Geometry courses for teachers

Goals: make sure that teachers 

1.  understand the basic concepts/formulae,
2.  convey the CORRECT ideas and proofs effectively in interesting ways,
3.  regconize the error patterns and the different stages of 
    understanding of students,
4.  pose, create, and study "new" problems.
    

1. Check whether the teachers know the basic definitions, formulae,
   and proofs/verifications.

   Examples: 
   perimeter formulae for rectangles, circles;
   area formulae for rectangles, parallelograms, trapezoids, circles;
   volume formulae for cones, prisms, spheres, 
   How to verify?
   How to prove?  (for volumes of cones and spheres, can only verify
                   at the k-12 level.)

2. Use tiles, unit cube, approximations to explain areas and volumes.
   Understand the fact that the formula  P = 2r \pi is really a result
   of the observation of  P/2r = \pi.
   Understand that approximation (cutting the circle/circular disk, 
   circular cone) help find the perimeter, area, volume formulae,
   
3. Identify error patterns, and make suitable suggestions for adjustments. 
   Be aware of the different stages of learning of students.

4. Use geo board and 12 unit loop to introduce geometrical concepts.
   a. construct triangles of different types.
   b. count how many triangles one can make and categorize them.
   c. "prove" that no equilateral triangle can be formed using
      lattice points as vertices, introduce Pick's theorem,
      generalizations, and many interesting aspects. How to find
      info on internet, e-mail professors....