OGAP Additive: Understanding the Equal Sign, 5/22/18

May 22, 2018

Understanding the Equal Sign

Understanding equality is an important foundation for addition and subtraction, as well as for developing algebraic reasoning. However, research shows that children often have misconceptions about the meaning of the equal sign that arise from their prior experience performing calculations. Look at these examples of student solutions to an OGAP item (PR 6). What do these students think the equal sign means?

Research shows that many students develop this misconception that the equal sign means "the answer is" rather than developing an understanding of the equal sign as a relationship between quantities. This is not surprising, given that most of the equations they see are in the form of a + b = ? Moreover, this misconception does not go away as students get older and can interfere with their learning of algebra. The good news is, there are several things you can do instructionally to prevent and/or correct this misconception:

Beginning in kindergarten and throughout grades 1 and 2, expose children to equal signs in various places in equations, such as 6 = 6, 7 = 8 − 1, 5 + 2 = 2 + 5, 4 + 1 = 3 + 2
Pose open number sentences with equal signs in various places, such as:

Pose a variety of true and false equations and ask students to determine if they are true or false, while defending their answer. (This takes the focus off finding the answer and puts it on the relationship). See this handout from the summer training for some examples you can use and adapt to focus on both equality and specific properties.
Help children understand the meaning of the sign by using the words "is the same value as" when reading an equation.

Action Item

Select an item from the Properties and Relationships section of the item bank that focuses on equality (e.g., PR 5, PR13, PR28, PR41) and give it to your students without any prior instruction.
What does the evidence show you about how your students making sense of the equal sign?
Do students need to compute to find the sum of both sides to solve the equation, or can they look at the relationships between the numbers on each side of the equation to figure it out?
What are some instructional next steps you can take to make sure they develop deeper understanding of equality as a relationship?

RESOURCES

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