Believe it or not, it was scarier to watch the video than to do the interview! I think I will tuck my hair behind my ears next time.

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Well done, Maria!

Very nice!

Maria –

Great job articulating the issues (and I thought your hair looked fine)!

Caroline

You look great Maria! However, don’t you think that it is difficult for a student to grasp the idea behind derivatives (for example) before practising the algorithms of derivation in some examples?

Jose

@Jose That’s a great question and the answer is that I don’t know. We don’t have any evidence one way or another and I’m not even sure that it’s a fair comparison. I know that it’s near impossible for US to grasp the concept that there may be a way to teach the ideas of derivatives without the algorithms, because we all learned the algorithms. Here’s another look at the same problem: I never learned how to manually find a square root. For my entire life I’ve used a calculator to find square roots. Do I still grasp square roots? I think so – my understanding might be a little different than those who learned to algorithmically find square roots, but their understanding probably didn’t include the understanding of radical functions in graphs (lacking easy graphing tools).

If you want students to understand algorithms, then you have to teach them algorithms. If you want them to understand graph behavior, then you have to teach them graph behavior. The question that we’re really going to have to wrestle with here is “What do we really want our students to understand about math?” That should be what guides us. If the answer includes that we want them to learn how to correctly use algorithms and pay attention to detail (valuable skills), then we should continue to teach algorithms. However, we should not delude ourselves that the important thing is to specifically learn the product, quotient, and chain rules … the point is to gain an understanding of how algorithms work and how to see when they are applied. It’s a shift in the principles-knowledge for why we teach something.

Perhaps we should be teaching different maths – math for future engineers. math for future doctors/health professionals, etc. Somewhere there is a “general math” course – the hardest of all to put together.

You did a great job in the interview. Also, your example about manually finding square roots really has me thinking.