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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

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.

Action Research
Conceptual Development
Higher Education
Grades 9-12
Geometry & Measurement
Problem Solving / Problem Posing
Professional Development / Teacher Education
Reasoning and Proof