Students' Understanding of the Equal Sign Not Equal, Professor Says

"The equal sign is pervasive and fundamentally linked to mathematics from
kindergarten through upper-level calculus," Robert M. Capraro says. "The
idea of symbols that convey relative meaning, such as the equal sign and
"less than" and "greater than" signs, is complex and they serve as a
precursor to ideas of variables, which also require the same level of
abstract thinking."

The problem is students memorize procedures without fully understanding the
mathematics, he notes.

"Students who have learned to memorize symbols and who have a limited
understanding of the equal sign will tend to solve problems such as 4+3+2=(
)+2 by adding the numbers on the left, and placing it in the parentheses,
then add those terms and create another equal sign with the new answer," he
explains. "So the work would look like 4+3+2=(9)+2=11.

"This response has been called a running equal sign -- similar to how a
calculator might work when the numbers and equal sign are entered as they
appear in the sentence," he explains. "However, this understanding is
incorrect. The correct solution makes both sides equal. So the understanding
should be 4+3+2=(7)+2. Now both sides of the equal sign equal 9."

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