There's More to 2+2=4 Than....

I observed a great math lesson this morning with one of my student teachers. She was introducing her first grade students to the idea of the horizontal  number line such as the one in the picture on the left (3 + 4 = 7).
Traditionally we have used language like "three plus four makes seven" or "three and four are seven". We now know that both these forms of language actually develop in children a misconception about what is happening in this piece of procedural knowledge. Children tend to think that the equals sign makes things happen. This can cause untold problems when they come to do serious algebra in middle and high school.

The key to later success in math, and algebra in particular, is to develop the equals sign as a sign of equality by helping children develop the appropriate concept-based language as they are learning the meaning of this number sentence. This key to later success is helping the children associate the equals sign with the idea, "is the same as". Three plus four is really just another way of writing seven. So is 2 + 5, and  1 + 6. 

The student, assisted by the cooperating teacher and school math specialist, then went on to ask if it was OK to write 7 = 3 + 4. As I would have predicted, the children had a really difficult time with this. Almost all of them decided that you could not write the sentence this way; "this is just wrong" as one student said. The teachers then did several activities  using small cubes in which they showed the children that it really didn't matter which way round they wrote it; it still meant the same thing.

It's attention to small details like this when teaching young children that make a profound difference years later when students learn more complex math ideas.