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

This post was featured in an episode of  This Week in Ontario Edublogs (Sept. 4, 2019), beginning at 35:54 . In Ontario, students need a minimum of three math credits to graduate high school, one of which must be at the grade 11 or 12 level. For students who are not pursuing a post-secondary path that requires mathematics, and/or who really struggle with math, the grade 11 college-pathway math course (MBF3C) is often the last mandatory math course they need to take to graduate. Teachers of this course face several challenges, such as the range of student abilities, range of student interest (particularly if a student is only in the course because they need it to graduate), and also the wide variety of topics in the course curriculum. Last year, we offered new support for MBF3C teachers in our board. At our first session with the teachers, we had round-table discussions on what they most wanted in the way of resources to help their stude nts succeed.  One of the topics that c

Before we begin, take a moment and read the number sentence below out loud . Don't think about it too much, just read it as you normally would to a class or colleague. On Language This past year, I have been doing more work in looking at how aspects of literacy creep into (and affect) how we teach and learn math. One theme that reoccured in different contexts was language, and paying close attention to what we say when we are teaching math. Over time, many of us adopt "shortcuts" when it comes to talking about the symbolic representation of mathematics. We may know what we mean to say, but for students who struggle, the meanings of these shortcuts are not always apparent, and might even cause confusion. The following are three very small, deliberate changes in language I am trying to work into my practice moving forward. Though each is a simple change, I'm having a hard time undoing decades of bad habits! "Equals" Based on some of our work on

One of my biggest learnings in my role as a board co-ordinator has been around mental math in elementary schools. To be honest, when I first heard the term, I assumed mental math had to do with memorization and just learning multiplication facts.  I now know it to be a procedure very rich in strategy, promoting flexibility of number, and the very important mathematical process  of representing  a problem. Being able to see the math not only contributes to the understanding of the question at hand, but also to assessing the reasonableness of the answer. Visualization and representation of mathematics does not come easily to me - I was the student who became good at math by memorizing procedures. I still have to put a lot of effort into picturing multiplication in an array or area model, or picturing factorization by splitting items into groups, or picturing what happens to fractions as they are operated upon. This past week, I had the opportunity to model the annotation process i

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 morning, as I try to get back into a routine ahead of Monday's return to work from March Break, I started reading Kathy Richardson's How Children Learn Number Concepts - A Guide to the Critical Learning Phases . This was a book that was given to me earlier this year after my role was expanded from working with grade 7-12 mathematics teachers to a full K-12 mathematics co-ordinator role. With only a background in intermediate & senior math, I've learned so much from primary and junior math teachers this year, and I'm eager to learn more about how students acquire concepts of number, relation, and computation. In her introduction, Richards describes what she calls Critical Learning Phases - "crucial mathematical ideas that students must understand if they are to find meaning in the mathematics they are expected to learn." These crucial ideas are "insights, rather than facts or procedures," meant to be carried forward as students engage in