Teaching the difficult work of thinking hard

When I was last in the classroom, I spoke a lot with my friends and colleagues about the hardest part of teaching in any subject–teaching how to think hard.

Imagine the student who reads a passage of text and says, “I don’t understand.” Instead of explaining, what if I say “think harder.” What should the student do? Mindfulness practice teaches that consciousness and attention are muscles that must be trained or they will be flabby and ineffective. How do we train the muscles of the brain? What is it that we do when we think hard about something?

recent post from Steve at the Math Forum at Drexel University, might help fill in some of the blanks. Steve’s post is a response to a New York Times article by Pam Belluck. Belluck discusses a Purdue study in which students who took an open response test after being introduced to a concept did better than those who studied or completed graphic organizers after being introduced.

I am not getting into the details of the study here, because I am more interested in what Steve writes. For half a year I taught geometry. I’m an English teacher by trade and passion and so I approached the teaching of geometry the same way I approach all subject matter, by beginning with the question of why it’s important and how it’s used in the real world and I felt like I was engaging them in powerful, real-world material and thinking.

After a unit in which students used area and perimeter to design a room in my house and then did very well on my unit tests one of my students had some words for me. “Mr.,” she said, “you’re a great English teacher and all, but you sure don’t know how to teach math. You have to show us the problems and then give us practice problems in the book so we can learn them.”

It’s emotionally easy to do drill problems–thinking hard is much more emotionally exhausting. Steve writes:

Many students who struggle with math have learned that their own thinking is irrelevant, and they discount it. They either give up or they struggle to find out what they should be thinking and write it down, without ever actually thinking it. I think that learning requires significant moments when one mulls something over, trying to make sense of it, putting one’s thinking together, and asking questions to which one wants the answer, keeping one’s attention internal, on the development and connecting of thoughts, rather than going to external sources. This, by the way, does not have to be an individual act. I think it is possible to do this in a group as well.

How can this be taught? Steve doesn’t offer all the answers, but he points us in the right direction–more thinking structured into the practice of learning and structured into learning strategically:

One of our research projects here is the Virtual math Teams project (http://mathforum.org/vmt/) and colleagues were wondering if the collaborative discourse we promote there might be even more effective [than an open-ended test]…More important is the impact on forming new ideas because the VMT participants initiate ideas and questions, discover, etc.—which is thinking work they could do in the test situation but are less likely to do there. I think this VMT process “leaves them along with their thoughts” on the front end of learning and makes it more likely that they will be interested and engaged, already connected to their own thinking, and thus have something rich to reflect on if they were to then do the open-ended test essay.

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