As part of an ongoing assignment, I have to visit an assigned blogger’s website and search through his/her archives until I find something that calls to me organically. For this week, it was this website: http://christopherdanielson.wordpress.com/
The post that instantly called to me was titled: “How many tens?”
Here is one from the archives.
Nearly a year ago, Griffin was seven years old and I was doing some thinking about the number course I teach for future elementary teachers. I decided to see how Griffin was thinking about place value.
Me: How many tens are in 32?
Griffin (seven years old at the time): Three, and then two leftover.
Me: How do you know that?
G: Thirty—that’s three tens, and then the zero means no ones.
Me: How many tens in 268?
G: [long thoughtful pause] Twenty-six, and then there would be 8 left over.
Me: What would you say to someone who thought there were six tens in 268?
G: I’d say there are 20 more than that.
That’s my boy.
When I finished reading this post, for some reason I couldn’t move past it. I lingered on the last sentence and then ended up re-reading the whole thing again. And then re-reading it again. I couldn’t articulate what exactly I liked or disliked about it, only that it made me feel curious, puzzled even. I needed to leave the assignment for now because I wasn’t getting anywhere with it and go for dinner with my family. At dinner, I decided to ask the same questions to my niece. H is eight years old, hates homework but LOVES math. Granted, she hates actually doing math homework but loves to problem solve and verbally solve questions throughout the day. She enjoys asking me multiplication questions and is always willing to help solve math questions for me.
Me: How many tens are in 32?
H: Three tens.
Me: How do you know that?
H: Thirty—that’s three tens.
Me: How many tens in 268?
H: 6.
Me: You sure?
H: There’s only 6 in the tens’ place so only 6 tens.
Me: What does the 2 in 268 represent?
H: 2 hundred.
Me: What would you say to someone who thought there were six tens in 268?
H: I’d say they are right.
I would be lying if I said I wasn’t disappointed. I was down right concern. I then explained to her why the answer wasn’t 6. I actually had to take out a paper and pen and draw it for her so she could understand. In the end she did but it made me wonder if any of her other classmates would have correctly answered. After looking at her math homework that were assigned, it truly made me aware of how anal teachers have become in regards to getting the correct answer. Her classmates and her have not been taught what it means to have the 6 in the ten’ place only that it is. How many tens are there? In her eyes, I can see that there is no other answer other than 6 because with the way she’s been taught, how can there be another answer?
I suppose what the post brought to light for me is how neglecting the little details just because I may want a specific answer or because it appears clear to me can end up completely misleading the teaching. In this case, the need for the students to understand place value ended up becoming more important than them understanding the concept of the number being in the tens’ place.
Stay Anonymous 