When I began my teaching career twenty years ago I was teaching fourth graders. I spent a decade with fourth and fifth graders before making the switch to first grade. One of the things I noticed when I made that move was how many things I told students, in my attempts to teach them something new, that would complicate their later learning.
For example, I told kids that if you add two numbers you’ll always get a larger answer. In first grade that makes perfect sense. It’s a way to help young children check their thinking and make sure they haven’t made an obvious error. By fourth and fifth, when students begin to understand negative numbers, this isn’t always true. Having internalized this idea makes later math more challenging.
Over the past ten years with first graders, kindergartners, and third graders, I’ve tried to keep this in mind as I introduce new ideas. Or reinforce ideas. Sometimes it gets to be a bit exhausting as I try to think through the many complexities of an idea that seemed simple at first.
Earlier this week I put up a fraction number line to help us build our understanding of benchmarks (using 0, 1/2, and 1 to help understand the size of various fractions specifically). I dragged the duct tape down the wall, annoyed at the whole process. I kept thinking that it wasn’t straight, the kids will just peel it off, etc. When I finished (and it’s really not that long) I stood back, ready to feel good. Then I realized I’d created a line segment, rather than a line. I wanted to just let it go. Students would be arriving in fifteen minutes and I had other things to do. But I couldn’t.
So I made each end of the line an arrow. I couldn’t accept my laziness messing with their geometry learning just because I was focused on their fraction understanding.
I purposely placed the 0 and the 3 at not-quite-the-end of each side of our line. I know my students are certain that the numbers could continue on past 3. I want them not to rule out the idea that the numbers could continue on the other direction as well. I also actually got out a yardstick in order to place the four numbers more accurately. Again, my laziness could have added a small disruption to their mathematical understanding if I had just eyeballed the locations. I’m not so good at eyeballing distances.
We’ve used the number line for two days so far and it, and all the fractions we’ve added, are still there. Fingers crossed that continues for a while longer.