Occasionally, students ask me questions about why math works the way it does. This doesn’t happen enough, in my opinion, but it does happen.  The latest is why, when we perform synthetic substitution, do we use the number as it is, but in synthetic division, there’s some sign trickery.  I have an answer for this.  It’s not super complicated either, but whenever I’ve given the explanation in the past it’s been frustrating and incomprehensible to students.  So, I don’t know if it is worth the time it takes to do that, and that kind of understanding is not necessary for skill performance.  But then, what am I doing? If we don’t care about understanding or make that kind of tradeoff of “well, they don’t really need to know this” that feels like the opposite of mathematics education.  I’m pretty good at explaining things like this, so I don’t think it’s me.  There is such a thing as developmental readiness and that’s what’s happening here.  I think.

What do you do when explanations are over the students’ heads?  Is that just a normal thing that resolves itself with further mathematics study and we shouldn’t worry about it?  I find “that’s just how it works” a completely unacceptable response.


2 responses to this post.

  1. Reason not the need. I would forget about whether it was “worth the time” and try to do my best to explain it. It is possible that they won’t understand it, but I would hope that after doing this a few times I might hit upon some way to make it easier to understand. In any case the student knows his or her question was heard and taken seriously and may revisit the question later when s/he can better understand it. K sometimes reads books that she cannot fully understand. Recently she told me about one of those books that “Every time I read this book it expands the capacity of my brain to understand it a little bit more the next time.”


    • We can never forget about time. Beyond that, a bad response or one that is too far out of the students’ zone of proximal development serves only to frustrate. Creating confusion is sometimes important and necessary, but creating frustration, when we know that will be the outcome, feels like a waste. I don’t know how best to serve the natural curiosity.


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