When is an exploration exploratory? A comparative analysis of geometry lessons
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Citation (published version)L Dietiker, Andrew Richman. "When is an exploration exploratory? A comparative analysis of geometry lessons.." The 2nd International Conference on Mathematics Textbook Research and Development (ICMT2) Conference. Rio de Janeiro, Brazil, 2017-05-07 - 2017-05-11
This paper presents a comparative analysis of two textbook lessons on the same topic from U.S. textbooks to learn how differently - designed “exploratory” lessons may structure content to enable or constrain student inquiry. One lesson, representative of a “reform - based” textbook, contains investigations of conditions of triangle congruence. The second is a “technology lab” on triangle congruence fro m a "traditional" textbook, the design of which is atypical for that textbook. Framing a lesson as a mathematical story, this analysis exposes three distinct ways that these lessons are different: (a) the proportion of the lesson in which mathematical questions remain unanswered, (b) the manner in which content unfolds to address each question, and (c) the way in which open mathematical questions overlap to increase the dynamically - changing number of questions that are pursued. This contrast of the two lessons illuminates how a lesson structure can prevent an "exploration" from being exploratory.