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*To*: xxxxx@xxxxxxxxxx*Subject*: STEM Ed Announcement: Art & Craft of Posing Problems*From*: "Mort Sternheim" <mort@k12s.phast.umass.edu>*Date*: Wed, 13 Aug 2014 17:22:17 -0400

This is not a UMass Amherst program Contact information is below. ============================================== Harvard Extension School Math E330: The Art & Craft of Posing Problems & Making Conjectures - Fall, 2014 beginning Sept. 3, 5:30-7:30 Instructor: Judah L. Schwartz, Professor of Education, HGSE (retired), Professor of Engineering Science & Education, MIT (retired) Course Description and Goals: This course is primarily designed for teachers of middle school and high school mathematics who want to deepen their understanding of the mathematics they teach and that their students are expected to learn. The underlying premises of this course are that 1) the key to effective teaching is the ability to pose a provocative and engaging next question at the proper moment, and 2) that the heart and soul of doing mathematics is making, exploring, proving and disproving conjectures . Using small exploratory interactive environments (applets) we will explore a variety of different approaches to familiar topics, such as linear functions; y = mx + b in both the x,y plane and the m,b plane, solving the equation f(x) = g(x) by transforming the graphs of f(x) and g(x), UNsolving equations and inequalities, formulating measures, generalizing geometric constructs, geometry from an algebraic perspective and algebra from a geometric perspective. Text: Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving, Volumes I & II, G. Polya & S. Sloan, Ishi Press, 2009 There may be occasional readings from other books throughout the semester Tentative Syllabus: Multiple representations & the meaning of understanding Families of functions & the need for function sense in math & modeling The function as the fundamental object of algebra The confounded roles of the equal sign assignment & comparison Formulating measures a step on the road to modeling The role of generalization in making conjectures Functions on the domain of shapes Parameter spaces Formulating functions & scaffolding word problems Symmetry and asymptotic argument in mathematics What does it mean for two problems to be similar? Term project: Students will be expected to design and present an original curricular unit that elicits conjecture and discussion and either proof or disproof. http://www.extension.harvard.edu/courses/14485 Joan Joan Thormann, Ph.D. Professor Educational Technology Lesley University 617.349.8387/ thormann@lesley.edu Subscribe to the STEM Ed. RSS feed at: http://www.umassk12.net/feed.xml

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