Fewer than 50% of middle school students understand that the equal sign in math means what is to the right and left of the symbol have the same value, says a recent study in Mathematics Teaching in the Middle School.
Many students believe the equal sign signifies an operation such as addition or that the symbol means “the answer” or connects the problem to the solution, the researchers say.
Not understanding what the equal sign means is one of the major stumbling blocks in learning algebra, the researchers say.
“Virtually all manipulations on equations require understanding that the equal sign represents a relation.” The operational view of the equal sign is a by-product of students’ math experiences in elementary school. Typically, students see the equal sign in number sentences that have an operation on the left side and an answer blank on the right.
“As a result, students associate the equal sign with the arithmetic operations performed to get a final answer,” the researchers write.
Very little attention is paid to the symbol in middle school curricular materials. When the researchers tested students with less typical equation-solving items (what value does m have in 4m +10=70), students who had a relational view of the equal sign performed better.
“This finding is noteworthy in that it suggests that even students having no experience with formal algebra (sixth- and seventh-grade students, in particular) have a better understanding of how to solve equations when they hold a relational view of the equal sign.”
“The importance of Equal Sign Understanding in the Middle Grades,” by Eric Knuth et al., Mathematics Teaching in the Middle School, Volume 13, Number 9, May 2008