Better Math Discussions

When I first started having students to present their work to the class, I quickly realized that wanting to have good student presentations was oh so removed from having good student presentations. Half the time, the work was hard to follow or the explanation didn't make a ton of sense to the rest of the class or the way they did the problem was so wrong as to not even really be useful for discussion or even when everything was great, the rest of the class wasn't remotely interested because they had just done the same problem in the same way so why did they need to hear another group explain what they had already done themselves? And kids were just not used to sitting through presentations done by other kids. They were restless, distracted, and lots of classroom management was required to get some semblance of presentation. Not to mention the fact that I don't think these presentations did much in terms of any sort of math learning. I think I was just doing them because I thought I was supposed to do so?

I loved "5 Practices for Orchestrating Productive Mathematics Discussions" when I first read it a few years ago. It was the most succinct and clear set of explanations for how to organize discussions around student work. The key idea for me was that it involved NOT calling on random groups to present and that it required giving students problems for which there are multiple approaches. The idea is that the teacher selects which work should be discussed and that there's a rhyme and reason to the work that's selected and the order in which it's presented.

Having an Apple TV and iPad in my classroom the past two years has also been very helpful for doing the selection of student work and sequencing it in an order that makes mathematical sense. Before the Apple TV, I would run around the room, taking notes and trying to then remember which group I wanted to go first and why. Also, even with my giant whiteboards, some students feel the need to write microscopically.

Now, I just take a picture of the various approaches that I want the class to discuss, put them in the order that I want using the Notability app (you could use any app that allows you to stick in pictures), and then projecting each picture in the correct order and big enough that even my tiny-handwriting students' work can be read.

My other breakthrough was that having problems with multiple approaches is key because it really is boring and pointless to hear presentations of the same thing you've already done. It's much more interesting to see and learn from different ways to the same problem. If the content doesn't lend itself to problems with multiple approaches, you can assign similar, but not the same, problems to different groups. It can make for a good progression when the problems build on each other or when each has only one element that has been tweaked.

I have also been working with students on making the presentations more useful. Instead of just talking about what they did from start to finish, every group after the first one is asked to explain what they did differently from the other groups and discuss the benefits and drawbacks of the approaches. At the end of presentations, I also ask students to summarize the different ways and discuss when we might use one versus another.

Another issue that I had is with putting up work that had mistakes in it. Students would freak and be horrified that their WRONG work was being shown to everyone.

It helped a lot when I stopped attributing which group the work with an error came from and emphasizing how useful the mistake was to our learning. It's February, and I'm finally getting to the point where students ask whether their mistake is interesting enough for showing to the class. Score.

The things I'm still struggling with for group presentations are how to talk less and make them talk more. I still find myself doing a lot of the "summarizing" and pointing out key aspects of the work to the class, and I want to push myself to turn that over to the students. I would also like to find more ways to increase the engagement of the students who are listening to the presenting group. Perhaps asking them to write a summary or some other response after presentations or require each group to ask a question of the presenters. Other ideas?

Student skills

I've been thinking a lot recently about the differences between successful and struggling students. It is obviously easier to be a successful student if the material comes easier to you, but there are plenty of students for whom the learning part is hard and yet who are quite successful and even more that are the opposite. There are a lot of specific student skills, such as organization, time management, ability to focus during instruction, etc that I think students at this age are aware they need in order to be successful. But there are also others that I think are less obvious to them: asking questions, knowing when you don't know, and the big one: persevering when something doesn't work at first. I feel like I need to start paying more attention to these intangibles and teach them to struggling students explicitly rather than being annoyed if they're not "motivated" to do well. Obviously, this presupposes that the material is being taught in a way that is accessible and engaging, but I think that while the teacher has an important role, the student's role is even more fundamental. A student who has these skills will likely do well regardless of the teacher while a student who doesn't will likely struggle no matter how talented the instruction.

So, some things that I've been trying to get at these "student skills":

1) Journal prompts asking students to reflect on how well they feel like they're doing with the current lesson, what questions they have, and how they're going to address their questions.

2) More journal prompts asking students to reflect more broadly on how they're studying and keeping themselves engaged during class.

3) One-on-one meetings with students where we set individual goals and talk about progress in meeting them. (I haven't done these as much as I'd like this year... this is a good reminder to start these back up.)

4) Emphasizing over and over again the importance of effort, perseverance, and asking questions and that this is what's under their control and should be the goal towards which they're working rather than an abstract "I want to get a good grade."

5) Distinguishing between general effort and reflective and directed effort... for example, homework credit is only given for assignments in which the answers have been checked and mistakes have been corrected (with ample opportunity and encouragement to ask questions in class), not just for attempting problems. Part of students' participation grade (10% of their  overall grade for my more-struggling classes) is predicated on asking thoughtful questions.

6) Focusing my comments on grade reports on progress made and effort expended and not just on results reached.

I'd love to hear of ways that others encourage students to push themselves and become better learners.

Some journal prompts: