procedures. Students were assessed at the beginning and the end of the year on place value understanding, routine computation, and novel computation. Students in the alternative classrooms, compared with their more traditionally taught peers, received fewer problems and spent more time with each problem, were asked more questions requesting them to describe and explain alternative strategies, talked more using longer responses, and showed higher levels of performance or gained more by the end of the year on most types of items. The results suggest that relationships between teaching and learning are a function of the instructional environment; different relationships emerged in the alternative classrooms than those that have been reported for more traditional classrooms.