Thoughts about PMET
Pólya on problem solving. I should do this if no one else will.
Tell them about the new magazine the MAA has started with NSF funding for the history of mathematics, Convergence. Encourage them to write for this magazine. Show them that my calendar is there. This is a great way to start class as prospective teachers need to have a broad understanding of mathematics. One thing that will help them get it is to begin each class with a discussion of mathematical events that have happened in the past on that date. This technique will ensure that you cover a variety of topics. Spend some time in advance so that you have a broader knowledge of the topics so that you can answer the questions that arise.
One must give concrete examples of abstract concepts. For example, in presenting the concept of a group, one always needs to give specific examples that the students can get their hands on. Math Equals (1978) by Terri Perl, there is a chapter on Emmy Noether and the mathematics included is a discussion of group theory. One group discussed is the set of permutations on three objects. Pictures of these are on p. 187. If one enlarges them with a photocopier, makes an overhead, and cuts them apart, then one can manipulate them on the overhead. Of course one might also want to give photocopies to the students, have them cut them out and fill in the group table. I have overheads.
Pascal's triangle is a topic that will come up somewhere in the curriculum. Be sure to show them Pascal's original work, Traite du triangle arithmetique (1654). The title page and and the triangle itself make splendid overheads. This is a wonderful place to have kids look for paterns.
Fibonacci. Note that it is in Pascal's triangle.
Euclid. Refer to the colored copy. Do examples from Book II on geometric algebra.
When algebra was hard. Al-Khwarizmi.
Where do complex numbers come from?
Dates: June 21
Bridges of Konigsburg. Need overhead of Euler.
Area of Circle: Kepler. Opus geometricum. Euler on Trigonometry (because the teacher must have a look forward).
Negative numbers. Folium of Descartes. Maseres.
Do a book display.
Zalaman Usiskin, Anthony Peressinik, Elena Anne Marchisotto, Dick Stanlye, Mathematics for High School Teachers. An Advanced Perspective. Prentice Hall, 2003.
George Polya: How to Solve It and Mathematical Discovery.
Victor J. Katz, The History of Mathematics, Brief Version, Pearson/Addison Wesley, 2004.
Jones, Bunt, Biedent ??