Course Syllabus
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:
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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Course Summary:
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