Posts Tagged ‘math education’


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.


Micro rewards have weird effects on decisions

Micro rewards have weird effects on decisions

How would you implement micro rewards for wrong steps in a classroom?  The idea would be to either have students get savvy enough that they didn’t take the reward automatically or else learn from the experience of receiving a reward that was short-term good and long-term bad.  The easy answer is candy.  Like, “I’ll give you a piece of candy if you eliminate 13x instead of 2x” when 2x is the right thing to do.  The extension and real lesson here is that sometimes people are trying to get you to do something that’s better for them than you by offering you a short term reward.  This article is really about game design, but it has instructional implications.

It’s easy to see the implications of rewarding correct steps.  This is shaping.  But even that is questionable according to the paper in the linked article.  The paper concludes that when someone is rewarded for correct steps, their learning is not transferable to novel problems, only to identical or very similar problems.

Super Teacher Tools

Super Teacher Tools

Maybe the neatest site I’ve seen for whole class math games.