I’m fascinated with school improvement thinking. I love the conversations that come from this thinking, especially from the teachers that are directly involved in this work. It was at a session a few weeks ago, mired in the debate about our dwindling math scores (like much of Ontario), that a colleague from the board asked me about what needed to be done next. I blurted out a grocery-store list of things that have improved my own math practice, but I couldn’t stop thinking about it. So I wanted to use this space to stretch out these ideas, possibly in a chronological order of instruction.
1. Class Profile
One of the first things I do every year is create a class profile of the mathematicians in front of me. I like to use PRIME number diagnostic tool to see the thinking of my new group of students. This helps inform the language I will be using, as well as potential areas to bring into my math instruction.
My Grade 7 students should be heading into Phase 5. So I’ve got some challenges ahead of me, but I know with some hard work, it can be done.
2. Growth Mindset
This has been the greatest shift in teaching, to me personally, in my career. To embrace and fully commit to the idea that EVERY kid can be successful is a game-changer. This is a radical departure from my bell-curve days, where I had to defend accusations from my admin that I too many successful kids. Growth Mindset, backed by scientific research, tells us that we can grow our brain. Through hard work we can learn and be successful. This has changed how I have embraced challenges, given feedback and encouraged hard work from my students. In getting my students to embrace and seek out challenges in math, we’ve all become more successful.
3. Building Content Knowledge
I am an expert in math. Now, this has been a hard-fought claim for me, but I’m sticking by it. The last math class/course I took was in high school (though does my Statistics course in university count?). My wife can share with you the gong-show that was my last time being the banker in Life. However, I’m claiming to be an expert because I fiercely build my knowledge of the content before I being instruction. I pull out my math resources, starting with my favourite: Making Math Meaningful by Marian Small. I do this before every unit of study. My experience has started off in Grade 1 and then progressed up to my current Grade 7. I know some Grade 8 material!
In building up my content knowledge, I am better prepared for all the thinking that my students may show, as well as where I can push my students to go next. I make sure I have a deep and exquisite understanding of the math we are learning. This is where the magic starts. When I understand the math, I can better teach the math.
Case in point: the formula for determining the area of a trapezoid. Isn’t this amazing? Look at how this formula gives us the area of the average between the top and bottom (b1 and b2), which really is the area of a rectangle! Wow! Magic!
4. Gap Closing
Before I start the grade-level material, I need to make sure my students are ready for it. I need to close any gaps in the learning that needed to happen before this. My go-to resource right now is Leaps and Bounds (again, by Marian Small). I give myself a few days to focus on this, giving me time to strengthen the math skills, before I start my grade-level material.
Not only does this resource help bring the students up to grade level, it offers amazing thinking opportunities for students to deepen their understanding of the math. One critique I’ve heard is that there is a lot of paper involved with this resource – true – but it is also relatively easy out-of-the-box resource to jump into.
5. Learning Goals and Success Criteria
This has been beneficial for me because it has gotten me to look deeply and critically at the curriculum. I can’t remember when it happened, though it was early in my career, and still heavily reliant on the textbook, when I realized that not all the curriculum was in the textbook. In creating LG&SC I can ensure that I am teaching the curriculum but also seeing connections among and between topics.
This has been beneficial for my students because in co-constructing these together, they have a say in how they will learn the math. They also know how they are going to be successful.
6. Process Expectations
This goes together with my Learning Goals and Success Criteria. When I started integrating the process expectations INTO my Success Criteria, it became a much richer instructional opportunity. Instead of just Demonstrate, Demonstrate, Demonstrate, I was able to go much deeper: reason and prove, connect, effectively communicate, etc. How awesome is it to bust out a sophisticated conjecture in the middle of a math talk?! Amazing!
7. Number Talks
I love number talks – and I’ve posted about them before. I use number talks at the beginning of each of my success criteria topics. I use this strategy to access the thinking, strengths and misconceptions from my students.
When looking to begin fractions, for example, I’ve used the above image and the question: “Which shape is more purple?”. This led to a fantastic conversation, with me uncovering their understanding of proportional reasoning, representations and comparisons of fractions.
One thing I’ve struggled with is not lecturing and fixing misconceptions in the conversations. However, what I find is that students will either fix the misconceptions from others or students will begin to fix their own.
8. Teaching THROUGH Problem Solving
This is by no means a new and innovative strategy for me. However, once I fully understood what teaching THROUGH problem solving meant, it really transformed my practice.
When I was first introduced into this strategy, I (mis)interpreted it as teaching problem solving. I was fully into teaching the templates, sending home weekly problems and having focused lessons on the 4-step problem solving method. However, what I was really doing is spending time focusing on the tool: What a great hammer! Let’s learn how to use the hammer! Let’s get assessed on how well we use the hammer! Instead, I needed to spend time learning what the tool what supposed to do.
Once I engaged the students in solving, stumbling and failing through rich problems my lessons became much more engaging. When I start with a relevant problem, then the struggle to solve it, my consolidation lessons have much richer schema to hold on to. The math now makes sense because the students have engaged in the math.
I love engaging in the process of working through problems. Since I have built up my content knowledge, I am prepared for where the kids are going and where they need to go. I can prompt on the fly and I’m primed to look for misconceptions. I can leverage the method to show the thinking to best move the class along: bansho, math congress, or gallery walk.
Pulling all the thinking together, after the number talk, after the problem solving, after the strategic lesson, after the independent practice, comes the important consolidation time. This has been a relatively new focus in that I am realizing how important it is. This may take a variety of forms, but my favourite is the anchor chart. I love co-constructing this with the students, though my fancy writing needs work! This is my final chance to fix misconceptions, bringing us back to the success criteria for that skill.
10. Exit Tickets
Are we ready to leave this skill? Have we fixed any misconceptions? What is the thinking for this skill?
Creating a good exit ticket has saved me so much time and energy. Responding to this thinking allows me to pull small groups for those who need it, or move on if appropriate.
I love teaching math. I love solving the problems related to math. I love how the province is focusing on math instruction. I look forward to seeing where this journey goes next.