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M4005 Geometry

January 18, 2006

Topics discussed in class

  1. Professional ethics in teaching mathematics. Responsibility to understand and respond to students and responsibility to the subject matter.
  2. What does it mean ``to demonstrate'' a proposition? Lincoln's thoughts.
  3. What is a mathematical definition? What role do definitions play in mathematics, and in demonstrations in particular?
  4. 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 to discuss issues.

What to think about for next class

  1. 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 appropriate for different grades.
  2. What is the role of definitions, propositions and demonstrations in the organization of geometric knowledge?
  3. What is the role of constructions?


  1. Read Chapter 1 of Stillwell.
  2. 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.
  3. Get familiar with Book I of Euclid.