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...

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 ...

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 past week, I took part in a discussion on Twitter about how to best curate and provide math resources for teachers. The Mathtastic PD series I wrote about in response garnered a little bit of interest, partially because it was delivered in a blended style - each session was designed around engaging participants both in-person, as well as remotely, at the same time . In the original post, I mentioned how it was important to us to create GOOD, effective, remote PD.  As someone who lives in a somewhat rural part of the province, and a two-hour drive from my board office, I have been on the receiving end of a lot of virtual presentations. And there's nothing worse than a fuzzy, poorly-mic'ed presenter whose slides aren't legible because of the camera angle. Well, maybe that one time I joined in the conversation via my Google Hangout connection and spooked the facilitator, because it was forgotten that I was even "there." So, at the risk of just stating co...

We just finished another three great days meeting as the Mathematics Leadership Network (MLN) - a group of educators from boards of education across Northeastern Ontario, looking to further our development as mathematics learners and leaders. Part of the learning in this latest round was centred on Michael Fullan's book, Indelible Leadership . In it, he discusses six big tensions when it comes to deep leadership. Two of those tensions - Lead & Learn in Equal Measure , and Feed & Be Fed by the System - really resonated with me. Both of these tensions underscore the importance of reflection in one's practice. When learning (a fundamental part of leading), Fullan quotes John Malloy in saying: "...there has to be...vehicles, protocols, processes to actually reflect upon the learning, to make meaning out of what is emerging from the learning and then articulate from that." In order to give new learning meaning, we need to take the time to consolidate what we l...

In 2015-2016, I was fortunate to be involved with a TLLP team that looked into flipping the classroom: transferring the focus of our courses away from the teacher and on to the learners. Once we had successfully flipped, we became interested in how we could deepen our students' educational experiences, specifically through rich assessments. In 2016-2017, our same team took on a second TLLP project, which is just finishing up now, that had us digging deep into Rich Tasks. While the first project was very successful for us - everyone in the group was able to flip their courses in different ways and we were seeing success with the students - the second project was a much tougher go.  The learning curve was steeper, and it seemed the more we learned, the harder it was to implement GOOD rich tasks. We kept coming back to: what makes a rich task RICH? We came to an understanding that an ideal rich task should be broad , but have personal components; it should challenge the stud...

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...

One of my goals this year is to work with math teachers to better track observations and conversations in their classrooms, to better triangulate their assessments. I find this is a big jump for many who have been teaching for a while - we are very comfortable with marks on pencil-and-paper tasks, but we're unsure how to assess and track what we see and hear on an ongoing basis.  Just this past week, though, we've been playing with new ways of collecting data that I'm pretty excited about! (To try and wrap my head around this last year,  I asked kindergarten and primary teachers how they best track what they see , and got lots of great ideas!)  At one of our schools, we are implementing new strategies for improving numeracy skills. How can we track this?  We created a paper checklist that can be used by teachers or observers in the moment to track when and how students are demonstrating good numeracy skills: Our "good numeracy skills" checklist, base...

I'm currently reading Start with Why: How great leaders inspire everyone to take action, by Simon Sinek.  It was a book I picked up at the beginning of the summer when my position this fall was still unknown. After a year as the Renewed Math Strategy Co-ordinator for my board, I was set to rebound back into the classroom. However, there was still a possibility of my board bringing me back as a co-ordinator (which is what ended up happening). Regardless of my position as a teacher or co-ordinator, I was hoping this book could help me lead learning, be it with students or with colleagues. I'm about half way through it now, and giving serious thought to my WHY. What drives me? What makes me want to push myself? Why did I choose this as a career? Through what lens am I viewing my role(s)?  Why find my WHY? According to Sinek, if I want to motivate, if I want to be trusted, and if I want to make a difference, I have to be authentic to my WHY . The more clarity I can brin...

Jonathan So ( @MrSoclassroom ) recently threw out an interesting challenge on Twitter for teachers: What are your top five, life-changing-as-a-teacher moments? His original post on his top five really got me thinking about what has made me stop, re-evaluate what I do, and change direction in how I teach. These are all fairly recent moments for me, so I'm guessing there's a little bit of memory bias in here, but here they are... :) In chronological-ish order of occurrence: 1) Flipping my Classes - Handing the responsibility of learning over to my students was definitely career-changing. I learned so much from my students in terms of how they learn (because they were each choosing to learn in their own way), and how they collaborate, and  I saw first-hand how the allowance of self-paced curriculum can reduce stress and deepen understanding. It was humbling as I discovered my lectures weren't a necessary part of the learning process (students mastered even some of the h...