let’s give them sometin’ to talk about
I am not a fan of quiet classrooms. I like it when students are willing to talk, ask questions, and put their thoughts out there. My room is in table groups of 4 so my students have to face one another and, *gasp*, discuss the math they are working on. Now I’m not trying to say I do good group work because I am not that awesome yet, but I do believe that I do a good job creating a classroom environment where students are willing to talk about the math at hand and ask each other questions.
At PCMI Bill Thill put together an evening of 10 minutes shorts for people to sign up and share something they do in their class that they love. I got to go first and my short was entitled “What’s the Question?”, which is a warm up format I came up with second semester last year that I loved and I think did a lot for creating a classroom environment of discussion. Note: I don’t think this is an activity I ‘borrowed’ from anyone, but if you read the following and know of someone else who does something similar please let me know so I can give credit.
the general set up:
Let’s say you are in my Precalculus class and we’ve been working with trigonometry. At this point you pretty much know what sine and cosine look like, you got right triangle trig down, and you can plunk down a 16 Point Unit Circle down in under 5 minutes (yes, I do make my kids do this). Now as my student you walk into class and see the following on the board:
Here’s how it works. Underneath each of those blue tiles is an answer a la Jeopardy. I pull off the first blue tile to reveal the following:
I give students about 30 seconds to absorb the solution and think of a question that it answers. They are allowed to talk to their group mates, but no cross-table talking. I use a die to randomly pick a table. I write out every question students say under the answer. And try not to offer too much commentary. I do this again for B and C.
what actually happens:
I often pull answers from the previous night’s assignment, so kids learned quickly to have out their homework. Since I don’t assign many problems it’s a quick skim before one of them is bouncing in their seat with “what is the solution to number 3?” Sometimes interesting discussions about why that is the solution to problem 3 happens and I will ask other students to work through their logic in explanation. I also accept non-math questions unrelated to our current studies. “What is the scariest expression I’ve ever seen?” “What is the most awesome looking rollercoaster ever?” “How many servings of ice cream did I have last night?” “What is can I phone a friend?” If something like the last one comes up, I move onto another group. I once had ‘2’ up on the board and had a student pull out “what is the only even prime?” That kid is made of win. I also have no problem hinting them in the direction I would like them to take their questions *cough*trigratios*cough*
There is a lot of group debates, good-natured heckling for comic answers, and positive phrase for the groups with mathematically relevant solutions. Sometimes they surprise me with things they learned the previous year. Sometimes they surprise me by not coming up with anything relevant, but that’s useful information to have heading into a lesson. There were a few times the blank faces helped me insert a ‘hey, remember this stuff?’ mini-lesson to get those light bulbs to go off.
Priority number 1 for me in doing this is to get them talking in math class. How often do we as math teachers face a sea of silence? I don’t want words to be like pulling teeth. The kids need to see that my classroom is a safe place to talk and be wrong and be silly and say the most dreaded three words: “I’m not sure.”
Priority number 2 is about making connections. Want to make sure they remember some important skills they are going to need from yesterday/last week/last unit/last year before you head into the topic of the day? Sure, you could ask, but kids are remarkable at faking knowledge and faking themselves into believing they actually have things down.
My third priority is inspired by Stephen Colbert’s The Word. For those not familiar, it’s a monologue with text offsetting what is spoken in a humorous way. But the kicker is that the first line of text is always the last line of text, thereby linking the beginning to the end. Here is a shot of what’s under C:
Now, I don’t need to tell math teachers how much the Pythagorean Theorem plays into trig ratios, but the kids? They didn’t even know there were trig identities before today. Now they’re primed. Now they know that Pythag is a key, so now they’re looking for where to make that connection in the lesson. And I have no problem with my kids beating me to the punchline of a lesson.
some fun stuff:
Why put just math stuff? Why not steal vocab words from English class? Plan mini-WCYDWT videos behind the blocks to see what questions the kids have? Something from current events, perhaps? Your own brand of geekery?
Now, I have a SmartBoard, but this works under a doc cam with a sheet of paper and sticky notes or on a whiteboard with three sheets of paper labeled A, B, and C taped to the board. Smartboard is just easier for me to make a page for each class and then compare guessed from the classes at the end of the day (Mmmm, data).
At PCMI the teacher topic is always “Making Connections”. The morning session crew do an amazing job of this and it made me want to spend more time on working those connections in between lessons. I cannot wait to do a better job working with complex numbers and vectors and rotation this upcoming year, but that is a topic for another post. What making up the A, B, and C’s did for me was provide a format for focusing on the connections. This is something I suspect we all try to do when we’re lesson planning, but by thinking about necessary skills from the lens of what type of questions do I think the kids will come up with was really inspiring to me. I also kept better focus on only one or two big things per lesson, which for my non-linear self was quite helpful.
But the laughter! How much laughter do you think the average person on the street would say is in math class? These kids are hilarious and creative and geeky and amazing. Kids that would never talk eventually started speaking up with some prompting and even though it often started with “what is 1 plus 1?”, at least it’s a start! I’m torn that I didn’t keep up with this warm up. I used it consistently for the first part of the semester and then I started panicking about time and getting through all the things I wanted to do and it fell by the wayside. Looking back now I can see how powerful it was for the class and I didn’t realize it at the time. One of my goals for this year is to do this at least once a week. I believe it will keep me focused and keep the formative feedback-loop going. I’ll keep you posted.