It was not clever materials, or puzzles, or teaching ideas that had made my class a better place for the children, where they had learned more than they had learned before, but the fact that it was a different kind of human situation. And it was not as an inventor of clever materials that I was of most use to these children, but as a human being who had done a few interesting things in his life, who had many interests, who loved books, reading, writing, sports, and above all music, who was generally fairly kindly and patient with them but who could now and then get very angry, who did not pretend to be something other than what he was, but generally said what he thought and showed what he felt, and who above all generally liked, enjoyed, trusted, and respected them. Almost any adult who felt and acted that way would have done about as well.

-John Holt, How Children Fail (revised 1982 edition)

I am at the Park City Mathematics Institute’s teacher program at the moment, and we are spending a great deal of time doing really deep thinking about mathematics. In particular as we discuss classroom practice, we are focusing on rich tasks that have a variety of entry points, elicit student thinking, and produce varied solution strategies. It’s great fun to think and talk about these things with other teachers, and to put together a common vision for what great mathematics teaching looks like.

There is a bit of an undercurrent against some of what we’ve been discussing, acknowledging that many of us are teachers in struggling schools, and all of us teach some struggling students. We have presented our students with rich tasks and asked them to think in new ways, and been rebuffed with “I don’t get it”, or random guesswork, or numbers copied from a neighbor.

We have discussed strategies to support these students, and have hit upon a number of good ideas, but these seem like tricks, difficult to put into practice on a regular basis, and band-aids rather than long term solutions. Thinking about John Holt’s idea, it strikes me that students in my class do not as a whole engage with math because I provide the perfect scaffolding, or use subtle discussion moves to make them more comfortable. Rather, the students who do not very much like math but are willing to try new things, experiment, and open themselves to new experiences in my class are the students who most like me, seem most interested in me and my life, and are willing to see my class as an interaction between humans who only mean the best for each other, rather than a place they are forced to be to undergo certain unpleasant experiences in order to move on to something else.

Michael PershanI wonder if we teachers need to find content-specific strategies for supporting struggling students. Maybe, just as general purpose problem solving strategies don’t really help kids get better at solving problems, general teaching strategies won’t help our teaching.

What I’m thinking is that we need to get specific — and by that I mean specific about the mathematical problems and topics — that our students are struggling with, and think through student support in those specific areas.

dkane47Post authorI think there are two different issues here — I agree with you that being more specific will make it easier to respond to struggling students. I have plenty of students who really struggled in some areas, only to excel when we moved into a new topic.

That said, I think of those areas as focused on content knowledge. I also think it’s important to consider socio-emotional safety, mindset, and beliefs about math — all of these are in play as well, and this is more what I’m talking about in this post. I would hypothesize that there is a certain barrier that gets built up by issues beyond content knowledge, and this barrier must be broken down in order to do any of the instruction we care about.

Michael PershanSocio-economic safety is crucial, but is there (realistically) anything a teacher can do about it? I ask that seriously.

I’d say the same thing about mindset and beliefs about math. We talk about these things as static properties of a student’s worldview, and we talk about how to change or replace those static properties with other, better, static properties.

But what if that’s all wrong? What if mindset and beliefs about math are actually as content dependent as questioning strategies, feedback, and problem solving strategies? What if we need to change the conversation from “what do my students think success looks like in math?” to “what do my students think success looks like in graphing two-variable equations?”

I’m skeptical that, as you suggest in this post, our students perceptions of us as interesting, nice people is separated from their perceptions of our class, or that those static perceptions of our personalities do much in the way of motivation. (I heard, in my first few years, “Yeah he’s nice but his class sucks” from a bunch of kids who weren’t giving me much of anything.) More likely to me is that our students perceptions of us are entangled with our ability to bring them to success.

dkane47Post authorInteresting. This is really pushing my thinking. I want to break this down a bit because I don’t want to conflate what I think are related but different ideas.

Mindset — a student acts upon the idea that they can be good at something by working hard and persevering. I think you have a good point about this being context-dependent. There’s no reason why math needs to be the grain size, I would agree students’ mindsets are more nuanced. They see a problem that is familiar to them, or framed in a familiar way, and they carry that mindset with them into their problem solving process. I have seen some students carry a mindset that, when they are in math class, they are not intelligent. They might be able to do math outside of math class, and also give up on something non-mathematical in math class, because they carry those emotions with them. That’s definitely a minority, though. I definitely see your point here, and also would want students to look at things they are working to get better at as more nuanced than just “math”.

Beliefs — a student’s ideas about what math class is about. Is it about getting right answers, following procedures, wondering things about the world, inventing new ways of doing things? I think, similar to mindset, a student may have different beliefs about different areas of content, but spending x amount of time in math class every day for 12 years causes them to carry some of these beliefs about math as a whole.

Socio-emotional safety — doing difficult math involves taking risks. Students will be willing to do this if they feel comfortable with and trust the students and teachers around them. I think I can make a big difference here, in particular with the way discussion and group/partner work is structured in my class. I see this as particular to the room and class culture that the student experiences each day. They will come with some baggage, but I believe I can make a big difference here, and this is the barrier I want to remove for students in their willingness to put themselves out there.

I’m hedging a bit here, but as I’m thinking about your argument, I think that all of these things actually vary day by day a great deal. A student can present in totally different ways consecutive days, based on any number of factors. A new topic can make a huge difference, or pre-teaching material after school to increase students’ confidence, or talking to them in the hallway. There are content variables, there are relationship variables, there are class culture variables. I like what you said about perceptions being entangled with our ability to bring them success — I’m rambling at this point, and I think that might get at the heart of the matter better than me trying to break down all these different ideas that are maybe actually all the same idea. I don’t know.