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Math for Teaching Program Core Classes - Syllabus & Course Information 

 

E - 330    The Art & Craft of Posing Problems & Making Conjectures        

 

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. Emphasis will be placed on learning to pose problems that stimulate exploration and inquiry.

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) 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.

* * *

The class meets online on Thursday 5:30 pm to 7:30 pm EDT. During class sessions we will all use the ZOOM software package that is now the HES standard. You will be getting, if you have not already gotten, information of how to download and use the ZOOM software.

Most weeks there will be assigned readings and/or problems drawn from the text, the mathMINDhabits website and other sources. Students are expected to post initial reactions to the readings and responses to the questions/problems of the web assignment no later than 5 pm EDT Monday of the following week. This will allow for students to read, consider and respond to one another's posts. Students are strongly urged to meet with one another in small groups [N<4, please !] after class and before Monday at 5 pm. Even if you work with a classmate each student is individually required to post reactions/responses by Monday at 5 pm.

Resource website:

https://sites.google.com/site/mathmindhabits/

Text:

  • Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving, Volumes I & II, G. Polya & S. Sloan, Ishi Press, 2009
  • There will be occasional readings from other books throughout the semester.
Chazan, Daniel, Beyond Formulas in Mathematics and Teaching: Dynamics of the High School Algebra Classroom, 2000, Teachers’ College Press

Brown, S. & Walter, M.,  The Art of Problem Posing, 2004, Psychology Press

Polya, G.,  How to Solve It: A New Aspect of Mathematical Method, 2004, Psychology Press

Lockhart, P., Measurement, 2012, Belknap Press of the Harvard University Press

Term Project:

Students are expected to design and present an original curricular unit that elicits conjecture and discussion and either proof or disproof.

 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 problems to be “similar”?




 

 

Course assignments are not weighted.  Syllabus


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