Last year, one of my professional development classes was about techniques for getting students to Think more actively in class. It was taught by my school’s headmaster, and he based it around this great Visible Thinking material that was made in Harvard’s Project Zero. (Here’s a link to their website: link!)
A lot of their materials are pretty obviously focused on English and history/social studies classes, so it was a bit of a challenge to adapt them to math class. But of course, I think that a lot of my stuff that works the best comes from practices outside of math.
I have used their “asking questions” strategy several times now in order to introduce new units. Usually I give students an equation with its graph and just ask them to ask questions about it. The only difficulty I have in that part is that I sometimes need to remind them that I am NOT looking for questions to which they know the answer — we want to get curious about this newish thing in front of us.
Here’s the sheet that I hand out:
*Awkward: there is no #2. I told my students it’s because #2 is gross, and we don’t do that in math class.
Here’s what we do:
- Each group makes list of questions — hopefully 5 each.
- Share on the board. Discuss them. What’s similar? What’s curious?
- Each group chooses two to investigate.
- Groups get 15 minutes to find answers. Keep a detailed record of their work.
- Groups share their findings.
Most recently, I did it to introduce different ways of moving graphs. These are a few of the questions my precalc kids had based on the worksheet above. That is, they actually made sentence that used correct grammar, and I rephrased them like this:
- What if we divided by 3?
- How would it look different if x^3?
- What if we had y^2?
- What if the equation was its inverse?
- What if we added 5?
- How make skinnier/larger?
- What is the purpose of this graph?
Sometimes, students end up asking all the most basic shift questions: how to move it up/down, left/right, make it more narrow/wide and how to flip it upside down. Then we don’t really have to spend any more time on those things and can move onto the trickier stuff. This class didn’t hit all of the basics, but I think they had cool questions.
Problems with the activity:
- It takes more than 1 class period, so it’s hard to maintain continuity.
- Doesn’t really engage everybody in the group.
- Students don’t take the write-up very seriously.
- Students don’t really learn from what the other groups share.
Most of the problems come after the initial aspect of making the questions. I think I need to make a few changes.
Change 1: only have groups of 2 or 3. Groups of 3 or 4 just aren’t working. Especially when it comes time to do the write-up.
Change 2: have groups report out using a poster. And I’ll show which sections must be included. Right now I’m thinking:
Hopefully this will help students to better understand their goal and to have a product that they feel more proud of.