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Teaching Geometry With Problems: Negotiating Instructional Situations and Mathematical Tasks

Patricio G. Herbst 

July 2006, Volume 37, Issue 4, Page 313

Abstract:
Two questions are asked that concern the work of teaching high school geometry with problems and engaging students in building a reasoned conjecture: What kinds of negotiation are needed in order to engage students in such activity? How do those negotiations impact the mathematical activity in which students participate? A teacher's work is analyzed in two classes with an area problem designed to bring about and prove a conjecture about the relationship between the medians and area of a triangle. The  article stresses that to understand the conditions of possibility to teach geometry with problems, questions of epistemological and instructional nature need to be asked — not only whether and how certain ideas can be conceived by students as they work on a problem but also whether and how the kind of activity that will allow such conception can be summoned by customary ways of transacting work for knowledge.

Keywords:
Action Research
Article
Conceptual Development
Higher Education
Grades 9-12
Geometry & Measurement
Teacher
Problems
Problem Solving / Problem Posing
Professional Development / Teacher Education
Reasoning and Proof
Representation
Theory