Identity Confusion: The Problem with the Equal Sign

Henry Borenson explains how we use the = sign in two very different ways.  The first way is operational, for example 10 + 15 = ______.  The second way we use the sign is relational, indicating equivalence between two sets of expressions, each of which includes one or more operations, for example 8 + 4 =_____ + 5.  But in 1999 a study of hundreds of first through six graders only 5%  solved problems like this correctly.

Borenson believes that because of this study we can conclude that the relational meaning  of the equal sign is not something that students find intuitive or self evident. When asked to fill in the answer to the problems above most students said that 12 belongs in the space because the answer follows the equal sign.  The equal sign seems to trigger the operational definition in most students’ minds. Some students thought the  + 5 was just there to confuse them.

Borenson recommends  introducing students in the second or third grade to the idea of balanced equations using concrete objects rather than numbers and the equal sign. Once students get the idea the equal sign can be introduced with the balancing explanation. Studies have shown that if the relational meaning of the equal sign is introduced in this way students are much more likely to grasp both ways.

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