Student Work Post #3

This is the worksheet that I made for one of the students in my placement last week. We had a substitute in the classroom and my mentor teacher left a note saying that she left a worksheet out for this student (let's call him Bob, for simplicity purposes). The sub and I couldn't find the worksheet, but I knew where my MT keeps her math binder, so I looked up a worksheet from the binder and copied the problems onto computer paper. Bob has been working on regrouping with double-digit subtraction one-on-one with Nikki and I while we are in the classroom. Bob has been struggling all year and our MT is in the process of testing for an IEP and/or cognitive impairment, so in the meantime, we have been trying to find out what he can do and working on from there separately from the other students. Because we have been working on regrouping with subtraction for a couple of weeks now, I chose problems that were a combination of problems, some needing regrouping and some not. By doing this, Bob is forced to actually look at the problem and figure out whether or not the problem requires him to regroup. Also, because I was working on this worksheet with Bob, I knew I would be able to observe him solving the problems and see how he goes about doing the subtraction problems to get a better idea of where his mathematical thinking is and how to keep him moving forward. A few of the strategies that I expected Bob to possibly use included, counting on with his fingers, counting backwards with his fingers, or using his knowledge of certain subtraction to get to the answer (such as 10-5 is 5, so 10-6 is one less, and is 4). I figured of the three, the most likely strategy that Bob would use would be the counting on strategy. While observing Bob, I learned that I was mostly correct. If the problem did not take very long to count backwards, such as when subtracting 3, Bob would use that method, however if he was subtracting a larger number like 7, he would use his fingers to count on. This reveals to me that while Bob has developed his understandings into mental math and finger representations, he is not thinking completely abstractly yet, with methods such as familiar fact families or memorized subtraction facts. Another striking thing that I learned about Bob's thinking is that when he is held accountable, he will work very hard, but if/when you walk away from him, he will not even attempt the work. That is why I posted two pictures this week. The top picture is what Bob was doing to his paper before I got the chance to sit down and work with him, while the bottom picture is the back side of the paper that he completely almost entirely on his own while I was checking other students' work but sitting next to him. I helped him through most of the first side of the paper, but when other students came to me asking to check their multiplication work, I got distracted and he continued working on his own, getting all of the problems he attempted correct. I think a big aspect of Bob's learning is holding him accountable and scaffolding him with enough work that he needs help at first, but does a significant number of problems on his own after he has had some practice with a teacher. I think the next step for Bob is to start mixing in some problems that involve three digit numbers so that he has to regroup a second time. He has not learned this yet, but I think it is an important step in truly understanding the place value concepts that are behind regrouping. I also think this will get him thinking more deeply about the times when he does need to regroup, because he will be working with a lot more changes in the numbers he is using.