Whenever someone asks me how to impact mathematics instruction, I say Number Sense. Yet, some may not be truly sure what I am referring to. Is she talking about a program, standards, pedagogy, professional development? What I am talking about is plugging the hole with a finger.
In the “The Boy Who Saved the Netherlands,” the lockkeeper’s son saved the town by placing his finger in a leak in the dike when the hole was small.
That is what I mean when I say Number Sense. I am talking about plugging the hole when then hole is small. In K – 2nd grade, the hole is smaller than it will ever be for a student. That is when we need to “plug it.” This is the moment to make a difference. Can we do it later, sure… but understand the hole will be bigger. It will take more fingers. If we want to plug the hole when it is small, then Number Sense is how we do it.
So, what is this Number Sense I am talking about? First, it is helping teachers to develop it for themselves. Number Sense is a thing that if I as an educator do not possess it, then I cannot help students to have it. I know this because I did NOT have Number Sense as a secondary math teacher. I had no Number Sense. I, as a math educator (ALL levels), have to have it so I can make good instructional decisions for students so they can develop it. It is about giving them experiences that allows their brains to grow and to develop it. It is not a worksheet or a computer program.
It is how do I make sense of quantity in the context of the world around me. It is can I look at 3 fingers and know that is 3 without counting? You just tried it. Now, try it again. Yep, still 3. Now, what about 5? Did you know 5? How? What about 3 fingers and 4 fingers? What is the maximum number of things that you know the quantity of without counting?
So that is step one of Number Sense and some of our students cannot do that. That is when the hole is small. They just didn’t get as many of the experiences they needed to have their brain grow and develop that. But the good news is that it is not too late. This can be developed at any time and any age.
The truth is, if students cannot know how many of something is without counting, then it is really, really hard for them to know 5 and 10. If they do not know 5 and 10, then they will not understand our number system which is base 10, based on 10. Which means it is almost impossible for them to know part-part whole which is foundational for fractions and algebra. There it is!
Why can’t our students do algebra, because they have no Number Sense. Algebra is not the gatekeeper for college and career readiness, Number Sense is. If I cannot see quantity, then how can I see “structure,” which is what algebra is, representing quantity abstractly. Then if I cannot see structure, then I cannot see space – Geometry. Number Sense is what is limiting access to algebra.
This is why I keep saying Number Sense. I want us to plug the whole when the hole is the smallest.