Gary Rubinstein, a teacher of mathematics at Stuyvesant High School, wrote a five-part series about whether the math taught in school is useful. This is the fourth installment, in which he delves into the history of math.

He begins:

Some of the most ancient math texts found on clay tablets from 1800 BCE in Mesopotamia are filled not with ledgers and bookkeeping but utterly ‘useless’ questions like “If you subtract the side length of a square from its area you get 870. What is the side length?” (BM 13901.2) along with lengthy algorithms for calculating the solution. Fast forward to 300 BCE in ancient Greece where they studied Euclid’s Elements, a Geometry book based mainly on using a compass and a straight edge to produce various Geometric shapes and then proving that the shapes created are what they were supposed to be like “Construct an isosceles triangle having each of the angles at the base double the remaining one. (In modern terminology to make a triangle whose three angles are 36, 72, and 72 degrees)” (Euclid IV. 10) Why the Babylonians cared to answer a question like this is not known though for the Greeks we do know that for them, at that time, Mathematics was a search for ideal truths.

In the 1700s and 1800s in this country, the only math topics taught were things that were ‘useful’ in life, like converting units of measurement and other things related to commerce. But over the past 300 years the math curriculum has grown so it has some topics that are useful (or potentially useful) and some that are more abstract and theoretical and certainly less useful than the others if not totally useless. In earlier posts I estimated that about 1/3 of the topics are useful while the rest are not.

In this post I want to examine the ‘useless’ topics and show why at least some of them have a value that transcends whether or not students will ever have an opportunity to use them in their adult lives.

In part 2 of this series I listed six topics that I felt were so useful that every student should master them before graduating high school. And if learning math that is useful is the only thing that matters, we could strip the curriculum down to just these things and the World would likely not end. As the parent of two kids who are now 15 and 12, I would be unhappy, though, if the only math my kids learned were these useful topics.

There are plenty of useless things that I want my kids to learn. When I was in school my favorite part of the day was actually not my math class but my band class. I loved playing the trumpet and took pride that I was first chair and I enjoyed practicing at home (though my family didn’t as much). I looked forward to the band concerts and band competitions we went on. But as much as I loved band and how it made me feel and challenged my determination and endurance sometime, is there anything more ‘useless’ than playing a trumpet? I suppose that some people go on to become professional trumpet players but not many. And I stopped playing the trumpet when I moved into a New York City apartment and now I dabble with another ‘useless’ instrument, the piano. The same could be said about Art. Aside from someone who becomes a professional housepainter, very few people will ever ‘use’ what they learn in Art class. What about poetry? If poetry just ceased to exist, would it really matter?

But of course the ‘use’ of poetry, art, and music isn’t that we are going to use them as adults but because they engage our minds. These creative fields offer us a type of challenge. Some people find these challenges fun. It causes our brains to release dopamine which is like a free drug.

For me, Math is a lot like playing a musical instrument. I like using my mind to discover some kind of pattern and then to see if I can prove that the pattern wasn’t just a coincidence. When I figure something out I get such a feeling of satisfaction. Often when something is too difficult for me to figure out myself I have to cheat and see how someone else figured something out and when I’m reading it it is, for me, like a page turner mystery novel. I’m getting near the end but not quite there yet and suddenly I can see where its going and even if I don’t, when I get to the end I think “Wow, how did I not figure that out myself, it seems so easy now.” And often the math topics that provide the most enjoyable adventure in trying to figure them out or just to understand why they work are the topics that are about as ‘useful’ as playing the trumpet.

In this post I’m going to briefly describe nine topics that are not particularly ‘useful’ but that I think all students should have the opportunity to experience. These topics, by the way, are already in the K-12 curriculum but they are mixed in with so many other less fruitful topics that they might get lost in the crowd. I’ll list these in order from earliest learned to latest learned

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