Generalization and Justification: The Challenge of Introducing Algebraic Reasoning Through Patterning Activities

摘要

The expectation that students be introduced to algebraic ideas at earlier grade levels places an increased burden on the classroom teacher to help students construct and justify generalizations. This study provides insight into the reasoning of 25 sixth-grade students as they approached patterning tasks in which they were required to develop and justify generalizations while using computer spreadsheets as an instructional tool. The students demonstrated both the potential and pitfalls of such activities. During whole-class discussions, students were generally able to provide appropriate generalizations and justify using generic examples. Students who used geometric schemes were more successful in providing general arguments and valid justifications. However, during small-group discussions, the students rarely justified their generalizations, with some students focusing more on particular values than on general relations. It is recommended that the various student strategies and justifications be brought to the forefront of classroom discussions so that students can examine the mathematical power and validity of the various strategies and justifications typically introduced by students.