DMI Chapter 4

I was amazed at how this reading really mirrors the second grade classroom I am in for this semester. The students I am working with are subtracting two digit numbers and learning the standard algorithm. In the reading, the first group of students really struggled because the algorithm was pushed onto them before they really understood the idea of tens and ones and regrouping. Although the second group didn't seem to enjoy the algorithm, they were driven to make sense of it because it came later in the year when they had a better understanding of adding tens and ones. In the case of Fiona (37-19) she lost track of the operation she was doing because she took 10 away from 30 and then she took 9 away from the 20 and forgot what to do with the 7. She confused her operations likely because she had several steps to solving this problem. Lynn's asking whether the 7 birds stayed or left was a helpful question because Fiona really had to think about what was happening with the numbers. Lynn said that Fiona usually got other problems like this after asking her this question once. I think Lynn pushed Fiona to ask herself what she was doing with the numbers so this knowledge transfered to later problems.

At the end of chapter 4, I found it interesting that Lynn noted that there was a lot less subtracting up which I think is because her students were working with the math behind the algorithm instead of just memorizing steps to complete a problem. As I said before, I am seeing some of the exact same things in my field placement as Lynn, especially subtracting up. Some students have a firm grasp on adding tens and ones and regrouping so the algorithm makes sense to them. However, many of the students struggle when I ask them to show me a problem in a different way that writing it as an algorithm. Students really struggle when subtracting two digit numbers that require regrouping. If the "bottom" number is larger than the number on top, they quickly resort to subtracting up. I strongly feel that this is because they do not see how the standard algorithm relates to tens and ones. The problem, I feel lies in the rushed manner in which teachers have to teach the curriculum. My CT is an amazing math teacher and she really pushes the students to use manipulatives or other strategies for addition and subtraction (making 10's, compensation, and so on) but the curriculum almost demands that students know the standard algorithm. Their math work books are almost entirely composed of problems written in the standard algorithm. This is a topic that is very interesting to me because I see it every week, and I am very curious to see how the students view the standard algorithm at the end of the year as they head toward 3rd grade!