Reflection on Memorable Math Teachers

Forward: Both the teachers I mention in this article are still active teachers at the high school and university levels, respectively. Because of this, I have decided that it is best to not record their last names.

Mrs. Lynn: Lynn taught my Grade 10 math class. I remember her mainly for her lack of understanding of probability, and insistence on not listening to an explanation on why another answer may be correct. Years later, after many probability and statistics classes, I still think back to this question:

You are a new kid in a school classroom made up of 10 boys and 10 girls. Initially you have an equal chance of meeting a boy or a girl. You have met 9 boys and 0 girls so far. What are the chances the next person you meet at random is a boy?

My answer was that there was a 1/11 chance, since there was only one boy in a class of eleven students. Lynn's answer was that there was a 50% chance. When I explained that the same logic could be applied to state that I have a 50% chance of winning the lottery, she agreed, stating that this was indeed the case.

Mr. Jim: Jim had a reputation as being a very difficult math instructor that was to be avoided at all costs. However, in order to complete a math minor, I needed a math class that fit into my schedule, and only Number Theory met this requirement. While I was hesitant about the course, Jim's enthusiasm about the subject material kept my attention, and this ended up being my favourite class that semester.

Reflection: In reflection, when I look back on these two separate instances, I had never made the connection until now how they were really flip sides of the same coin. Before now, when I thought of Lynn's misunderstanding of probability, I thought it was due to a lack of being able to properly grasp the subject material. Now that I look at these two instances "side-by-side", I realize that it was really due to Lynn's lack of interest of the subject material. From the interest would have developed curiosity to explore the material in further depth, and from curiosity would have come understanding.

On the flip side, Jim was an extremely curious person, who spent most of this free time finding new math problems or "hands-on" puzzle toys to challenge his students with. His curiosity led to his knowledge and passion for mathematics, which in turn encouraged his students.

I will be modelling my mathematics teaching career on Jim. Well, with the exception of the part where I instil fear in prospective students.