Regrouping and Calculators

I read Lynn's case study in the DMI book this week with a lot of interest because I am also in a second grade classroom where they are working with regrouping in much the same way that she talked about doing in her classroom. I understood some of her frustration when she said there was a disconnect between the games they would play with trading ones and tens to when they actually tried to do addition with regrouping on their paper. Line 41-45 discusses this scenario where students that had a good grasp of ones and tens still wanted to count by ones when faced with two digit numbers.

Today our class worked on regrouping with their rubix cubes for awhile until they went back to their desks to work on a worksheet and it took a little convincing for them to not all discard their cubes right away. My students probably would not know what to do with a traditional algorithm right away though because they are in the stage where they are trying to really solidify what it means to "regroup" and to have a really good understanding of the tens and the ones place. They are really able to make sense of it like Lynn's students in her class. I was very impressed when I did my math interviews with my students today. I had selected some word problems that asked for multiplication and division. I knew they hadn't discussed that in class yet, at least not while I was there or that my CT had mentioned. Even so, every student was able to correctly solve the problems and was able to explain it to me. What made me even more excited was that I interviewed 3 students and there were 3 different methods used. These students were really able to make sense of the numbers to solve problems they might not have experienced before.

In the Groves article about calculator use I was pleasantly surprised to see how young and in what manner they were using calculators. I liked the quote, "There is no evidence that children became reliant on calculators at the expense of their ability to use other methods of computation" (128). The students in K-2 were able to explore numbers far beyond their reach if they did not have a computer that allowed them to experience many of the patterns that are very important in math. Looking back on my own math experience with calculators, I don't remember having access to them until about fifth grade. Even so, I remember being strongly encouraged not to use them and we definately did not spend time exploring different math ideas on the calculator. Since calculators are far from a new invention it has puzzled me as to why few teachers have really embraced them as a resource. I was impressed that when the teacher asked students to divide 64 by 7 the students were quickly able to look at their response in decimals and think of it as being a bit more than nine. The teacher made the point that this equation would have been over their heads if they weren't allowed to use a calculator and it also provided an important look at decimals. I know this article definately gave me a new outlook on the use of calculators, especially in the younger grades.