1. Megan Ponce & Bronwyn Thomas
26/2/2015
Homework Assignment: #7 - Interview
Setting
Megan and I interviewed a nine-year-old girl, Isa. The interview took around 35 minutes
to complete; although we did not have time to complete all the interview questions. Isa seemed
very calm throughout the interview. She seemed doubtful of her answers at times and a little
uneasy when we asked her to stop working with paper. Overall she gave her best effort and was
happy to cooperate. The black pen in the following attached pictures are notes we added after the
interview to aid our understanding of her work.
Reporting and Interpretation
1) Isa has a good understanding of the meaning of
subtraction as a difference. Isa showed this understanding
when working out the first number relationships question
(picture 1). We asked Isa what number she thought was
closer to 26, 12 or 35. This question is looking for students
to figure out the difference between 26 and 12, and also, 26
and 35. Isa recognized that she needed to subtract 12 from
26 in order to find the difference. Isa then repeated this
method for 35 (picture 1). To find the difference between 26
and 35, she subtracted 26 from 35.
She instinctually knew that
because a difference of 9 was a
smaller difference than 14 that meant 35 was
closer to 26 than 12. Isa also demonstrated that
she understood subtraction as difference and vice versa in question
number 9 (picture 2). We told Isa that ‘Teresa has read 34 books this
year. If she reads 125 books she will win a prize’. Then we asked Isa
how many books would Teresa have to read in order to get a prize? To
work out this problem, Isa subtracted 34 from 125 (the number of
books already read from the total number of books that needs to be
read). Isa realized she needed to find the difference and she did this by
subtracting. Therefore she understands that subtraction can be thought of as difference.
2) Isa understands place value. When we asked Isa to explain how she worked out the
answer to 29+30+31 (picture 3), she told us that she first added 30+31 to get an answer of 61.
Next she added the remaining 29 onto 61. She told us that she did this by adding 6+2 to get an
answer of 8. She then added 9+1 to get an answer of 10. She then told us that she added 80+10 to
get the final answer of 90. We asked Isa why she added 80 onto 10 when she previously had
Picture 1
Picture 2

2. Megan Ponce & Bronwyn Thomas
26/2/2015
done 6+2 = 8. She told us that even though she thought of
the problem as 6+2, she knew 6+2 was really representing
60+20 which made 80. She told us that she simply added the
zero on after she worked out that 6+2 = 8 to get 80. This
tells us that she understands place value as she knew that
when she added “6+2”, she was aware that 6 and 2 didn’t
actually represent 6 lots of 1 and 2 lots of 1 but instead they
represented 6 lots of 10 and 2 lots of 10. *The picture used
for this example is from our notes as interviewees - she
completed this problem without paper* Isa also
demonstrated her understanding of place value when she
solved 49+54 in her head (picture 4), as shown in our notes
below. First Isa added 4 and 5 to get 9, then added 9 and 4 to
get 13. Next Isa added these sums, 90 and 13, by adding
90+10 to get 100, then added the remaining 3 to get 103. Isa showed that
she knew that when she added 4 and 5 to get 9 this really meant 90 since these numbers came
from the tens place. Additionally Isa knew that since the 9 and 4 came from the ones place this
just meant 13.
3) Isa also showed a good understanding of
approximation. In another number relationships problem, we
asked Isa what number was closer to 84, 51 or 96 (picture 5).
She wrote down the three numbers with 84 in the middle (see
picture on the right). She looked at it for a few seconds before
answering with ‘96’. We asked her why she thought 96 was
closer to 84 than 54. She told us she could tell this because 84
and 96 are roughly 10 away from each other whereas, 84 and
54 are roughly 30 away from each other. Since 30 is larger than
10, that means 96 is closer to 84 that 54. Isa also showed
approximation skills when we asked her how many students
were present in class today. She said she thought 22 students
Picture 5
Picture 3
Picture 4

3. Megan Ponce & Bronwyn Thomas
26/2/2015
were present because there were ‘roughly 3 students missing’. Isa attempted to name the missing
students but she couldn’t. This showed us that she had taken an educated guess. We asked her
how she got 22 if she thought that roughly 3 students were missing. She told us that she got 22
because she thinks there is around 25 children in the class to begin with.
4) Lastly, Isa showed us that she could decompose
numbers. We saw this decomposition when we asked Isa
a contextual problem that read, “Jamar spent $18 on
comic books. Charles spent 3 and a half times as much as
Jamar. How much money did Charles spend?” (Picture
6). Isa knew that she needed to multiply 18 by 3.5 to find
the solution and that she could make this easier by
breaking down the ‘scary looking’ number. The first step
Isa took to work out this problem was to decompose 3.5
into 3 and 0.5. To find what 18 multiplied by 0.5 was, Isa
solved for half of 18 by dividing 18 by 2 and writing this
down. Although she found it difficult to articulate why
she had divided 18 by 2, she told us that “the question
wasn’t just asking for 3 times as much, it said 3.5 times
as much and so I divided 18 by 2 to get the half”. She
then multiplied 18 by the remaining 3 to get 54. She recognized it would be
much easier to multiple 18 by 3 than 3.5. Isa also demonstrated that she could decompose
numbers when she solved 49+54 in her head (picture 7). As mentioned above, Isa solved this
problem by first adding 5 and 4 to get 9 and then adding 9 and 4 to get 13. Essentially, Isa broke
up 49 into 40 and 9, and broke up 54 into 50 and 4 to make her mental addition simpler. Plus, to
get her final answer Isa added 13 and 90 by breaking up 13 into 10 and 3 and adding them to 90
separately.
Picture 6
Picture 7

4. Megan Ponce & Bronwyn Thomas
26/2/2015
Reflections
Reflection - Bronwyn
I started the interview by telling Isa my name and where I am from. I asked her if she
knew where England was as I didn’t want to start the interview by confusing her! I wish I had
asked Isa more about herself and what she enjoys doing in her free time. This could have made
her feel more relaxed during the interview. If there was less time pressure, we would have taken
more time to talk to Isa about her interests. We let her know before the interview started that we
were not looking for right or wrong answers and that we might not even know the answer to the
question but instead, I was purely interested in the way she thought about the question. I said it
would make us a better teacher if we knew how she worked out a problem which means we will
be asking a lot of ‘why’ questions.
For the first half of the interview, I asked Isa questions while Megan took notes. During
the second half, I was note taker. I found it challenging to make notes while Isa was solving a
problem as sometimes, it’s hard to follow along their methodology, especially if your
expectation is for the problem to be solved a different way. While taking notes during one of the
division questions, Isa told us she had ‘dropped the 8’. It would difficult to take notes on this as I
wasn’t sure what she meant by ‘drop the 8’. I wrote it down how she said it, expecting to be able
to go back and look over my notes to work out what she had done. However, when I went back
over my notes, I was still confused as to the meaning. In hindsight, I would have asked her what
she meant at the time. Apart from this incident, I felt that Megan and I were really strong at
asking Isa how she worked out the problem and why she did it this way. She responded really
well to these questions and for the most part, we understood exactly what she was thinking.
I really enjoyed conducting this interview! It was very interesting to see how a
child thinks about the problems presented. It was clear to me that Isa was missing manipulation

5. Megan Ponce & Bronwyn Thomas
26/2/2015
skills. For example, 49+54 could be thought of as 50+53. Isa worked it out a more time
consuming and challenging way which gave her the right answer. It wasn’t wrong or bad that Isa
worked it out this way, it was simply interesting to me. It really made me think about class and
Jo Boaler’s book. We spend a lot of time in school learning traditional algorithms for specific
problems that we miss simple manipulations!
Reflection- Megan
I had such a great time interviewing Isa. We made an immediate connection because we
exchanged where we are from and we ended up both being from California. Everyone in our
group was very friendly and approachable but this just got us off to a great start. I feel like I did
well as an interviewer. I made sure to keep the pace slow and when she looked uncertain or had
questions about what she could do I encouraged her to solve the problem in any way she wanted
and offered a repeat of the question as many times as she needed. Looking back it took careful
attention as the interviewer to gather everything that she was doing that indicated her thinking so
I am glad that there were two of us interviewing her! For example, I noticed that her fingers were
twitching as if she might be using them to count but she was also mouthing numbers but not
saying them out loud. In order to catch all of this is was nice to have two sets of eyes. I feel that I
asked hard questions that really pushed Isa to dig deeper in her math explanations which we
weren’t doing as much at the start of the interview. I had so much fun working with her, I only
wish we had more time to get to know one another and to ask more math questions!

6. Megan Ponce & Bronwyn Thomas
26/2/2015
Isa’s work

7. Megan Ponce & Bronwyn Thomas
26/2/2015
Isa’s work