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January 18, 2006
Topics discussed in class
- Professional ethics in teaching mathematics. Responsibility
to understand and respond to students and responsibility to the subject
- What does it mean ``to demonstrate'' a proposition?
- What is a mathematical definition? What role do definitions
play in mathematics, and in demonstrations in particular?
- The foundations of Euclid's Geometry.
What we did
Madden talked about items 1 and 3 up to about 4:20. After this, students worked
cooperatively on problems to be assigned as homework. We paused as appropriate
What to think about for next class
- If geometry is an organized body of knowledge, HOW is it organized? The
two textbooks that you have (Euclid and Stillwell) organize geometry in different
ways. There are other ways of organizing geometry for teaching that are
for different grades.
- What is the role of definitions, propositions and demonstrations in the
organization of geometric knowledge?
- What is the role of constructions?
- Read Chapter 1 of Stillwell.
- Do problems in sections 1 and 2 of the homework sheet (available
for download here); written work will be collected on Wednesday, January
25. I will clarify what is required on Monday.
- Get familiar with Book I of Euclid.