Equality is a fundamental concept in algebra. It is noted through use of an equal sign, represents a relationship of equivalence, and can be conceptualized by the idea of balance. Despite the importance of the equal sign, there is tons of research that shows that students
often have serious misconceptions about what the equal sign means. The research has mostly been conducted with elementary through high school students, but using an assessment included in this unit, I have found it is equally true of adult learners.

Many adult education students think the equal sign means “the answer” or “what you get when you do the operation.” Students who think this way tend to answer questions like 12 + 5 = ___ + 6 incorrectly, writing a 17 in the blank. Students also get thrown when they see things like 14 = 17 – ___, because the operation is taking place on the right side of the equation.

This misunderstanding makes sense if you think about students’ prior experiences with the equal sign. They have been seeing equality in arithmetic for years; most of it has looked like 7 × 8 =___ or 25 × 18 = ____. Even the use of a calculator can reinforce this misconception—just push the “=” and the answer appears.

This association of the equal sign with “the answer” as opposed to understanding it as signifying balance or equivalence can be especially problematic when students encounter the symbol in algebra. If students understand the equal sign to mean balance, it makes sense to perform the same operations on either side of the equation. Without an understanding of a balance point between the two sides of the equation, the rule,
“Whatever you do to one side you have to do to the other,” becomes a disconnected rule that students struggle to memorize and use.

The problems in this unit were chosen to help students understand the meaning of the equal sign. This is not something we can just tell students and expect to fully take root—they have a deeply-seated misconception that won’t be corrected easily. These activities are intended to help draw out students’ intuitive sense for keeping things in balance and connecting that to the formal use and notation of the equal sign.