Mathematics: It’s not about doing one thing or the other thing. It’s about the kids.



So, the past few days, as test results have been released, have brought with it the annual debate about mathematics instruction and it’s current state in Ontario. While I am not an expert by any means, I am someone on the ground, in the classroom, on the battlefield, if you will. And I’m someone who is exceptionally passionate about mathematics instruction and assessment.

I’m going to say what I think, straight out. So, here goes.

  1. We need to make our mathematics classrooms places of student voice, engagement and wonder.  This doesn’t mean that we don’t engage is rigorous mathematics that involves computation,  the development of fluency, and a strong foundation of mathematics principles.
  2. Mathematics instruction needs to be grounded in understanding WHY mathematics works the way it does. This means that students must be active participants in the learning though asking questions, debating procedures and discovering some of the beauty on their own. But it doesn’t mean that we don’t also learn and practice standard algorithms, formulae and procedural aspects of mathematics.
  3. Mathematics assessments need to be authentic — they need to give students a chance and opportunity to share their thinking and their understanding. This doesn’t mean that we don’t give tests, but perhaps it means that our questions give students opportunities to show their thinking in  a different way than we are anticipating in our answer key.
  4. Mathematics classrooms need to be safe places, just like all our other classroom spaces. For me, this means we work on our memorization and our mental math abilities, our fluency skills, our number skills in a way that is not hampered by competition, by time or by penalization for not knowing the answer right away.

In the end, I believe that mathematics instruction needs to be responsive to our students. We need to know who they are as learners and build our program around them. As one of my most respected mentors said this summer, we need to make sure we are doing enough mathematics to be good at mathematics. And so, for me, in my classroom, this means that we engage in problem solving on a regular basis, that we do number talks, and practice our mental math skills. That we debate answers, and that we tackle big concepts. But it also means that I tailor direct instruction (which is not the same as ‘surface’ instruction) to what my students know and where they need to go next. It means we practice standard algorithms and formulae when we are ready to. After all, those were developed over hundreds of years by skilled mathematicians — why would we just drop our students in there as a starting place? It means we do homework tasks that involve critical thinking and reflection and write tests and other tasks that are authentic and relevant to what we have learned and how we best learn it.

With any change, there is always a dip before there is a rise. Do I think our approach to mathematics instruction needs to change? No, not necessarily. Not if we are striving to teach in a way that is relevant and meaningful and engaging for our students. Not if we are encouraging our students to be active participants in their learning. Do we need to change our curriculum? Maybe. As others have said, the front part of the document contains a wealth of mathematical skills that we all use every day. The rest, however, reads like a checklist of things we have to check off, in that order. I don’t think teaching with those checklists in mind is a helpful practice. Rather, considering what the big concepts are, and then helping our students develop the skills and understanding to go deeper in those concepts is how our curriculum needs to shift.

I do a lot of professional reading — and many books have influenced my thinking and understanding: Jo Boaler’s Mathematical Minders; Hattie et al’s Visible Learning for Mathematics, just to name the two most prominent. And of course, I’d be lost in my journey without the amazing people I work with, both ‘in real life’ and on Twitter.

At the end of the day, it’s still a journey. We are all still learning and growing. And this means that we are all changing. The way I will teach mathematics this year will be different than the way I taught mathematics last year. That doesn’t mean that I think that how I taught last year was wrong; it just means that I’m still learning, that I’m striving to do things better. At the end of the day, it’s not about ME. It’s about those 25 (give or take a few) precious young people who will come into our classroom on Tuesday morning that I have the amazing honour to work with each day for the next ten months. It’s my responsibility to do what’s best for them. And I can’t wait.