What is Math? part 3: A homemade subject

This is the final article on this mini-series exploring the question “What is Math?”. This final perspective is called the Social-Humanist perspective which simply says that all of mathematics is made by humans and it exists in the social consciousness. Even more simply, it is a social construct similar to race or gender. I am aware the nobody would argue that people aren’t the ones that practice math. However, as we have seen, and many that we will possibly visit in the future, there are philosophical perspectives that say that we did not invent the subject but only discover it. To explain this I want to start with a question, one that I was presented by a professor and it displays this idea in the best way. Why are there 360 degrees in a circle? Why that number specifically?

Let’s travel back in time to before math was a subject of study, to when agriculture was starting to be the foundation of economies. Without food, there is no mathematics. So as farming begins people begin to notice how different seasons affect crops differently. In Egypt, the Nile river floods every year and provides necessary nutrients to the next years’ crops. So you need a way to measure the time from one flooding to the next flooding, or from one hunting season to the next. So all one would need is a stick and massive amounts of patience and some intelligence, you place the stick in the ground, mark where the sun is and watch the shadow as it moves each day during the year. Repeating this every year and it was noticed that the sun repeated its starting point (made a full circle) every 360 + 5 days, thus 360 + 5 days in a year. I write it that way on purpose. The ancient Babylonians had a base 60 counting system, and the ancient Latin Americans had a base 20 counting system. Both of those counting systems fit very nicely with 360. So the extra 5 days were used for celebration and gratitude. This is not very precise or perfect in any way, but its utility is incredible. I say it isn’t precise because as the subject of mathematics counting and measurement gets better we found there it isn’t exactly 365 days in a year, just as there aren’t exactly 24 hours a day.

This view does not put an emphasis on applied mathematics as opposed to pure mathematics, that distinction is only between who does the math. Pure mathematics is math that is done by mathematicians and applied mathematics is math that is done by engineers or physicists, it does not mean that pure mathematics cannot be applied.

Now if we applied this to the thought experiment that we have been building the last two articles. A teacher who holds this view, who believes that mathematics is done wholly by people for people, then the way they go about teaching changes. They are able to talk about the history of the math, give context to it and point out the impact that the invention of that particular math had at that time. What did the world look like before, and what did the world look like after it, or was it the method that the mathematician used that was more important than their results? This perspective treats math as a science, allows for trial and error. It is this aspect that is missing in math education. Math is taught in a purely rational way, reason is the only way to solve problems and come to a conclusion in the Greek Tradition. One has a set of definitions and axioms, and from there using flawless logic and conclusion can be met. Yet mathematics is done rather empirically, there are trial and error, there are hypothesis’ and repeated experiments to see if the conclusions hold over time. Of course after all the experiments, then reason is used to come back to that conclusion, or the rationality seems obvious. But that is only true to people who have struggled through the reasoning.

The other impact of this philosophy is that, if applied in full, it demands reform of math education at every level. Changing the courses taught, the way they are taught, the abolishment of standardized testing, and more.
Students are already aware that the education system doesn’t work for all students, it doesn’t promote well being, continues to disenfranchise students that are part of historically/currently suppressed groups.
If we are going to continue to claim that education is a key part in the development of a person, then that education should benefit that development not hinder it.

This mini-series probably should have been the first set of articles, but it is here. I will continue to refer back to this particular article as my thesis, that mathematics is human and affected by all human activities.