August 13, 2010

The equal sign problem

An interesting piece of research has just come out on the misconceptions with the equal sign (=).

Students' understanding of the equal sign not equal

According to the research, US students exhibit this misconception much more often than students in other countries. It has to do with thinking of the = sign as an operator. Kind of like thinking that = means "to do" the operation.

For example, a student with that misconception tends to solve the problem

7 + 6 = ____ + 2

by adding 7 + 6, and placing the answer on the empty line.

The correct way is of course to think of the equality: 7 + 6 equals 13, so the other side has to equal 13 too. 11 fulfills this little equation:

7 + 6 = 11 + 2

I have known of this problem for years, and have tried to include problems in my Math Mammoth books to help children NOT to develop this wrong idea. For example, children solve


200 + 50 + 6 = ____ + 200 + 50 in the place value section.

Or, I use problems where they have to put either <, >, or = in between (one the line here, but I like to use boxes in the books):

20 + 9  _______ 90 + 2

8 + 6   ________  7 + 7


Or, just simple missing addend problems from the very start (1st grade):

3 + _____ = 5.


Remember, students exhibiting the misconception would add 3 and 5, and put 8 on the empty line. But we can teach kids to think of this problem as "3 and how many more makes 5". It is a starting point in understanding the equal sign in the correct way.

Then they should also (later on) encounter the same problem this way:

5 = ____ + 3

And other variations.
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