Number sense certainly seems to be at the forefront of many math teachers’ minds these days. I know we have talked about it in my math department (high school) several times, bemoaning its lack and wondering how best to remedy that lack. And it has popped up on twitter pretty regularly. The most recent reference came from Tracy Zager with this post.

My gut response was that this was simplification of the scope of difficulties that students have in math, but Tracy asked me to look at the whole article and see what I thought. Although I had homework, I couldn’t stay away from it. As I read through it, I thought of the students I have worked with and all the different ways they have struggled in math class. Most of my math students have been identified with disabilities. The rest fall into that category of having “difficulties” in math. For many of them, number sense was at the root of their problems. However, it was often accompanied by complicating factors.

Some students have processing issues. I recall a student who would close her eyes and just think. If you could wait long enough, she would provide a response that was usually on track, although she couldn’t articulate her thought process. Another student would work a problem correctly and explain her work clearly. Five minutes later, she would get totally lost on a similar problem. Last year I had a student who seemed to have great number sense, as well as a great understanding of how things work. However, as soon as I tried to move him to the abstract or to generalize, I lost him. For students like these, the difficulty is more than just poor number sense.

In the article, Nancy Jordan does acknowledge that not all difficulties in math result from poor number sense. However, her main focus is encouraging early screening and intervention, similar to the screenings that happen for reading. She references research that supports the importance of number sense, as well as her own research that shows number sense as an early indicator of math difficulties and disabilities. She also offers some specific tasks that might help develop number sense.

So to answer Tracy’s question…After reading this article, I do agree that early identification and intervention based on number sense screenings would likely lead to improved results. I want to read more; I want to see more research in this and related areas. Further research in this area would perhaps help isolate and identify other factors that later impact success in math. And I want to know what the research can tell me to help the students that I have who struggle in math.

Jordan, N. 2007. “The Need for Number Sense.” Educational Leadership 65(2):63-65.

on July 19, 2014 at 8:22 pm |tjzagerLeslie, Thank you so much for this thoughtful response! I really appreciate it, and totally agree with the complexity and individuality you describe. I’m certainly not saying that number sense work is the cure-all, for any populations. But I do appreciate having some research pushback to the tendency for more drill and memorization whenever students are struggling in math.

The reason I became interested in the article in the first place is I’m writing about developing mathematical intuition in the classroom. It’s something we don’t do enough of in math ed, even though it’s very hard for anyone to do math without it. What I’ve observed, (and I’d love your input on this!), is that kids who might benefit from more opportunities to build intuition usually get fewer opportunities. They’re just told to memorize, or follow algorithms. Or an educator (teacher/edtech) “breaks the problem” down for the kids and they just “follow the steps,” so they don’t get the experience–and resulting understanding–of thinking it through for themselves. The next time they face a similar problem, they’re not wiser for their past experience. We spend lots of time and repetition on procedural skills, but not much time or repetition on building a feel, visualizing, estimating, having a hunch, making sense, etc.

Building intuitive understanding of numbers and space won’t make processing or memory or attention issues go away. But that doesn’t mean we shouldn’t develop intuitive understanding of numbers and space, right?

I’d love to keep thinking this through together. And good luck on your homework! 🙂