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Pedagogical Content Tools: Integrating Student Reasoning and Mathematics in Instruction

Chris Rasmussen, Karen Marrongelle 

November 2006, Volume 37, Issue 5, Page 388

Abstract:
Teaching in a manner consistent with reform recommendations is a challenging and often overwhelming task. Part of this challenge involves using students’ thinking and understanding as a basis for the development of mathematical ideas (cf. NCTM, 2000). The purpose of this article is to address this challenge by developing the notion of pedagogical  content tool. A pedagogical content tool is a device such as a graph, diagram, equation, or verbal statement that a teacher intentionally uses to connect to student thinking while moving the mathematical agenda forward. We tender two examples of pedagogical content tools: Transformational record and generative alternative. These two pedagogical content tools are put forth as instructional counterparts to the Realistic Mathematics Education (RME) design heuristics of emergent models and guided reinvention,  respectively. We illustrate the pedagogical content tools of transformational record and generative alternative by drawing on examples from two classroom teaching experiments in undergraduate differential equations.

Keywords:
Action Research
Article
Algebra
Calculus and Higher Level Mathematics
Conceptual Development
Grades 6-8
Communication
Curriculum
Math Coordinator / Coach
Numbers and Operations
Teacher
Problems
Professional Development / Teacher Education
Representation
Theory