Great find! Thanks for passing it along.

Skilling, K., Bobis, J., Martin, A.J. et al. (2016). What secondary teachers think and do about student engagement in mathematics. Mathematics Education Research Journal, 28(4), 545-566. http://doi.org/10.1007/s13394-016-0179-x

For practical reasons (at least pre-computer) almost all pre-college mathematics (and much college math) focuses on techniques for solving certain kinds of problems. At least in my experience the more I grew interested in what I would call “real” math (i.e. proving/deriving results) the less interesting/engaging the game of trying to figure out a way of finding an elementary function representation of various integrals became. Indeed, my grades and classroom participation suffered substantially because my engagement focused on questions of why/how rather than what neat tricks helped solve a problem.

Now I don’t claim to be representative but I think this does reveal a general issue. Students aren’t dumb and if what your tests, homework or classroom exercises focus on is problem solving one can’t drive their engagement with discussion of why/how. My experience teaching and watching others teach inclines me to believe that if the performance you expect out of your students is problem solving (not clever reasoning/novel ideas) engagement comes out of making that problem solving into a fun game while attempting to explain too much about the why of the rules of that game just puts them to sleep and confuses them.

On the other hand if what you want is engagement with the ideas/concepts (i.e. real math) what you need to do is test/evaluate the students on clever arguments (be it proofs/derivations in a college class, novel ways of counting up winning hands in a HS probability class, or clever, non-rote, uses of property/set membership reasoning in a grade school class). However, I fear this later approach is impossible in a setting where there is an expectation that students leave the class knowing how to solve problems of a certain kind. (No, ‘fake’ creativity doesn’t count…even questions that require creative approaches the first time are rote solutions once the student becomes familiar with them).

This is my problem! I believe and preach all of these things, but I always feel the pressure to keep moving. At every level I have taught…K-8 and now college. There is only so much time in a year or a semester, especially when students are expected to perform well on that EOG or final exam. I struggle with this every day and often don’t feel like I have the right resources to be able to slow down to give mastery the time it needs to develop.

Thanks for these, Sarah. I’ve added them to the post.

Mark – Wow. You know all the above responses. I’ve followed you. So my guess is this question isn’t something you are struggling with in terms of pedagogy. You’re a risk taker and will try new things; you listen to other’s ideas and test them out. I’m thinking you are dealing with something other than “teaching” math. So…ask. Ask what’s up. And listen. Really listen. Kids have so much bumping around in their heads and we can’t peek inside. Could be math. Could be this student is one of those who truly has a math learning disability. Most people don’t even know this is a very real neurological/biological/environmental disability. You know Daniel Ansari. He’s tops for the neuroscience part. The intervention part is a bit more tricky.

But…it could be outside stress; dynamics outside of your control, to an extent. What you can do is listen – hear. Then teach coping strategies using some age appropriate cognitive behavior techniques to combat negative self talk and cognitive distortions we create and play over and over in our heads. (If only I took my own advice!) You might not ever see the benefit of this; you might get push back. But I can guarantee, if you ask, and listen, no matter the response, this student will know that someone noticed and cared. And you will know you exhausted your toolkit. If help is needed that you can’t provide (for example if there is a learning disorder or personal stress), you have built the case it’s time to look for other reasons – like going to your general practitioner for a persistent health issue which finally requires seeing a specialist.