Understanding the Equal Sign

Challenge

Some children misperceive the equal sign as an instruction to compute rather than understanding the equal sign as a symbol that shows two expressions have the same value. These children will often place a 5 in the blank when given 2 + 3 = _ + 4. Practice with addition facts may actually strengthen this misconception if children are repeatedly given left to right “4 plus 2 makes 6” formatted facts. This can become a significant stumbling block in a child’s development of algebraic reasoning.

Teachers

  • Explicitly teach the equal sign means “the same value as.” In lower grades you may say, “6 marbles is the same as 4 marbles and 2 marbles.”
  • Avoid the input-output model to describe equations. Numbers are not placed into a machine with the answer spit out. The equal sign is not an operation that “makes” a number.
  • Use a variety equation formats. For example: 3 = 5 – 2 or 9 = 9 or 2 + 6 = 10 – 2

Students

  • Represent a variety of equation formats with concrete objects and pictorials.
  • Describe their own representations of equations using “same value as” to express equality.
  • Solve for unknowns in equations such as 8 + _ = 3 + 9.

Source: Teaching the Meaning of the Equal Sign to Children with Learning Disabilities: Moving from Concrete to Abstractions by Ruth Beatty and Joan Moss at the University of Toronto. Published in The Learning of Mathematics, NCTM’s 69th Yearbook, 2007.