When my mentor, Peter Harrison, retired twenty years ago, he remarked to me that “mathematics was dead”. He said it with the same confidence and resignation that the famous DJ Lester Bangs told a young William Miller in the film “Almost Famous”, that rock and roll was dead and he had arrived only for the death rattle.
Luckily, rock and roll is very much alive. Unfortunately, I cannot say the same for mathematics.
It’s all but dead.
The best way to explain how it’s dead, is to continue with comparisons to music. In 2023, math education is in the firm grip of pedagogy, the philosophical idea of how to teach something better, On the surface, there would seem nothing alarmist about that, in fact quite the opposite — don’t we want to improve how our students learn mathematics? Absolutely.
Except, the current culture of math education has lost all interest and curiosity for what students are actually learning. Imagine having a great stereo system, with the very best speakers you could buy today. Now imagine the record collection you are stuck with is K-Tel records from the 70’s. When I started teaching, most of mathematics that I saw at conferences would be worthy of being classified as in “The Age of Bowie”.
That is math education in a nutshell: high quality of delivery and low quality of content. Content has become a poor understudy to pedagogy in the teaching of mathematics. Now the idea/picture of content that I am alluding is not the image of a stuffy teacher, filled with such knowledge, and doesn’t know how to teach it — that is just as problematic as great pedagogy with no content.
It’s about the actual quality and aesthetic of the math problem, puzzle, conundrum, proof, and historical question in front of you — not cluttered up by you or I. Here’s the problem and get out of their way.
It’s not so much content knowledge, it’s the curiosity for it. That’s dead. There seems to be much more of an appetite to purchase speakers than there is to purchase music.
And so, that’s also the reason this climate of math education is also a silent crisis — because most of math education has signed off on this, thinking math education is only about pedagogy. When I started teaching, that p-word wasn’t even around. We just believed in prioritizing student understanding/relationships first and then the quality of mathematics second.
Rich mathematical content and problems have been around for thousands of years. Pedagogy, with now the dangerous nothing-burger movement called “Science of Math” becoming popular with teachers, has only been around this century. They are so drunk on pedagogy — and the evidence is sketchy as the people running it — that they are proud to wave the flag of bureaucratic compliance.
In another universe it would be the Joy of Math: Focusing on Content to Improve Curiosity.
In this one, it’s this one.
It’s a classic case of tail wagging the dog. Worse, even the best pedagogical ideas are teacher and administration facing priorities. Content, the actual quality of the problem, given only token consideration, is student facing. Number theory, an actual branch of mathematics, that has captured the imagination of so many mathematicians over centuries, is not even a topic in math education. The irony is that there is this zealous emphasis on factual fluency/memorization — K-Tel records. Number theory is Pink Floyd.
We are simply listening to the worst music on Bose Speakers.
As such, math education is no longer about engendering lifetime joy and curiosity in mathematics. It’s simply about making the delivery model more efficient for compliance and classroom management, all while believing that mathematics is being delivered. If there was ever a real life situation of The Emperor’s New Clothes that brought that cautionary fable to life, it’s the current status of math education.
The joyless romp through K to 12 mathematics begins with alienation in elementary school and ends with some level of anxiety/trauma in high school. Math education, with its head so far in the sand, just chalks all this up to as some reasonable tax for learning mathematics. No. The reason why there are these historically toxic outcomes is because the mathematical content is boring and students are tested ad nauseam on it. But, we still have had decades of these yawning, political debates about what is wrong with math education.
Over twenty years ago, Paul Lockhart wrote an underground essay called “A Mathematician’s Lament”, which eventually turned into his first book several years later. This early passage captures the unattended crisis in a powerful economy of words.
Everyone knows that something is wrong. The politicians say, “we need higher standards.” The schools say, “we need more money and equipment.” Educators say one thing, and teachers 3 say another. They are all wrong. The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, “math class is stupid and boring,” and they are right.
The math classroom continues to be stupid and boring, except math educators believe it is in a much better state. In terms of teaching practices, yes. In terms of the mathematical content that is more akin to listening to The Beatles or Pink Floyd, the answer is an emphatic and embarrassing no.
Sadly, most teachers would yearn for new content, to have their own learning of mathematics be romanticized. But, since it has been almost shaded into obscurity in math education and conferences — with most companies, who provide resource material, playing along — teachers and the world of mathematics are the furthest apart they have ever been.
The reconciliation of the two is improbable. What should have been in an inalienable right for every student— to learn high quality mathematics — is a vision that no longer can be supported by the current climate.
What are we to do?