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Amanda A. Thompson
Saginaw Valley State University
Methods of Teaching Mathematics
November 5, 2002
Mathematics Student Interview/Assessment Report
Introduction
I interviewed a girl in the second grade class I am working in for Methods of Teaching Mathematics. I began the interview by explaining the process to the student and telling her what kind of questions I would be asking. I assured her that the goal was not for her to give the right answers and that she would not be graded on her response. I told her I simply wanted to learn about how she did counting. With that I began the interview.
Interview Questions
Interview Results
I learned several things about this young girl’s number sense and counting ability. First, her rote counting was very strong. She predicted she could count to 1200. This took me by surprise, but I’m assuming she heard or saw this number somewhere and probably has not been formally introduced to it during her schooling. When I asked her to try, she did so and was able to count into her hundreds. She did stumble over a few numbers in the two hundreds. For example, she went right from 106 to 111. She did not have this problem when counting from 6 to 11, however. I believe she still struggles with adding the hundred prefix to the number sequence.
I then started counting a group of numbers and asked her to count on from them. She did fine with most of the sequences. However, she stumbled on a few. When given the set 204, 205, 206, she then said “207, 208, 209, 300.” This tells me that she probably has not had much exposure to using numbers in the 200s and 300s. I saw further evidence of this when I gave her the sequence 192, 193, 194. She was confident in her reply of “195, 196, 197, 198, 199,” but she hesitated at 200 and it took some thinking to get that number out. She then, however, continued correctly in the 200s.
I saw similar circumstances when I had her do the same activity counting backwards. On most of the sequences she did fine. When given 24, 23, 22, 21 she thought hard and counted back “20, 19, 18.” She was able to count back correctly when given 46, 45, 44 as well. When given the sequence 81, 80, 79, she thought about it and continued “78, 76, 75, 74.” I’m sure she’s not had much practice counting back these larger numbers before, and that prompted her to leave out 77.
I then continued to see how she could count in sets. Counting by twos was fine when she was given the sequence 2,4,6. However, she could not answer when I asked her to count up by twos starting with 3,5,7. I believe she has probably not had a lot of practice with the odd number sequence, and has only counted by twos using even numbers. I asked her if she had ever counted that way before, and she said she had not. I think once she is introduced to these concepts she will grasp them just fine. Counting by tens was also easy for her when starting at 10 and continuing on to 100. However, when asked to count by tens starting on another number, she was unable to do so. I asked her to count by tens starting at 24, and even prompted her with 34, 44, yet she was still unable to answer. Similarly, when I asked her to count by fives she had no trouble counting out “5, 10,15, 20…” But when given the sequence asked to start at 10 and count at fives she was not able to do so, even when I gave her the next number, 15. If she continues on with counting and learning these next concepts she should learn them quite well.
Using counters was fairly easy for her. I put out a pile of twenty and asked her to count them. She looked at them and counted in her head and got 19. I suggested that she try putting her fingers on them as she counted and see what number she got. When she did so, she used one-to-one correspondence and was able to keep track of which ones she counted. She came up with the correct answer of 20 this time. I pointed out that last time she counted 19, and asked her which answer she thought was right. She said “20,” and when asked why she replied that she had touched them when she counted. I then proceeded to add blocks of ten. She was able to count the following sequence both forward and backward with no problems: 20, 30, 40, 50, 60, 70, 60, 50, 60, 70.
I next looked at her ability to write numbers. I asked her what the biggest number she thought she could right was. She did not know. When prompted to take a guess, she still did not answer. I decided to move on from this question. I had her begin writing her numbers and she wrote 1-30 with no problems. I then wrote the number 37 and asked her to write one number larger. She did so. I wrote 54 and asked her to write one number smaller. She did so again. I did the same exercise with numbers in the hundred and again she had no trouble. I think that perhaps she is more of a visual learner – she seems to count better when she can write the number or touch something. I would have liked to explore this further and she if she could WRITE some of the sequences she struggled on earlier, but we ran out of time and I had to finish the interview. If I were able to interview her again I would test this hypothesis.
Summary and Future Plan
This student seems to be at an average level for counting in the second grade. She seems to have a good grasp on rote counting, counting one/two more or less, one-to-one correspondence, and she is able to keep track and be consistent in her counting. She seems fairly confident in her counting ability. The only concern I have in this area was at the end she said “I did bad, didn’t I?” I assured her she did an excellent job and got most of the answers right even though she wasn’t being graded. I think that this was just the apprehension of being in the interview situation: from what I have observed from her in the classroom she seems to be very confident in her mathematical ability.
From my interview and my interactions with this student in the classroom, I think she has a bright outlook in her mathematics education. As her teacher I would continue to develop her counting ability, introducing her to and giving her practice in three-digit numbers and counting by twos, five’s, and tens. I would probably also introduce this student to a 100-number chart at this point, so she can began to see the relationship of numbers when counting by two, tens, and five’s. I would also make sure she has a lot of chances to count backwards, as well as forwards in larger numbers. Furthermore, I would continue to monitor how confident she feels in performing mathematics operations, and focus on making her feel capable. However, I am confident that with lots of practice in the mathematics topics that they are currently covering, this student should perfect her counting skills with few, if any, problems.
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