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STEM Ed Announcement: Art & Craft of Posing Problems
- To: xxxxx@xxxxxxxxxx
- Subject: STEM Ed Announcement: Art & Craft of Posing Problems
- From: "Mort Sternheim" <email@example.com>
- 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
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.
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
Multiple representations & the meaning of understanding
Families of functions & the need for function sense in math &
The function as the fundamental object of algebra
The confounded roles of the equal sign assignment &
Formulating measures a step on the road to modeling
The role of generalization in making conjectures
Functions on the domain of shapes
Formulating functions & scaffolding word problems
Symmetry and asymptotic argument in mathematics
What does it mean for two problems to be similar?
Students will be expected to design and present an original curricular
unit that elicits conjecture and discussion and either proof or
Joan Thormann, Ph.D.
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