Model the Learning

Last year, I had a great conversation with a colleague around math assessment. We were talking primarily about how to best triangulate products, observations, and conversations to form an overall balanced assessment of student learning, but a side conversation has really stuck with me. She told me that on her math tests, for any given learning goal, she gives the students four levels of questions to choose from. The students can then decide how to best demonstrate their understanding of that expectation. I love the idea of student voice and student choice in how learning is demonstrated. But it's taken me about a year to really wrap my head around this idea, and to start working with teachers in my board to try it out. Traditionally... Traditionally, on a test, I might ask students three or four questions all on the same expectation. It might look something like this: Like most teachers, I started with an easy problem, and each subsequent problem gets a little more invo...

In addition to working with grade K-5 teams on numeracy collaborative inquiries this year, I have been fortunate enough to also participate in literacy collaborative inquiries when they happen on the same days. I have very little literacy background, so I'm learning tonnes! I find it very exciting to see and hear how our students are learning, particularly in ways I've never stopped to consider. Earlier this year, I met with a group of grade K-3 teachers as they explored students' ability to predict what might happen in a story. Starting in Kindergarten, the teachers introduced a book to the students by showing them the cover, and then worked with students to access three factors in order to make predictions: they look at the picture on the cover, they consider the title, and they activate their schema . Aside...  Schema (SKEE-mah): relevant background knowledge, experience, or prior knowledge within a context.   I was blown away to learn that students as young as 4...

This post was featured in an episode of  This Week in Ontario Edublogs (July 11, 2018), beginning at 34:42 . Over the past week, we have been piloting diagnostic questions with students to get an idea of their understanding of equivalence. We gave students a series of questions, all having to do with the understanding of what the equal sign represents. One question, though, really challenged my idea of what "higher order" strategies we were hoping to see in our students. Here's the question: If 4x + 8 = 52, what is 2x + 4? Take a moment to figure it out. What is your answer? How did you come to that answer? If you're like my colleagues and myself (and most of the students of whom we asked the question), your instinct might have been to solve for x using the first expression, ...and then substitute that value for x in the second expression: So in this case, 2x + 4 = 26. As students advance to higher order strategies when learning math, we ...

Last week, I was fortunate enough to attend three days of workshops with Cathy Fosnot ( @ctfosnot ) in North Bay. This was a great opportunity to see so many constructs in person that I had previously only learned about through her books, or the podcasts with #notabookstudy and #themathpod. It was amazing to see "math congress," "mini-lessons," and "gallery walks" come to life! Also last week, I wrote about how math teachers can change how they ask questions in order to probe for concept development, rather than probing for just the answer. Inspired by what I had seen in North Bay, I wanted to try out this different style of questioning first hand. While working with different learners this week, I tried going past just getting the answer, and encouraged them to show me how they got their answer, or to draw a picture, or to explain their thinking in words, or tell me how they know their answer could be right. The results were disastrous. Learners be...

Our final question in The Math Pod (#themathpod) twitter chat this past week ( see the archive here ), was built on Cathy Fosnot's challenge for us in the first podcast: What is the difference between questions meant to guide students to a specific answer vs. questioning to support development as a mathematician? So in the chat we asked: What kind of questions can we ask to support development as a mathematician? What would you actually say to your students? Here are some of the answers from the participants in the chat: What kind of questions can we ask to support development as a mathematician? What would you say to your students? Tell me about what you're doing. What do you wonder? Tell me more? How did you know that? What if i change this? Really??? (especially when they're right!) Can you explain what she just said? What made you think of that? How did you figure that out? What does this remind you of? Have you seen what (anoth...