Talking Negative Numbers With Young Children

This is what happened. My son was working on subtraction in grade one.

Here are things that had to happen for him to get to learning how to subtract:

• progressing through the landscape of counting. That is, he knows that, for example, the symbol “5” in this case would refer to a set of 5 M&Ms. Further back, he recited the rote counting numbers, probably hundreds of times, as small children do. (If you are a parent, you also know that random renditions of the ABC song and Christmas carols happen more than you might prefer…)
• working with adding, with concrete objects. That is, adding as combining two sets.
• working with skip counting, for example, on a hundreds chart. One thing he knows quite well is doubles, like 4+4=8.
• doing and inventing word problems to show he understands adding.

Now he is working on subtraction. My thinking here, based on Fosnot’s, Clement’s, and Lawson’s landscapes, is that subtraction is first instantiated at “removal”. The picture shows above that I showed him “difference” on the number line, which you might think is much further along the continuum.

Here is what happened. We tried a few expressions with M&Ms. Then he said, 3–7=0. I suspect this might be quite a common perspective for kids. They are taught, after all, that numbers start at zero.

But there is no reason to shy away from negative numbers. Kids should be shown mathematical ideas when they are ready. It’s not about the grade level. Integers don’t appear here in curriculum until grade 6.

More to the point, we NEEDED the concept of negatives to make his math work.

Here is what happened:

• we removed 3 M&Ms, and got to 0. We talked about how we can’t remove M&Ms that are not there.
• I quickly sketched the open number line to show the removal.
• We got to zero on the number line.
• I asked, “can we keep going?” Callum said “yes”.
• I prompted him with “minus one”. He kept going “minus two, minus three, minus four”.
• I mentioned temperature, and we looked at a thermometer. The context is readily there, in the world, for those of us who count heat, or lack thereof, in Celsius degrees.

There is a tendency, I think, to “hide” mathematical concepts from young children. I don’t think we should. I think we should talk about infinity with three year olds. That’s where I am coming from. Most importantly, bring out mathematical ideas when kids are ready. Bring out mathematical ideas when they are needed. We needed negative numbers to answer Callum’s question. So we “found” them on a number line.