The only past that math education seems to have is one that needs to be left behind…
Math education, in its noble attempt to be progressive and au courant , has discarded the past in terms of anything that was relevant in the 20th century. In terms of pedagogy, that definitely has been welcomed, encouraging deeper and more nuanced ideas of how kids learn mathematics. As such, the general tenor of math conferences and workshops is to mine the present to build the future.
The problem is that while pedagogy has definitely improved, the quality of mathematical content has taken a rather steep dive over the last half century.
I have textbooks from the early 50’s all the way to almost the present. You can see the decline of attention to mathematics in the way the forewords were written. Forewords, especially starting around the mid 60’s, had a far more romantic and wider scope for learning mathematics. As well, the language used in these foreword pages spoke to a sophistication of mathematics that was assumed by the writers for the students they wrote for. Regrettably, through time, the vision of the purpose of mathematics as a human endeavor has been shaded more or less into obscurity, replaced by technical efficiency for STEM careers and practical endeavors.
Our teaching of mathematics might have improved, but why we teach it has been washed of any impractical notions that could stain the productivity narrative that has overtaken math education. We are left with a bleached curriculum, with any evidence of human awe and wonder left in margins — if even that.
There is very little collective attention to the history of mathematics, which then renders the currency of everything in our rear view mirror as dated. Being swept away in this general nose-up to the past is mathematical wisdom that grew up in this Golden Age of Mathematical content.
In my CMC-South Presentation, I realized that most of my presentation was rear view mirror stuff — content, historical mentions, elderly educators, and old problems.
The person that anchored my presentation was Peter Taylor, a professor at Queens university in Kingston, Ontario.
Over ten years ago, Peter Taylor was given the highest award for mathematics teaching in Canada. He was awarded primarily for seeing the subject of mathematics through an aesthetic lens. This was further fleshed out in a deep interview that involved drawing parallels between literature/poetry and mathematics.
In English, books are chosen first, and then curriculum is designed around these works of art. In mathematics, curriculum is written and then books are written after. And, as you read the rest of the excerpt, much of the alienation comes from this sterile construction of mathematics.
Peter Taylor wrote a great article about this a few years back.
We are currently NOT teaching mathematics in the spirit of its long evolution of awe and wonder. And, part of the reason for that is that people like Peter Taylor — giants in the field of mathematics/math education — don’t have the needed platform to amplify their towering wisdom.
The mathematics should speak for itself. The need for contextualizing and labeling to elevate its worth and attention is like giving students inorganic mathematics. Putting context in for context’s sake only shortchanges the mathematics.
We all have encountered enough ridiculous situations in where trigonometry has to come to some practical rescue. Have you ever wondered what the angle of elevation is when you look up at the top of flag? I haven’t. But, hey, let’s bring in a couple of kids, tell a story — without mentioning how they know the distance to the flagpole — and ask that burning question of angle of elevation.
Get rid of the story and stop putting mathematics as a supporting actor. And, stop asking it do things it cannot do — it cannot cut a pan of brownies equally into 8 pieces. Ever.
We are drifting away from our past. And, generally, as mentioned above, is a good thing. But, we have thrown the baby out with the bath water, and lost some beautiful and needed reflection from those that taught us.
Taught us to always put mathematics first.