16 September - response - Integrating history of mathematics

I believe math history should be incorporated into my teachings because there are certainly some students who simply like history. Apart from that, teaching history of math and showing how math is developed is one of the key aspects to understanding where math comes from. Since the axiomatic approach has taken hold of all mathematics, students get the polished subject in the end, without seeing what it took to get there. For example, it might take fifty years to reach a good definition. When we see end result, the main question that comes to mind is "why would you have it this way", which can only be answered by studying how it was made.
A concrete example of this would be the idea of a "limit", which came from the problem of rigorizing infinitesimals. Calculus is presented to students in a polished way, with the introduction of limits. I believe that this is very misleading to the students and is very disingenuous towards the enterprise and journey of mathematics in our society.

A quote that struck me was: "history can provide role models of human activity." Most high school textbooks, seem to be focused too much on making math "useful". This might be an over-correction to the known problem of students asking "why would I need to know this". Perhaps it would be best to inspire instead. Showing small biographies of mathematicians and their accomplishments can be a way of achieving this. A lot of mathematicians grew up in poverty or had to deal with many societal pressures. Some of them who made discoveries at a young age (i.e. Abel), can definitely inspire the young generation. When leaving out the makers and most of the story of mathematics, it becomes dehumanized. As the author puts it, "mathematics is often regarded as a discipline which is largely disconnected from social and cultural concerns and influences." Therefore, I believe, just like the author, that the teaching of history is indispensable in teaching mathematics.

I wholeheartedly agree with the author. After reading the article I've already decided to take on the section "7.4 Ideas and examples for classroom implementation" for my own future classes. I think it would be great for students to "participate in a situation in which they have to decipher and understand a
known piece of correct mathematics but whose treatment is not modern. "(p.206) Not only would they grow as students, but this undertaking would help me grow as a teacher as well.