A recent report shows that only 20% of educators think funding for STEM subjects will increase this year. This is particularly disturbing given that we haven’t even come close to providing adequate support for these subjects in recent years. And, in my view, one part of the STEM curriculum that needs particular attention is mathematics. I have just surveyed several math textbooks across grade levels and have found no references to chaos or complexity theory – twentieth century math topics that are particularly germane to the world in which we all live. In fact, we are a full decade into the twenty first century and we have yet to include ANY twentieth century math into the curriculum at all. Zero, nada, zilch. It is as if the previous 100 years didn’t exist.
Adding to this tragedy is that there are lots of concepts in this field that are fully understandable by students, especially in high school. If you understand anything about quadratic equations, for example, you are equipped to start exploring a branch of mathematics that will knock your socks off.
Why does this matter? Well, let history be our guide. When Newton formulated his laws of motion, he also developed a new branch of mathematics (along with Leibnitz) that was needed to allow the expression and use of these laws – the mathematics of calculus. Some have even gone so far as to suggest that calculus was essential for the Industrial Revolution. So, let’s get this straight – our top math class in high school is calculus which is tantamount to saying that we are preparing our kids for a world dominated by steam engines. We should be ashamed.
Fast forward to today. We live in a world of great complexity and chaos (and chaos means something very specific to mathematicians.) Whether it is freak weather patterns, economic collapses, or any of the other big topics in the news today, chaos and complexity rule the day. Fortunately there is a mathematical formalism that allows us to explore and perhaps understand some of these phenomena – and ultimately will provide the tools to avert global disruptions sometime in the future. But how are we to even get started on this task if we don’t expose our students to some simple, but amazingly rich, mathematical concepts while we still have the chance?
Of course it turns out that most of the processes that produce chaotic behavior are recursive, and thus hard to do with paper and pencil. They are, however, easy to explore with computers using nothing more complex that a spreadsheet program. And, to be sure, once you start wandering down that rabbit hole, you’ll find amazing riches in the exploration of even more complex mathematical systems for which students can write their own programs!
In 1990 I wrote a book (Chaotic Microworlds: Personal Computing and the Art of Mathematics) that went out of print after selling about 250 copies – mostly to Waldorf schools. There was nothing in that book that any high school student couldn’t master, but I was told that the topic wasn’t in the curriculum, so nobody wanted to incorporate it. Yes, there were (and are) a few renegade math teachers doing wonderful stuff in the area, but the topic has yet to become mainstreamed.
Well, guess what. Over 20 years later the topic is even more important than it was then, yet it still isn’t in our curriculum. It isn’t just that we aren’t preparing students for their futures, we aren’t even preparing them for the present!
And, against this backdrop 80% of teachers think funding for science, technology, engineering and mathematics will either remain anemic or drop even further. This isn’t chaos – it is a disaster in the making.