Is our view of mathematical understanding too vague? (video article)
Richard Andrew
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In my early years of teaching, I believed that as a teacher, my job was primarily to teach procedures. After all, I had to get through the syllabus, and the syllabus contained many procedures.
I also believed that if my students gained sufficient practice with the procedures, they would ‘understand the mathematics’.
Understand the mathematics? What the heck does that mean?
At the time, I had no idea. Nor did I know that I had no idea.?
That’s the thing about lacking awareness - you're usually unaware that you lack it.
I have reason to believe that, in many mathematics classes across the globe, too many students spend too much time in too many lessons not understanding the mathematics they are working on.
But again, what are we talking about? What does ‘not understanding the maths’ mean?
In the video below, I suggest a much more precise way of looking at mathematical understanding.
If we adopt this more precise way of viewing mathematical understanding, we'll end up with more students being happy, engaged and feeling a part of the learning process.
Check out the 3-min video …?
Your turn ...
If you would like some information on PD that will have you (or your department) presenting mathematics in ways that promote deep understanding and agency, let us know in the comments.
maths teacher | flipped learning expert | AI experimenter | content creator | teacher trainer
2 年I couldn't agree more; conceptual understanding must be in line with procedural knowledge. For example, I never taught any of the formulas in Analytic Geometry, but one; the gradient. And while doing so, I first introduce the idea behind the gradient; that we compare the change in y by change in x. Then comes the discussion; how can we compare? how can we find the change? what is change anyway? Then we end up with the formula together, and until the end of the content, I always refer to the "change in y / change in x" description while calculating the gradient. This approach has many benefits; (1) students do not need to memorise several formulas, which are actually the same thing in different ways, hence (2) they do not need to memorise the question types, like "if the coordinates of two points are given, I will use this formula to find the line equation, if one point and gradient are given, I will use that formula", etc., and hopefully (3) they realise that maths is not so hard after all, and (4) students can remember the definition and construct the formula themselves, even if they don't remember, and (5) this way, I, or another teacher, can jump into the idea of "rate of change" when differentiation is being introduced.