CHANGES IN SCHOOL STUDENTS’ OBSERVATIONS AND REASONING DURING A 4-PHASE TEACHING SEQUENCE

Abstract

We examine the written responses of fifteen students (aged about 14½ years) to a homework task and their responses to the same task in a subsequent lesson. Students were asked to make observations about the sum of three consecutive numbers and to explain why they think these are true, thereby giving students the opportunity to engage in structural reasoning. The teaching sequence had four phases designed to allow students to make, share and develop their observations and reasoning, and we found a clear improvement in the quality of students’ responses. As far as students’ reasoning is concerned, this suggests limitations may stem at least in part from a lack of familiarity with the nature of mathematical reasoning.