Borrower and carry and regroup? Oh my!

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The picture on the left is from one of my 9th graders. We were reviewing multiplying decimals (an elementary skill). The student did not understand place value and thus did not understand how to carry when she was multiplying. She did not have the number sense to realize that her answers were incorrect.
The picture on the right is my son’s 2nd grade math home work based on the new state standards. He is being asked to show his number sense and understanding of place value by showing that he is not simply adding a 7 and a 2 then adding a 2 and a 1.  He is showing that he understands that the 2 and 1 are in the tens place thus he is really adding a 20 and a 10.
This problem seems simple to us as adults that learned math in a traditional manner- by following the rules our teacher taught without a genuine understanding of what was really going on.  Most of us were probably decent students that knew how to play the “game” of school and followed a lot of rules for a long time.  When we got out of school and stopped practicing our rules much of our math skills have escaped our memory.
If we weren’t so good at following these rules we used the excuse of “I’m just not very good at math.”
I want to challenge that notion. I think many people struggle with math for 2 reasons. 
1. We struggle because it takes work and practice. You have to put forth some effort. But we are pretty lazy (I have been there… I don’t want to do the work so I am going to complain that it is too hard.)
2. We struggle because we don’t understand what’s really going on. We want quick simple rules to follow (because we are lazy-see #1) but we don’t remember the rules because we don’t realize what is going on. It doesnt stick with us because we havent made real sense of the concept.
Teacher have long been guilty of teaching the rules so kids will pass the tests. Kids bef for rules because it is easier than actually thinking about whats going on.

I became a math teacher because I always wanted to know why we were following all these rules. Until I understood the why, I couldn’t follow the rules correctly. I didn’t have many teachers that were willing to help me with the why.  I struggled to figure it out on my own.  I hope the new standards and approaches to math education will change our thinking and feelings about math and will help get rid of math’s bad reputation. 

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