The Smallest Things Can Cause Huge Problems for Students
It is often the case,
for the mathematically-insecure, that the slightest point of confusion can
completely undermine their determination.
Consider a beginning Algebra student that is learning how to evaluate functions
A confident student is
likely to make the same error as the insecure student, but their reactions will
be totally different. Below would be a
typical incorrect answer that students will make:
The correct answer is
3, and the mistake is that -22 = -4, because it is really subtract
two-squared. And when students make this mistake it provides a great chance to
help them learn to read math, especially how exponents are written and what
Here’s what the
students actually read:
A confident student
will be receptive to this without much encouragement from you. However, the insecure student will completely
shut down, having found validation of their worst fears about their future in
There are times when
leaving traps for students is a great way to expose a misconception, and in
those cases, preemptively trying to prevent them from making the mistake would
actually, in the long run, be counter-productive. Students would likely be mimicking what’s
being taught, but would never uncover their misconception through correct
answer getting. Mistakes are a huge part
of learning and good math teaching is not about getting kids to avoid wrong
answers, but instead to learn from them.
But there are times
when explaining a common mistake, rooted in some prerequisite knowledge, is
worth uncovering ahead of time. This -22
squared is one of those things, in my opinion, that is appropriately explained
before the mistakes are made.
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