Sense of Number versus Number sense

I know I have talked and written about this extensively over the past 12 years but it seems in Ontario this age-old argument is coming back with a vengeance.

Now some may say that my title is misleading that there really is no difference but over the past couple of years I have really thought hard about this very topic. Over these years I have seen students come into my classroom with amazing fact recall. In fact, I have never seen a community that has spent countless hours practising math facts and algorithms. But I have also seen over this time I have also seen students have a lack of what those facts truly mean.

Our new government is calling for a “back to basics” and let’s get rid of “discovery math” but all of this is rhetoric by politicians who don’t understand how students development a sense of number. I see it in my own daughter. Izzy has trouble in math for numerous reasons, one of which is a low working memory but another is her understanding of place value. For Izzy, she is reworking on understanding unitization, grouping, and counting by fives and tens. At the moment she is playing Duck Duck Moose and app that helps build those foundational skills.

But back to my classroom experience. Many of my students struggled with the very same problems that Izzy has. They struggle to understand part-whole relationships in number, they struggle to understand estimation skills and most importantly they struggle with understanding reasonability of number. And now I think back to the thinking of our Governments call. They fear that this generation cannot do the math, they fear they don’t know how to make quick change but the reality is they have no sense of number or how our number system works.

When I think about how students learn I think about Dr. Alex Lawson’s work on developmental learning. This is also a great article that she has written: .

I don’t have many answers right now but I do know that learning of mathematics needs to be a balanced approach. Math needs skills but they need to be developed properly.

As students are developing skills trying ideas like Which one Doesn’t Belong, Building spatial sense, Estimation 180 or even Math Before Bed. All of these are amazing activities to help your students build a sense of number. Combine these activities with rich problems and then purposeful practise and now we are building students up to be successful mathematicians.

So as we plan and think about our math curriculum over the summer I encourage you to think about how we are making our students think about numbers along with teaching number sense. A final thought as well, as math teachers continue to teach as I know you teach. You are strong individuals with sound pedagogy. Show students what mathematics is about, how it is a beautiful language, how it is comprised of beautiful and elegant thinking. That it isn’t just rules and magic tricks. Please do not get discouraged by politicians or other professions that have no idea how children learn. In the end, be true to yourself no matter what.