Hannah Brannon

EDEE431

Dr. Ann Wallace

11/11/02

Student Interview Assignment

The student that I interviewed is the daughter of one of my friends. “M” turned five at the end of September, and attends a Montessori school in West Ashley. Although “M’s” parents are divorced, they get a long well and are both very active in her education. I interviewed “M” at my house, and although she had gone home sick that day, she seemed excited to do the interview. Her mom sat in on the interview which made it a little difficult because it was awkward when “M” got a problem incorrect. I never told “M” if her response was correct of incorrect, but her mother and I obviously knew. Nevertheless, I was pleased with how the interview went.

Interview Task	Student Response	Thoughts/Comments
Counting Unifix Cubes
How many blocks do you see?	5	How did you get that?
	I just went (counted each cube in head my moving eyes from cube to cube).	Okay.
2 sets of five blocks shown: Now how many blocks do you see?	10	How did you know that?
	I just went 1,2,3,4,5,6,7,8,9,10. (Doesn’t point with fingers, but is sitting on hands and counting by moving eyes.)	Can you show me how you did that by pointing with your fingers?
	Points to each cube and says: 1,2,3,4,5,6,7,8,9,10.	Okay.
Add two blocks to the original 10. Now how many?	12	How did you get that?
	I just counted 1,2,3,4,5,6,7,8,9,10,11,12.	I can tell that “M” is getting tired of this repetition and that no matter what set of cubes I give her, she’s going to count up from one, so I decide to move on.
Finger Patterns
Can you shown me two on your fingers?	Holds up index and middle finger on one hand.	Okay.
Four?	Holds up index, middle, ring, and pinky fingers on one hand.	Alright.
Eight?	She counts up from one with five fingers on one hand and three on the other. The three on the second hand are the index, middle, and rings finger.	From this I can tell that “M” really has no doubles reference, but counts up from one every time.
Chips
How many cubes are there here?	10	How did you get that?
	I just went 1,2,3,4,5,6,7,8,9,10 (moves eyes from cube to cube).	Okay.
If I take three cubes away, how many are left? (I remove three cubes.)	7	How did you get that?
	I went 1,2,3,4,5,6,7 (moves eyes from cube to cube).	Okay, and how many chips do I have in my hand?
	(Pauses) 5	How do you know that?
	I don’t know.	Well how many cubes did we start with?
	10	And how many are shown here?
	7	So, how many are in my hand?
	5	I show her what’s in my hand.
	3, I mean 3.
Okay, how many cubes are there now?	10	Gets that by once again counting each cube up from one.
How many will I have left if I take away 5? (I remove five cubes.)	5	Once again counts up from one.
And how many are in my hand?	I don’t know.
(I put out four sets of two cubes.) How many cubes are there now?	8	Okay, how did you get that?
	I just went 1,2,3,4,5,6,7,8. (Moves eyes to each cube as she counts.)	Okay.
How many are left if I take away two? (I remove two cubes.)	6	Show me how you got that.
	I just went 1,2,3,4,5,6. (Moves her eyes from cube to cube as she counts up.)	So how many are there in my hand?
	I don’t remember.	Okay. I decide to move on to the next activity as she is getting bored.
Spatial Tasks
(I make a design using tangram pieces while “M” is closing her eyes.) Can you make a design that looks just like this?	Forms design without trouble.	Okay.
(I form a pattern using the tangram pieces while “M” is closing her eyes.) Can you continue this pattern?	Continues pattern without trouble.
Number Relations
(I write the number sentence 2+2= on the chalkboard on the board.) Can you read this to me?	Two plus two is	Okay, what does this symbol mean? (I point to the equals sign)
	Equals	Okay, do you know the answer?
	4!	How did you know that?
	I just know it.
(I write 4+4= on the chalkboard.) What is this?	8	How did you get that?
	I thought 1,2,3,4,5,6,7,8.	(I assume that she is double counting in her head as I don’t see her using her fingers.) Did you use your fingers to help you at all because that’s ok to do?
	No, I just used my head.
Thinking Strategies
(I write 9+3= on the chalkboard.) What is this?	12	I see her counting under her breath up from one to 12.
I write 9+4= on the chalkboard.) What about this?	13	She gets this one fairly quickly, so I once again ask, How did you get that?
	The same way as the other ones.	Okay.
What about this? (I write 10-3= on the chalkboard.) What do you think that is?	8	How did you get that?
	Because 10, 9,8 means 8.	I know that she knew what to do and her reasoning was logical, she just couldn’t get past the 8 being the third number taken away so the answer would be 7.
Conservation
I gave both myself and “M” a cup. I put out 12 cubes and told “M”: We are going to both put these cubes in our cups at the same time until I say stop. We do this until we both have five cubes in our cups. I say stop, put one cube in my cup while she does nothing. We then begin putting cubes in our cups together. At the end, “M” has 10 cubes in her cup, and I have 11. I ask, do you think my cup has more, your cup has more, or they are the same.	They are the same.	Okay.
We repeat this activity, and I ask again, do you think my cup has more, your cup has more, or they are the same.	They are the same.	Okay. I do not push the issue anymore. I realize that this is not a time to teach, and leave it at that.
Number Representation
Can you write your numbers on this chalkboard for me? Write as high as you can go.	Writes 1-12 without trouble, but from there writes 31, 41, 51, 61, 71, 81, 91, 02, etc. instead of 13, 14, 15, 16, 17, 18, 19, 20, etc.	At this point, I end the interview because “M” is getting tired and knows that there is a toy that she wants next door.

I think that “M” has a solid understanding of mathematics for a child her age. Although she does not yet have a solid tens, fives, or doubles reference, she can count up from one, double count, and read and solve simple mathematical sentences. “M” did not use finger counting as a math strategy even after I told her that it was alright, but counted everything in her head. Most of the time, I could tell how she was thinking because she would move her lips while thinking and talking to herself. I was pleased when “M” was able to recreate the design with tangram pieces and also when she was able to continue a simple pattern. This also shows a solid level of mathematical understanding for a child her age. Perhaps the most interesting part of the interview was when I asked “M” to solve the problem 10-3=, and she responded 8. Even though the answer was incorrect, she had solid reasoning. Overall, “M” had a solid understanding of the tasks, and although she had more difficulty with some of the questions than others, she got the overall idea of what she was being asked.

I really enjoyed conducting the interview with “M”. I think that it helped that I know her well from prior situations, but she was excited to help me. When she came over, she said “So what’s this homework I have to help you with?” It was difficult to not make teaching opportunities out of incorrect answers, but I think that it was better in the long run. The most interesting part of the interview was when I really saw “M’s” reasoning for the subtraction problem 10-3=. All of the problems up until here, she had simply counted from one and double counted, but here I was able to really understand how she was thinking. I also thought that the Piagetian test of understanding of conservation was interesting. I had just watched a video about this, and I thought for sure she would understand that my cup had more cubes than hers, but when she did not see it after two tries, I was sure that she did not understand. This interview was a great learning experience, and I look forward to seeing how children’s mathematical concepts differ in the future!