The Burn It Down and Start Again Mathematics Curriculum
If you can even imagine burning all our curriculum documents, and starting to write them again, you might be considered a “progressive”, to use that useless and hopelessly outdated phrase from the Education Wars (1900-present). We don’t have to actually do it, after all, and we will still need the ideas, thoughts, writings, and achievements of the past to guide us, but it’s a useful thought experiment.
The least biased form of curriculum reform could begin from a place of intellectual humbleness, of modesty. It could begin with the question:
Why do we teach mathematics?
Having answered “why”, we would naturally move on to “what”. What knowledge and skills are necessary to teach, from the domain of mathematics, given our stated “why”?
It’s a useful thought experiment in any avenue of life however, to ask these sorts of questions:
What would this look like, if it was totally different?
If we had to start all over again, where would we begin?
An easy way to try this for yourself. Imagine there were no Republican and Democratic parties. How would the US political system begin again? What would that look like? You can get even further with this thought experiment: are political parties still necessary? What would a world without political parties look like?
With regards to math curriculum, the idea is not entirely new. There already exists a book called Burn Math Class. The author, Jason Wilkes, attempts to describe how he would start anew, building concepts from the ground up. This book was for me, only partly successful, but it’s very interesting.
A “starting anew” would have certain benefits:
- removing baggage from the past-ideological statements, for example
- removing clutter and jargon from the curriculum
- bringing in more modern concepts of mathematics
And some drawbacks too- ignoring the tried and true, in favour of new fads, for example.
One benefit of this approach, at least as a thought experiment, is that, having taken away everything, we would then have to have a very good reason to put things back in. You must justify every single topic you include, either for its utility, aesthetic value, or as a piece of the “foundation” for later mathematics.
You want to argue that calculus is still the “top” of K-12 mathematics? Make your argument. You want calculus taught to grade 2s? Sure-just show how you can do it by making the big ideas (incremental change over time) accessible to 7 year olds.
We may find that certain topics are in there “just because” they always have been. How many different grades do we really need to learn about flips, slides, and turns in? Does it make sense to look at rotational symmetry without reference to symmetry groups?
(Visualizing mathematics wherever and whenever they can would be in, in my ideal curriculum.)
Can we justify our narrow look at experimental and theoretical probability, which we typically do in elementary, which leaves out fair and finite games, risk assessment, anti-gambling education, and so on?
Which “modern” mathematics will we decide have enough utility to be added in.
Consider this a partial menu:
- graph theory
- category theory
- game theory
- number theory (beyond arithmetic)
- topology
- set theory?*
- this last may give many pause, given failed 1960s “New Math”.
There is a gigantic world of newer and more interesting mathematics out there, than what we show to kids. Many of these topics are more interesting and possibly useful than some of the things we currently teach.
Consider that starting again would a bit like decluttering your basement. Take out the things you aren’t using, and what remains? Hopefully that which is essential.
There would be lively arguments as mathematicians, teachers, parents, and education professors advocated for those things they are passionate about. Slowly, gradually, something new would take shape and form.
Me, I would advocate for starting with something like, “arithmetic is faster counting”, and teaching about infinity to 8 year-olds. You might have different ideas in mind.
What is in your ideal mathematics curriculum? Why even teach mathematics?
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