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...

I've been speaking with many secondary school teachers recently about how we might track observations and conversations in the math classroom, for the purpose of assigning a level of understanding and formally contributing to a student's overall achievement in a course.  When it comes to keeping track of marks, many teachers feel uncomfortable with evaluating what they see and hear in the classroom, much more so than evaluating what they see on paper. We feel, perhaps because observations are not as tactile as a handed-in worksheet, that an evaluation of what we see in class is more subjective, and may be called into question more than an evaluation of a product. As teachers, we are often much more comfortable using products to evaluate student understanding.  We trust our professional judgment with products (without even questioning it) much more than with observations. But in reality, this process is not that different than when we create and evaluate paper prod...

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 ...

This past fall, we continued a series of cross-panel co-teaching days with some of our grade 7/8/9 math teachers. In addition to co-designing and co-teaching a lesson in a grade 9 classroom, we also spent part of the day dedicated to digging a little deeper into a continuum of concept development for proportional reasoning. Ahead of time, we asked each teacher to give the following task to their students. Calculators and manipulatives were allowed, and the question could be read to the students, but no instruction or guidance was allocated. The point of the task was two-fold. First, we wanted to introduce teachers to the idea of how students develop proportional thinking. In upper elementary grades and in secondary math courses, we often jump right into the more advanced concepts, without looking back to see how students learned the basics (or even if they have learned the basics). Second, we wanted to give teachers a chance to see how their students would fare on a question...