July 2006, Vol. 37, Issue 4
Teaching Geometry With Problems: Negotiating Instructional Situations and Mathematical Tasks
Patricio G. Herbst
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.
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