("G" is Grayson Wheatley; "S" is the student.)
G – OK, so Julia, I am interested in how you think about mathematics. So, I would like for you to talk to me a little bit about a couple of problems. Let me just start with: What would 21 + 19 be?
S – 40
G – How did you think about that?
S – I just did 20 and then 10 and 9 and 1.
G – Where did that 20 come from that you used?
S – 21
G – So you took the 20 from the 21 and what did you do next?
S – I took the 20 and the 10 from the 19 and put the 9 and the 1 together.
G – OK, great. See, I am interested in how you are thinking about that. What would 32 and 18 be?
S – 50
G – And how did you think about that?
S – 30 and the 10 would be 40 and then the 8 and the 2.
G – What would 100 minus 65 be?
S – 40 no 35.
G – And how did you think about that?
S – I subtracted.
G – And how did you subtract?
S – I added 65 to 100.
G – So you have 100. Did you start with 100? And, then what did you do next?
S – I started with 60. I went up to 100.
G – So you built up.
S – And then I went back 5.
G – So when you start at 60 and said up to 100 was?
S – 40 and then subtracted.
G – Interesting way of ding it. There are many ways to approaching the problem, but that is really a neat way of thinking about it. Lets see… 105 minus 12.
S – 92
G – Tell me how you thought about it.
S – I took the 12 and I minused from the 105…
G - So started from the 102.
S – You said 105.
G – Oh, so you started with the 105 and what did you do next?
S – Subtracted 10 from that.
G – OK, you subtracted 10 and that gave you…
S – 10 from 105…95 and then minus 2.
G- OK, so you broke that up and subtracted the 10 and then the 2. Interesting way of thinking about it.