The Road To Learning Mathematics Goes Through Struggle, Not Efficiency
This past weekend, I found myself dragged down into the bleak hole of “Math Wars” debate on Twitter. None of the people who were bemoaning current methods and pedagogy are actual current K to 12 math educators — which should alert to you to the asymptotic limits of these conversations.
For the back-to-basics folks, it’s times tables/math facts/standard algorithms/direct instruction or Bust. What has ironically prompted this heated demand to go back is the collective idea of seeing too many kids struggling with mathematics.
Not only do these people have the completely wrong idea about what struggle is and how it has been the organic narrative for the entire history of mathematics, but they have chosen to stigmatize and demonize that word, to desire to extricate it from the learning and lexicon of mathematics. To apply superficial gauze and bandages of poorly explained algorithms like long multiplication and long division to minimize the bleeding of this struggle.
This struggle, of course, gets into the water of media, and is tethered to test scores to further legitimize the idea that students struggling is an epidemic that needs to be stopped — at all costs.
If you are going to put students and teachers on the clock, that resolution to a math problem or understanding has to occur by the end of the class, then of course struggle will lead to anxiety and frustration. That is why the environment of the Growth Mindset is critical in facilitating this kind of mathematical turbulence — and enjoying the ride!
Without struggle, you cheapen the mathematical experience — at best. At worst, you set these students up for anxiety and frustration when they cannot solve a problem that is not like the one they have seen in a textbook or practiced dozens of times. Or, they cannot solve it within the time it takes to boil an egg.
One of the best courses ever created in Ontario, was removed rather quickly after its introduction. While never publicly acknowledged, the guess was that too many kids were struggling with…struggling. If, as mentioned in the paragraph below that some of the problems could take days or longer, then of course they were set up for failure.
When would they have been exposed to such struggle?
This downhill-struggle-free path in learning mathematics leads to a complete dead end. If students have not struggled — and enjoyed their struggle — their resilience gas tank will be on Empty.
So will be their appreciation for how mathematics is learned.
You shouldn’t have to “get it” the first time, or even the second time. If struggle is installed with empathy and celebration, students will want to explore alternate routes or insights — with enthusiasm.
With the quick-fix algorithm, that is all they will want. They will not develop the patience for irresolution.
Patience is not your ability to wait, but your attitude while you wait.
In mathematics, it makes all the difference in the world. The answer is as only as good as the journey with your peers. And, if that journey is not littered with natural struggle, then students are not engaged in mathematical thinking.
I repeat. If students are not actively engaged in mathematical struggle in safe and supportive environments, then they are not engaged in mathematical thinking. They are engaged in mathematical mimicking.
If you want to bow down to speed and correctness, and superficial test scores, then go right ahead with this stripped down representation of mathematics.
Sure, math facts are absolutely critical and foundational to learning mathematics.But, I have zero interest in the answer for 13 x 13 being left isolated from 12 x 12. Both are squares. The larger square is built with two 12 x 1 rectangular strips and a 1 x 1 square in the corner. 144 + 12 + 12 + 1 = 169. A Pythagorean triple lies in wait.
If you thought that took too long and/or is unnecessary, then I am sure you will also want the derivative rules in calculus given to students without derivation from first principles. Giving students the Power Rule for differentiation without going through first principles is ridiculous. You might as well stop right there with teaching that course…unless you want kids to merely thump out the answers with mere memory…like they did when they memorized times tables.
The back-to-basics groups never mentions the following words when related to mathematics — beauty, joy, wonder, truth, justice, love, magic, mysterious, whimsical, creative, etc.
It’s a Spartan offering of utility and compliance. That’s not mathematics. That has never been mathematics. So all this hue and cry about giving children a better math education, free from struggle, is going to have the exact opposite effect — failure. Maybe not failure in terms of marks, as then the whole curriculum will be a string of memorizing formulas and aping rarely explained algorithms. But, surely a failure in seeing mathematics reflected and refracted through so many vibrant colours.
For me, I like my mathematics in full blown color. To render it down to something black and white — to make political hay — is something I am glad I don’t have to deal with. For me, it is unconscionable.
Without struggle. Without passionately advocating for struggle, I am at a loss as to how or even why you would teach mathematics. Just give out flash cards and a series of “Mathematics for Dummies” books to everyone, and be done with it. One of the by-products of positive struggle will be that students will develop their own efficiencies and their own short-cuts, to as James Tanton says — avoiding hard work!
Mathematical struggle doesn’t lead you to the oasis. It is the oasis.
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Sunil Singh is the author of Pi of Life: The Hidden Happiness of Mathematics(2017) and Math Recess(2019)