Math PD During Our School-Based Learning Day! Focus: Open Response & Open Ended Questions

The launch point for today's PD

Today we had a 1/2 day PD session for most of our staff. This year our focus at Parkview is Math. We got to sit with Tara Fuerth, our school's math consultant. I don't normally have an opportunity to participate in school-based PD so it was a treat to get to sit in today (Thanks, Mr. Huggard!).  We were talking about using open questions in our math classes. I don't specifically teach math this year, but I appreciate decent PD so to be sure I walked away with some value for my time, I thought I'd blog while we went and perhaps some of you who DO teach math on a regular basis can gain additional value from my afternoon. Here's some quick notes about what went on.

There was some discussion about how teachers have started clarifying with their students that when using the I-chart (the part when it says "understand") isn't as much about saying whether you understand the question or not, but rather first they need to identify any of the words in the question that they don't understand. This made me think - Wouldn't it be interesting to use Padlet or something else to collect this kind of vocabulary and thinking as they go?

My favourite part of the afternoon was reading about the four strategies for creating open questions in math (from the article Beyond One Right Answer by Marian Small). 

We discussed parts of the article we agreed with and areas of challenge this sort of thinking presents. There was some conversation about how EQAO does not match this shift to "many answers, many questions, same concept". If this is where they're putting the money in support of the research then how is the province helping real learning occur with its continued focus on the scores from a test that is all closed questions? And what happens when they enter high school? Is there open-ended learning happening in the high school math class? Doubtful. It would be nice, but the majority of high school teachers we've chatted with are definitely NOT doing these sorts of things in their classes, particularly the senior grades because "preparation for post secondary". 

"Change in learning is bottom-driven. It always has been," one of our seasoned teachers noted. "Elementary teachers and students will push the change into the high schools and from there into the colleges and universities." I have certainly noticed that pedagogical change seems stymied because of the "prepare them for University" mantra and that University is definitely NOT following the research of what makes for the best sort of learning for students. But I'd never thought about it quite like he said it. I hope that's true, so the change moves up eventually, but I think it's sad in some way that this is the case. 

"There is no 'wrong' way to present mathematical learning to students," Tara said. The concept was there is not one "right" way of teaching, only ways of delivery of differing effectiveness for each student, and we probably won't do open questions all the time and that's okay. Flashback to that quote from Chris Moore I heard at EdCampSWO, "You can be where you are, but you can't stay there."

Doing an open problem at the beginning of the unit allows us to have a diagnostic of where the students in the class are and informs differentiation for the rest of the unit. It's an idea several of us have used: Have the text book for the upcoming year available for students who can already prove that they know this stuff so they can move on, etc. 

Rather than sending the fast finishers and Level 4s to "help other students who are struggling" (who is the trained teacher here? the 10 year old or you?) instead have them plan and use technology to create a tutorial or a lesson or a presentation explaining that concept or the big ideas etc. (plug for tech integration #2) ;)

As always, more time is required for deeper learning to occur. (There's a video here but it may not appear if you're viewing this post on mobile). 

Creativity takes time. 

If an open question does not always have to have more than one answer or more than one fact set, but can simply have more than one strategy then ANY math question can be made into an "open" question by asking for several strategies. But this is generally not the way we define an open question in math. "Think about how your brain was engaged for each question," Tara told us. Open ended questions allow for deeper levels of thinking and (gasp!) creativity, while most closed questions rely on shallower thought processes.

Two questions: One open, open closed.

I also shared this great poster I found on Twitter since it seemed to connect.

 Instead Of... via @sbruyns

All in all, it was an afternoon well spent.