Why teach math? Response

 

Before reading the article, I think a little bit of mathematical history is helpful when incorporated into teaching. From my personal learning experience in math, it seems that math is presented often upfront as “you need to learn this because it exists”, and while there are usually good links and development in the order they are presented, exactly why they are presented remains a myth. Much of the “why” reasoning relies on the student to reflect on. I think that for the most part, mathematics taught in k-12 level is about solving very real problems that we could find in history that we might no longer think of them as problems. I believe that using questions posed by people in the early days could give meaning to modern problems that we so easily solve without thinking too much about why we solve them. I would prefer to integrate tales and historical accounts of math problems and present them as the introduction of my lesson followed by how we solve these problems. For instance, multiplication is sometimes presented merely as an operation that we give meaning to, by counting groups, and having a basic multiplication table along with an arithmetic method of multiplying anything more than 2 digits. If I were to present on the same idea, I would use some tales or stories to convince students why multiplication is a very helpful concept. For instance, in ancient China the general population might know addition or subtraction but maybe not multiplication, and number quickly grew out of scope on the level of a city. When people need to pax tax on their harvest, adding up each person’s amount will take very long, but if they pay a similar amount, learning how to multiply would make the problem trivial, as we do now.

Reading the article, I have noticed that the introduction articulates the idea of mathematical presentation as linear and exploration as non-linear, and I agree very much with it. It connects me to when I am presenting mathematical work to someone else, maybe my professor or my peer, where say you have a proof of a statement. You can give a single instance of why it’s false, or use some formal structure to prove its correctness. However, much of the hard work lies on finding a false instance of constructing the structure for proof, but those facts are hidden when presented to someone else. It also makes me think about NP problems, where solutions are easily verified but arriving at the solution might never happen in our lifespan.

I specifically like this line “To learn mathematics, then, is not only to become acquainted with and competent in handling the symbols and the logical syntax of theories, and to accumulate knowledge of new results presented as finished products. It also includes the understanding of the motivations for certain problems and questions” (202). This agrees with my impression of knowing why we solve problems, presumably because they are of value to scientific research that ultimately comes down to everyday items. While not every student might be making these items and making use of math purely as mathematicians, I believe exposing them to the possible usage and results make the topic less boring.

My closing impression is that I am impressed with the article’s math reference. It spans many topics and provide famous examples, famous mathematicians’ opinion on history of mathematics in teaching. It broadens my prospective as to why we should look at problems not only as something that I must learn or present but why they are developed, and most importantly, recognize that they might not be easy results and have been developed over centuries.