# The Equal Sign Means Relationship, Not Action

Blog post #1 in the series, *Lies We Tell Our Students*

**The Story**

A while back, I was working in a fifth-grade classroom, and as a warm-up, I put the following equation on the board:

8 + 4 = 1 + 11

I then asked the students, “Is this statement true or false?” After waiting several seconds, I asked them to raise their hands to indicate their votes. At that point, two students voted for true, and the other 22 students voted that the statement was false.

Being the good teacher that I am, I asked the students to discuss their thinking, believing that those two students who said it was true would quickly convince the others. However, when I brought the class back together and once again asked my questions, 24 hands went up stating that the answer was false.

“Yikes!” I said, “What’s going on here? This statement is actually true. Can you tell me what you’re thinking?”

“Mrs. Rimbey,” started one of those original two students, ”8 + 4 does not equal 1.”

**The Lie**

I’ve since come to learn that
this is not an isolated case. Many students across the grade levels believe
that the equal sign is a symbol that indicates the action of *finding the
answer*, when, in fact, it actually signals a relationship between the
expressions on each side. In the vast majority of classrooms, students develop
this misconception because virtually every equation they see in the early
grades follows the same format: 3 + 3 = 6; 4 x 4 = 16; 20 – 13 = 7; and so forth.
The “answer” appears last.

**The Truth**

So, what do we do about this?
We can be sure to provide students with multiple daily opportunities to see
equations written in different formats, pointing out that the equal sign
indicates an *equal relationship*, not the action of finding the answer.
Provide examples with the “answer first” (e.g., 6 = 2 + 4), with “nothing to
do” (e.g., 1000 = 1000), or with “no answer” (e.g., 3^{2} + 4^{2}
= 20 + 5).

**The Series**

This blog post is the first
of a series that addresses the *lies we tell our students*. It’s important
to note that these lies are not deliberate untruths. Rather, they are rules,
procedures, mnemonics, and tricks we teach kids in an effort to make math
easier for them. Sometimes the lies come in the form of omission, such as the
example of the equal sign, shared above, where we don’t provide enough varied
examples. Sometimes they come in the form of half-truths, such as *addition
and multiplication always make bigger*, which is only true with natural
numbers (not including 0).

**In Summary**

To sum up this week’s *Lies
We Tell Our Students: *

- The inadvertent lie: The equal sign indicates the
*action*of*finding the answer*. - The truth: The equal sign indicates
*relationship*, not action.

As always, we love hearing from you! Do you think your students fully understand the meaning of the equal sign? Have you tried any of these (or other) strategies with your students? Please share your thoughts in the comments box, below.

**Next Steps for Teachers: **Use a variety of equation structures with
students on a daily basis (see examples above). Consider making a set of 4-6
“true-false cards” each day to show the class. Simply write one equation on
each card, using a variety of formats, making some true and some false. Then
ask the students whether each is true or false and to justify their answers.

**Next Steps for Leaders:** Discuss the meaning of the equal sign with
grade levels, focusing on the notion that the equal sign indicates *relationship*,
not the *action of finding the answer*. Although this concept typically
appears the K-1 math standards, this misconception continues to exist in middle
school and beyond. Discuss ways to avoid this misconception in each grade
level, and then share their ideas across grade levels.

**Kimberly Rimbey,
Ph.D., works with teachers and leaders to develop system-wide change in
mathematics teaching and learning.**