Five-Minute Transcription with Between Lines Analysis
T. Look at these two groups of counters, which group do you think has more counters?
S. They are the same.
T. Why do you think they are the same?
S. Because I counted them in my head and they are the same number.
This shows me that the student is aware there is the same number of counters in each group and he counted them to make sure.
T. (After spreading one row of the counters apart.) Which group of counters has more counters now?
S. They are still the same.
This shows me that the space between the row spread out did not confuse the student.
T. How do you know they are still the same?
S. Because you did not add or take away any, you just spread them apart.
The student understood that in order for the number to change there had to be counters added or taken away.
T. Good Observation.
T. I have this group of counters here, could you count and tell me how many there are?
S. Yes, 1,2,3,4…10 (he counted them one by one)
T. If I were to take three blocks away from the ten how many blocks would we have?
S. There would be seven.
T. How did you get your answer?
S. I started with three and counted up to get ten and that was seven more.
In this particular task he took three blocks and placed them in a group then added seven more to it in another little group to reach ten. When all he had to do was take three away and then count what was left. I thought this was interesting he made it an addition problem. Wish I would have investigated more into his subtraction skills.
T. What if I had my ten original blocks again and I added two more blocks to it, how many would I have?
S. You would have twelve blocks. (Visibly counting on his fingers)
T. How did you reach this answer?
S. I counted starting at ten and went up two more. Am I right?
He used the counting up method and used his fingers this time instead of the counters. I feel that he is more comfortable with addition than he is subtraction.
T. Yes that is great thinking.
T. I can see that you are a pretty good counter, how high can you count?
S. I can go really high!
T. Well can you count to one hundred for me?
S. 1,2,3…100 With no errors.
He counted all the way to one hundred and he appeared to be very pleased with himself.
T. That is great. Can you count by twos starting with the number 2?
S. No, I don’t know what that is.
T. It is where you count, skipping a number in between like this, 2,4,6, and the student then joined in 8,10,12, and continued all the way to 20 on his own.
At this point I could tell that we got the concept after I had given him the first three numbers so I feel that he has had some exposure to counting by twos.
S. I can do that I just didn’t know that is what it was called.
At this point I realized he didn’t know what I was asking when I said can you count by twos, he had never had it addressed as counting by twos.
T. Good job, we call that counting by twos.
T. Can you count by tens?
S. Yes, 10,20…100 No errors
T. That is good counting; what might come after 100 counting by tens?
I was trying to push the child further because he automatically stopped at 100.
S. I don’t know
I feel I should have given another opportunity to go above one hundred here.
T. Okay that is just fine, can you count by tens starting at 24 for me?
S. After a pause 34, 44,54,64,74,75,76,77,78,79,80,90,100.
This is very interesting he began just fine he then reached 74 and counted by ones to 80 and then continued to 100 by tens. I think he got off task and started counting by ones and then started counting by tens again at the end. He just seems to always want to end on 100 no matter where be begins.
T. What about if we started at 56 and tried counting by tens?
S. 66,76,86,96,100.
I asked him to do this again because I wanted to see how he did so I started with 56 and he did great until he then said 96, 100. I feel that he thinks he must stop at 100, like there is nothing past that.
T. Sounds good. Can you count backwards from 25? Start at 25 and go all the way down to 1?
S. 25,26,27,28..35
T. That is good counting, but remember we want to go backwards so how about we start at 10 and go backwards.
S. 10,9,8,7,8,9,10.
He really struggled with the concept of counting backwards every time we tried this concept. This reinforces the questions I had earlier in the interview about subtraction. He turned his subtraction problem into an addition problem, so I wonder if that stems from his inability to count backwards. Wish I could have explored this.
T. Let’s move on and look at some of these counters. Can you take these counter’s and tell me how many there are?
S. Students counts one by one all the way to 32.
T. Now can you group these counters in groups of ten and count them?
S. (He counts out ten three times and makes three piles.) I have two left over that won’t fit in a group.
T. Why will they not fit in a group?
S. Because there has to be ten and there are only two.
I feel that he had some sense of his tens and ones in place value; he knew that he had two left over because there were ten in the other groups and two was not enough to make a ten group.
T. So how many are over here in these three groups?
S. Thirty.
T. And you have these left over which is what?
S. Two blocks.
T. So what number do you have?
S. Thirty two in all.
T. So if I asked you which group you thought was the ones group what which one would you pick?
S. These two right here, because these over here each have tens in them and this one only has two in it. So these are the ones and those over there (pointing at the three groups of ten) are the tens.
This response reinforced the idea that he is somewhat familiar and comfortable with the tens and ones place and he understands that the three groups of tens represent the number thirty and there are two left over and that makes thirty two.
T. That is great thinking. So I am going to write a number and I want you to circle the number in the tens place and tell me what it means? (I wrote the number 342)
S. He circled the three and said that meant there were thirty with six left over.
T. How did you reach that answer?
S. The three is in the tens place and then I added the four and two in the ones place and got six.
After this task I feel that the student is not familiar with the hundreds place value and he feels that the number furthest to the left must be the tens place, and I found it interesting that he added the remaining two numbers and thought that was the ones place. I wish I would have had him show me with the counters his answer, and also given him an example where the last two numbers added up to be over ten and see what he would do then.