ED 616

In Connie ___'s second grade classroom, the students do a math page every day upon entering the classroom from lunch recess. This is in addition to the math manipulatives and games that they use at other times of the day. I chose to correct one set to identify one student that seemed to be having a few problems.

Cassie was one of the students that was having a slightly difficult time with her adding. In looking at the problem sheet, you can see that most of her problems revolved around sums adding up to 8, 9, and 10. Fourteen of the twenty seven problems were related to these three numbers. Of the fourteen, she missed six, or about half of them. Of the six, four were repeats (8+2 and 2+8 & 4+6 and 6+4). The other two had corresponding problems, but those were correct. I prepared a worksheet for her that emphasized these numbers and placed them in different orders.

The following day, I approached Cassie and asked her if she would help me do an assignment for my math professor. She became very excited and eagerly followed me to a small table to work, away from the distractions of the other children. I then told her we would be doing some math problems together, but that I was going to ask her how she did each problem. I also encouraged her to think out loud.

She began the first problem and immediately brought her right hand up into the air. She balled up her fist and punched it down, saying the number 4. She then counted up from there, punching her fist down with each number until she had five fingers sticking up. She then stated she had nine and wrote it on the page. I asked her what would happen if she started with five and she stated it would be the same. She then demonstrated it to me. For the next problem, she did it the same way and came up with the correct answer.

When she saw the 2+8 problem, she quickly blurted out 11 and said she just knew that one. I asked her if her fist method was needed and she shook her head no. I asked her to try it with her fist and she was a little surprised at the result. Oops, she said, realizing her mistake immediately.

About every three problems, she would blurt out an answer without checking, but she did improve and was able to remember it correctly the second time the problem came around. All in all, she got every problem correct by the time she wrote the answer on the paper. We ended the session by talking about math problems that added up to 8, 9, and 10. She said that she needed to check her answer with her hands more often to make sure it was correct. I also suggested she go just a little slower and to realize that these were not time tests. It was more important that she got the problems correct. Finally, we talked about the role of doubles in adding. She could look at 5+5 and see that it was similar to 4+6, being one number away. She seemed to understand the relationship, but this will probably take more time and practice to cement the idea.

In analyzing the mistakes Cassie made, it seems that her difficulty lies in trying to go too fast in her math problems. When she slows down and follows through with her tried and true method, she succeeds. She is in the midst of transferring her proven method to memory. She will need to continue working so that she memorizes the facts correctly. This will be especially true when she starts doing addition and subtraction above ten.

Interestingly enough, when she did subtraction problems using the same numbers, she only missed one problem out of twenty-seven. One happened to be the same as what had been worked on in the addition, but the others were correct. When subtraction is usually the more difficult operation, it makes me wonder what makes it easier for her.

The math case study revealed some of the misconceptions that students can have in mathematics. Reading about them in the math text is one thing, but actually working on it with a real student is entirely different. When I have my own classroom, it will be much more difficult to work with students on such an individualized basis. Teachers have to be able to analyze quickly. This assignment definitely leads to such skills in teaching.