Messy Mathematics

This post is really a vehicle to get a comment that I received on my blog more face time. I thought the potency of the words could not be ignored. It was in response to my post entitled Measuring Roots.

To get the full story, first read that particular entry. Basically, I was reliving my encounter with a small boy where he challenged me to answer a square root problem. He let the answer slip prematurely, and quickly rephrased his question. It was very obvious that he had the answer in mind before the question had begun.

Using this idea, I wrote:

“For students, no matter how young, math begins with an answer. You then form a question, jeopardy style, to help disguise the number. In this case, the child’s thinking shone through because he leaked his answer prematurely.”

If you read on through the post, I refer to this phenomenon as a problem, and I do not agree that answer-first mathematics is a positive thing. (I have since changed the wording in an attempt to make my personal views more apparent.) Shawn Urban (@stefras) posted the following comment on the post; it is a impassioned statement from an educator that we all should read:

I stopped reading this post as soon as I read the point that, for students, math begins with an answer. (Don’t worry, I plan to read the rest of the post. But I needed to respond to this; it is so mind-blowing.)
I learned under Dr. David Pimm of Open University (UK) and the University of Alberta (CAN) during my Diploma in Math Education studies. He argues that math begins with a question; in fact, it does not exist until a question is asked. All the demonstrating and lecturing about math in the world does not involve math until a mathematical question is asked.
This discrepancy is very revealing. It tells us what math is and what math education is. Most students learn to expect math questions and problems to be short, quick, to the point, solvable and structured around “clean” answers (often related in some way to integer components). They anticipate the answers before they anticipate the questions. I am not sure if they even consider the math.
I wonder what they are really learning? Is it math? What to them is math? Is this why so many students are so disconnected with math and why they are proud to have failed it and ashamed to have aced it? After all, from their perspective, if answers they anticipate before math, what have they aced?
I think we have done students a great disservice if they ace math in elementary, secondary and even tertiary school without ever actually learning that math is all about the question, the quest and struggle to tackle it and the discovery of pattern that limits to (an) answer(s). They completely miss the point and the empowering strength of math process and pattern. And in the end they really have nothing to use in their lives beyond the “math” lesson.
So, why do they need to learn this? That question makes so much sense now.”

What view of mathematics do you subscribe to? Do you advocate “clean” answers, or embrace the messy nature of mathematics. Something to think about and reflect on. 
Nat Banting

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