Finding Balance

How do we teach students about the equal sign in math?

Professor Tim Whiteford brought this up in a meeting recently. Says Tim: “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.” (see Tim’s full blog post on the equal sign)

I remember having this misconception as a child, and children in the U.S. continue to struggle with it today. I was looking at the 3rd grade NECAP released items last year and noticed lots of students got this question wrong: 1+4+?=6+14. (Many students incorrectly chose 1, which makes sense because 1+4+1=6.)

Researchers at Texas A&M University found that 70% of U.S. middle school students lack understanding about the equal sign. Students in other countries like Korea and China do not have the same misconceptions. When students begin algebra in middle school, understanding the equal sign is critical for their success. (full article here)

On the bright side, this seems like a relatively easy thing to fix. I visited a second grade class the other day and watched the students excitedly working with a number balance scale. Their teacher used this tool to help them develop their concept of equality as a relationship, as opposed to an operation. If you don’t have a number balance scale, here is a very nice virtual pan balance scale from NCTM Illuminations, and a virtual number balance scale.

We can also mix up the way we write equations. I could decide to write 7=9-2 instead of 9-2=7.

At what age do students need to learn the correct meaning of the equal sign? Why wait? This is a Mathematics Common Core State Standard for first grade: 1.OA.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.