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Josh's Operational Conjectures: Abductions of a Splitting Operation and the Construction of New Fractional Schemes

Anderson Norton 

July 2008, Volume 39, Issue 4, Page 401

Abstract:
This article reports on students' learning through conjecturing, by drawing on a semester-long teaching experiment with 6 sixth-grade students. It focuses on 1 of the students, Josh, who developed especially powerful ways of operating over the course of the teaching experiment. Through a fine-grained analysis of Josh’s actions, this article integrates Piaget's scheme theory (1950/2001) and Peirce’s logic of abduction (1998) into a new theory about conjecturing that explains Josh’s learning.  

Keywords:
Grade 6
Research Studies
Article
Conceptual Development
Curriculum
Math Coordinator / Coach
Teacher
Fractions / Decimals / Percents / Rational Numbers
Professional Development / Teacher Education
Representation
Theory