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STEM Ed Announcement: Art & Craft of Posing Problems



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
 
 

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