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Conjectures and Refutations in Grade 5 Mathematics

David A. Cramer 

January 2002, Volume 33, Issue 1, Page 5

Abstract:
This article makes a contribution toward clarifying what mathematical reasoning is and what it looks like in school contexts. It describes one pattern of reasoning observed in the mathematical activity of students in a Grade 5 class and discusses ways in which this pattern is or is not mathematical in order to clarify the features of a pattern of reasoning that are important for making such a judgment. The pattern  involves conjecturing a general rule, testing that rule, and then either using it for further exploration, rejecting it, or modifying it. Each element of reasoning in this pattern is described in terms of the ways of reasoning used and the degree of formulation of the reasoning. A distinction is made between mathematical reasoning and scientific  reasoning in mathematics, on the basis of the criteria used to accept or reject reasoning in each domain.

Keywords:
Grade 5
Quantitative
Article
Algebra
Conceptual Development
Math Coordinator / Coach
Numbers and Operations
Teacher
Problems
Problem Solving / Problem Posing
Reasoning and Proof
Representation
Theory