Wednesday, June 19, 2013

Let's Talk About the Equal Sign

Wow! The misconceptions a small little symbol can make!  Who knew the (=) sign could cause so many problems?  Where does this all start?  In KINDERGARTEN my friends!

So let's think about it....students are told and have been convinced to believe this symbol (=) actually means, "Put your answer here".  This is how we are teaching math to them.  Just find the answer!  Don't believe me?....take a look at this research below:

"About 70 percent of middle grades students in the United States exhibit misconceptions, but nearly none of the international students in Korea and China have a misunderstanding about the equal sign, and Turkish students exhibited far less incidence of the misconception than the U.S. students," note Robert M. Capraro and Mary Margaret Capraro of the Department of Teaching, Learning and Culture at Texas A&M.
So why are U.S. students having so many misconceptions?  It really boils down to two reasons...the teachers and the U.S. textbooks.  The problem begins with our thinking that the (=) sign is 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 + 3 = ____ + 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 + 3 equals 10, so the other side has to equal 10 too. 8 fulfills this little equation:

7 + 3 = 8 + 2
So how can we fix this problem starting at the kindergarten level?  I have two ideas of how to "see" the equal sign in action!
The first one is using a pan balance and showing how 5+1=6 on one side and how 5+1=6 on the other side balances the scale or makes it "equal"

The next example I have that works well in kindergarten is using Monkey Math. You can purchase this little guys lots of places including Amazon.  Here is what he looks like: 

The children really LOVE him!  You can tell from the picture how he works.  The kids must balance his arms using the weighted bananas or his eyes look crazy!  Super cute and a great way to show how combinations of numbers can be used to "equal" the other side.  There is also an app out and it looks like this:
I would love to hear your comments or suggestions for helping little ones understand this tricky but oh so important symbol!

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