Mathematics Education: Five Bold Pillars For The Next Decade
I just got back from Jasper, Alberta. I was there for the annual math conference for Alberta math educators. For three days, this was my view.
Seeing the Canadian Rocky Mountains for the first time is breathtaking. They dwarf whatever might be in your imagination about their majesty and size. That physical humbling by one of nature’s gifts set the perfect tone for the math conference, and the clarion calls for a higher purpose of learning mathematics that reverberated with all the attendees.
It also made perfect sense, poetic sense, that the two keynote speakers were Francis Su and James Tanton. The embodiment of flourishing and humanizing as passionate themes in learning mathematics is in abundance with those two, and they earnestly shared their humanness ideas of mathematics with packed rooms of math educators.
- Mathematics is for Flourishing
Is it? Should we approach mathematics through this Why lens? Should be tether the learning of mathematics to higher, wiser, and more ancient ideas of the good life, eudaimonia? Francis Su, who was the former President of Mathematical Association of America, would confidently say “yes”.
But, for the large collective, caught between the spokes and the gears of the machinery of education, our “yes” might be punctuated with sighing, frustration, and even hopelessness. Mathematics is currently not taught with this idea, to give us a sense of wellness, balance, and grace. In fact, it is generally taught at the complete opposite, in terms of experience — anxious, hurried, and competitive.
If we invite people like Francis Su and James Tanton to speak at conferences as keynote speakers, to illuminate paths that should be taken, and we don’t take those paths, then what is the point in bringing them in. The tax of pushing — ham fisting — mathematics through bean counting, benchmarks, over baked assessment, over scaffolding of ideas, and of course, time constraints has unsurprisingly resulted in consistent and historic…anxiety.
93 %. That should surprise nobody reading this. And yet, very little is being done other than reporting something that has been obvious for generations. We need to flourish as society. Mathematics allows for that. We now need to allow for that.
2. The Staircase Model of Learning Mathematics Doesn’t Work
Well, it works for what it was intended to do. To sort. To sift. To install gates. To efficiently measure. Very few who leave the staircase at the top leave with any meaningful curiosity about the subject. The exiting memory is completely wrapped around grades, GPA, and college entrance. Children do not benefit from this linear and narrow journey, especially with the depth of mathematics that they should be exposed to. The math curriculum should be more like an Escher staircase, filled with many doors to explore, each possibly taking the student on a quirky but wondrous route — continually binding understanding.
I created an image to show the difference between what standard K to 12 is like vs what it could and should be like. It actually got over 100 shares in one hour on Facebook. That shouldn’t surprise you. Most classroom teachers wish they could set students, themselves, and mathematics free. Instead, we climb the stairs, tired and anxious, and wholly burnt out by the end.
3. Build a Stronger Bridge Between Arithmetic and Algebra.
We don’t spend enough time on arithmetic. It’s embarrassing. We jettison that topic, leaving our students with an unstable appreciation and understanding of it — jeopardizing their future experience with mathematics.
Take a question like 37 x 27. I don’t care about the answer if it is given in this non-context form. So, just go to your smartphone calculator and punch out 999. But, if you are going to wade into thinking about this question and what can be mined from it, stopping at long multiplication is an announcement to the world that math education is stuck in the 19th century.
Below is just one of the “trivial” question that I unpacked at The Museum of Mathematics in our full Chasing Rabbits PD on November 5.
The first exploration took us to a staircase of why two negatives equal a positive. Another staircase took us to some math history and how Vedic mathematics approached such a question — utilizing and reinforcing the idea of place value. Where do the “1's” come from(7 x 7). Where do the “10's” come from(3 x 7 and 7 x 2). And the “100's” come from “3 x 2”. A little bit of fun redistribution, and we get 999. The third idea to be extracted come from the Russian Peasant method. Why did I only point to the odd numbers and total up the respective sum in the right column? Hmmm…something to chew on, right! Do the question but with 32 x 27. Look at the result in each row. Mathematical “equilibrium” is always attained…
4. Emphasize Mathematical Thinking not Mathematical Understanding
These two ideas are used almost interchangeably, so you might naturally wonder why there is a distinction and why one needs to be emphasized. Well, for one, understanding is a terminus for mathematics. It is the endpoint after hours, days, weeks, months, and sometimes years, of toiling, struggling, plodding, reflecting, wondering, and musing about the problem in front of you. It doesn’t come cheaply. If it does, you didn’t buy mathematical understanding, you bought mathematical familiarity.
Mathematical understanding is highly desired, but not always obtainable — and it doesn’t carry a stopwatch. Mathematical thinking is the precursor to any understanding which might follow. It is accessible to all. Even if you are confused about an idea, and maybe going down a broken “staircase”, you still are exploring and are involved in mathematical thinking. Being confused? That is part of mathematical thinking. Stumped? Also mathematical thinking. Understanding comes with pressure to know right this minute or soon thereafter. Thinking just means you are involved in the problem. And, the only way one gets to the oasis of mathematical understanding is by being involved in the entire journey there — thinking.
5. Expand The Lens of Equity to Include Math History
All efforts to (re) humanize mathematics will involve a collective effort to know and appreciate where mathematics originated and migrated over the course of its history. If we are still teaching K to 12 mathematics through either a sterile lens(no history) or one that is skewed with Western narrative, then we will shortchange our equity ideas. We will only end up giving all kids access to the same distortion of the roots of mathematics.
When he talk about history, we end up in the warm well of storytelling — the most powerful way to teach and connect. So much ancient wisdom lies in the history of any subject, but for mathematics it is a colorful exposition of its unflinching humanity.
There are some days that I think mathematics is more human than us. We treat mathematics like an animal in a cage, trying desperately to domesticate it for a purpose that has caused millions of unhealthy experiences — success. We collar it with benchmarks, tests, exams, dry objectives, inert goals, unexplained demarcation of topics, etc.
The next decade must be about recapturing the spirit, wonder, and magic that is native to mathematics, but not so native to the industry of math education. Change will not occur overnight. It probably will take the better part of this century. I don’t mind. I won’t be around to see it.
But, hopefully my kids will…
