In-class timed writing (6 min.) Write about two of your most memorable mathematics teachers

In-class timed writing (6 min.)
Write about two of your most memorable mathematics teachers


I don't remember the names of any of my math. teachers; Does that mean none were memorable or that I am getting old and forgetful? I do remember two teachers by faces, one a high school teacher (grade 8 or 9) and the other a freshman-year university professor. Its their method of teaching that has stuck in my memory.

The former, sort of combined trigonometry and geometry together. She was very methodical, well organized, and captivating. I still remember to this day how she explained trigonometric functions cos(theta) and sin(theta) in terms of coordinates of a unit circle, with cos(theta) as the horizontal axis and sin(theta) as the vertical axis. In this graphical representation, we could easily find out the values for cosine of simple angles like (0, 45, 90, 180, 270, and 360) degrees could be read right out of the circle. She also showed us how tangent of an angle could be thought of as the line tangent to the perimeter of the unit circle at the end point of the angle.

The latter was also methodical and well organized; however, the way he taught the subject was dry and non-interesting. He did not explain the meaning behind mathematical concepts such as derivation and integration, namely, derivative of a function being the slope of the function evaluated at a given point, and integration as the area under the curve or graphical representation of a function.

Reflection on how this forms my ideas about teaching


I think the above two are examples of relational vs instrumental teaching styles. I definitely hold the belief that 'understanding of concepts' should be the underlying goal while topics are introduced, if not possible at the beginning, then at some later point where connections can be made such that things make more sense and therefore stay with an individual for a long time. To me, this is not
an either or situation, i.e. both methods are valid and there is a place and time for each. The job of a teacher is to flip-flop or go
back and forth, depending on the situation.