Number Interview Kit Report

Alanah Bresnehan Student Number 212210385 ESM210 Introduction:

On the 13th August 2013 two Year 2 students were interviewed on their understanding and

recognition of counting, place value, addition and subtraction. Through these interviews the

students were exposed to a set of questions in the ‘Deakin University Number Interview Kit.’

Each interview was conducted in around 30 minutes where the children answered questions

according to what they believed the answer would be, they were not told whether they were

right or wrong, this is because the record was to notice different principles and strategies

students when working out problems. During the interview they used counters to answer some

questions and also pen and paper in aid to writing the question down in a particular way. The

interview was then record in an A4 booklet, which the questions were sourced. For the rest of

this report the students will be referred to student ‘A’ and student ‘B’.

Recognizing Counting Strategies:

During the interview many different strategies arose in how the students decided to work out a

particular answers. The two students showed similarities and differences to their working out

and also answers. This can be evident through part one and two of the interview where the

students tended to use a ‘counting on’ or ‘counting back’ method. With this strategy a child

should ‘recognize the starting number and the previous number,’ (Reys et al., 2012, pg. 152)

Both student ‘A’ and student ‘B’ used this method when asked what the number was before and

after their favourite number (Appendix A, Q. 1.7). For student ‘B’ this task was easy enough to

count backwards. Through part two the students were asked to find numbers between two

other numerals. With this task both used the counting on method, however, student ‘A’ used

perceptual counting. A ‘perceptual counter will demonstrate the one-‐to-‐one principle’ (New

South Wales – Department of Education, 2012) by using his fingers to make sure he can count in

an order.

Alanah Bresnehan Student Number 212210385 ESM210

When being introduced to part 3 the students were encouraged to use the counters to figure out

the grouping of numbers. The difference between the two students is that student ‘A’ tended to

use one-‐to-‐one correspondence when answering each of the questions. He used each object as

one place value and counted each counter individually. In contrast to his

strategy student ‘B’ used subitising to recognize groups within groups.

When answering question 3.1 student ‘B’ instantly answered 6, when

asked how he managed to figure it out he replied with the explanation

that he recognized two groups of 3 which equal 6.

Student ‘B’ also used the idea of skip counting when creating groups of counters. He managed to

take the counters from one group to the other by counting in twos, and then when exposed to an

odd number he would add on the remaining one.

In part 8 there was a different array of how the students came to forming answers to the

questions asked. For student ‘A’, he had to use a counting on method along with using

perceptual counting, as he had to use either his fingers or counters to assist him in seeing a

visual representation of the numbers. This is highlighted through student ‘A’ answer to question

8.2 (Appendix A). Student ‘B’ tended to form different understandings on how to answer the

questions. When asked the same question he responded he responded with

the right answer. Continually, he was asked how he managed to get the

answer. According to student ‘B’ he was able to notice that ‘2+2’ equaled four

and then he doubled it. Using the double idea he was able to notice the

formation of number groups witin the answer of eight.

Image 1.1: Student ‘B’’s grouping strategy, which can be seen as subtising.

Image 1.2: Student ‘B’’s use of noticing doubles and also recognizing groups within groups of numbers.

Alanah Bresnehan Student Number 212210385 ESM210 Throughout the interviews the recognition of multiple strategies from each child are evident.

However student ‘B’ seems to have an overall better understanding of numbers and the

different elements they can posses. Student ‘A’ leaned to the particular strategy of one-‐to-‐one

correspondence, when answering the simultaneous questions. Student ‘B’ juxtaposed student‘A’,

as the student used different methods according to what the question was asking and also how

the numbers were set out in the number sentences.


Table 1.1

Alanah Bresnehan Student Number 212210385 ESM210 Growth Points and Developing Learning in the Future:

The use of the Early Numeracy Research Project Growth Points (2013) in mathematics ensures

that each students understanding can be placed on a point in which they can be assessed and

also helped to improve them in mathematics. The Victorian Department of Education and Early

Childhood Development describe ‘growth points as key "stepping stones" along paths to

mathematical understanding’ (2013). Though these growth points are made to show a students

progress most students may be able to touch on two or three of the points, however they may

have not completely understood the complete growth point. This can be highlighted through

student ‘A’ as he manages to use strategies to aid him to the right answer he cannot complete

the growth points.

The difference between the students and growth points can be seen in table 1.1. This table

depicts that student ‘B’ has a wider understanding on counting, place value, addition and

subtraction compared to student ‘A’. In the table the highlighted points are the spots which the

students excelled when answering questions. The reasoning behind Student ‘A’ being placed

considerably lower compared to Student ‘B’. Under the heading of counting Student ‘A’ mainly

only used a counting on, one-‐to-‐one correspondence to achieve an answer when asked how he

managed to find answer he communicated that he used his fingers in a form of perceptual

counting, as seen in parts 2, 3, 4, and 8 of the interview. It’s hard to pin point on to a certain

growth point because the student uses part of each growth point 2, 3 and 4 (as highlighted in

Table 1.1). Though tends to disregard the other elements of the growth point. Student ‘B’ is seen

to have grasped the idea of counting. This can be seen as he can begin at a ‘non-‐zero-‐starting

point’ (Victorian Department of Education and Childhood Development, 2013). Question 1.8

asks the students to think of the smallest number they know, he recognizes that there are

numbers past zero and that they form negatives.


The students understanding of place value is a little simpler than trying to pin point their

counting growth points. During all the questions in part six the students were asked to say what

the number was on a designated flashcard. For Student ‘B’ it was easy to recognize the place

values of four and five digit numbers which allowed him to be placed at growth point five of the

Early Numeracy Research Project Growth Points spectrum. On the other hand, Student ‘B’ when

asked the same set of questions easily recognized the three digit numbers, however, when asked

the four and five digit number question he tended to try and break the numbers up into two

different numbers. For example instead of answering ‘3217’ as 3 thousand, 2 hundred and

seventeen, he managed to see the number as ‘3 thousand seventy-‐teen’ (Question 6.3, Appendix

1). With this indication he was made to sit on growth point two.

Lastly, the understanding of addition and subtraction allowed the students to showcase the

different ways in which they saw the problems. Both students were evident to be on one end of

the spectrum to the other. Student ‘A’ didn’t show any strategies other than one-‐to-‐one

correspondence when answering questions. He didn’t use any other strategy when

encountering harder questions to allow him a quicker response. In comparison, Student ‘B’

showed evidence of doubling, rounding, counting on and also perceptual counting. Through

part eight of the interview the student used doubling to find out how many more sheep there

were in the paddock buy recognizing that ‘5+5’ equals ten, then used counting on to add on the

extra one (Question 8.3, Appendix 1). By the student using these strategies to form an answer

he was able to answer the question quicker and more effectively.

These two students were certainly on different ends of the growth point spectrum. For future

learning I believe that Student ‘A’, in particular, needs to work on their place value which will

Alanah Bresnehan Student Number 212210385 ESM210 then aid him when counting on past 100, particularly when skip counting. Exposing him to other

addition and subtraction strategies such as doubling and even using a number tree will help him

find how numbers can fit into each other. For Student ‘B’ his growth points are all on the highest

side of the spectrum, with this in mind I believe that moving him onto new topics such as

multiplication and division, and also possibly measurement.

Conclusion:

Through interviewing the two children I have learnt that students can have different notions on

what numbers are, what they are used for and how to work with them. With the Deakin

University NIK it has allowed me to witness physically and also through reflection how children

have different strategies to working numerical problems out, whether it be mentally or

perceptually. I have also found through this study that children can be on different paths to

learning mathematics according to how they go about using the number strategies. Comparing

these two students has also formed and idea of how teachers can evolve and mature a child’s

mathematical ideas and concepts. With these interviews it has reiterated the idea that

‘mathematics aims to instill in students an appreciation of the elegance and power of

mathematical reasoning.’ (AusVELS, 2012) Which these two students are evolving and aiming

to become.

Alanah Bresnehan Student Number 212210385 ESM210 Referencing:

• State Government of Victoria, 2012, Mathematics – Rationale, AusVELS, 16th August

2013, <http://ausvels.vcaa.vic.edu.au/Mathematics/Overview/Rationale-‐and-‐Aims>

• New South Wales Government, 2012, Perceptual Counters, Numeracy Continuum K-‐10,

17th August 2013, <http://numeracycontinuum.com/aspects-‐of-‐the-‐

continuum/aspect2/9-‐aspect-‐2/35-‐perceptual-‐counters>

• Victorian Government – Department of Education and Early Childhood Development,

2013, Victorian Government, 17th August 2013, <

http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths

/pages/enrpframe.aspx>

• Reys, R, Lindquirst, M, Lambdin, D. V., Smith, N. L., Rogers, A, Falle, J, Frid, S, Bennett, S,

2012, Helping Children Learn Mathematics, John Wiley and Sons, Milton

Number Interview Kit Report

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Transcript of Number Interview Kit Report