The research setting

4.4.1 The researcher

Denscombe (1998) states that,

“Qualitative data, whether words or images, are the product of a process of interpretation” .. “ .. the researcher’s self plays a significant role in the production and interpretation of qualitative data. … The researcher’s self is inevitably an integral part of the analysis, and should be acknowledged as such.” (p208)

I have, in a preceding chapter, described the motivation for my research – i.e. that though no longer a practising primary teacher, in my current role as a teacher of teachers, it is still important to me that I learn more about the ways in which children learn mathematics most effectively. My

professional experience in primary classrooms has provided me with innumerable experiences of children apparently failing to transfer

knowledge. It has, however, also provided me with even more extensive experience of children successfully learning mathematics by developing knowledge and understanding in very disparate ways. I believe my experience in the classroom also has provided me with appreciation of a vast range of socio-cultural and affective, rather than only cognitive, factors that influence children’s learning.

As a teacher and researcher I am part of the learning setting in which my research subjects work. I am, myself, therefore, an external resource and I agree with Denscombe when he goes on to say that the,

“researcher’s self should not be regarded as a limitation to the research but a crucial resource”. (p209)

So, having described, in very broad terms, what I want to achieve, it is now appropriate to consider the research setting, and to offer some rationale for decisions that were made.

4.4.2 The school

In acknowledging that I would be asking to work with children many times and that I would need co-operation from teachers and parents, I chose to conduct my research in a school in which I have previously worked. It is several years since I worked there so I was not known to any of the children nor most of the staff. The head teacher and some of the teachers, however, did know me and I knew that I could rely on their support.

4.4.3 Class

Because I had already analysed the curriculum and had selected my domain focus, it was appropriate for me to work with children in Year 4. In this year group, children are introduced, for the first time, to negative numbers. It was important, for my research, to explore children’s re-use of existing (and particularly recently constructed) knowledge and I felt that in order to be sure whether any existing knowledge in evidence was “recently constructed”, it had to relate to something that I could be confident they had only recently been taught. (See my comments in “Chapter 6: Discussion of Findings” regarding “informal” knowledge about negative numbers.) At my research school, there are two Year 4 classes. Both classes are timetabled together for mathematics lessons and are “set” in 3 ability groups across the year group. Children in both classes

were therefore “eligible” for inclusion in my research and parental consent was sought for all children in the year group. (See Appendix 1 “Consent Form”)

4.4.4 Children

Children were selected from all of those whose parents consented to their inclusion.

I had learned from the Webkit phase of my research that the groups I had worked with then were too large – that in those groups (of 6-7) some individuals did not engage or contribute, allowing the more confident and vociferous to dominate the group. I chose, for this phase, to work with smaller groups. I did not want to work with individual children as that would constitute more of an interview. Although Wagner (2006) had reported on work with individual students, I considered it important for children to have peers with whom they could share their ideas and thoughts as I believe that they would be more relaxed and would use each other to scaffold their learning. Also, I was concerned that one-to- one interviews might be intimidating for such young children.

Pairing of children might have worked well for discussion and argument within the pairs – however, from a pragmatic viewpoint, this would cause problems if a child was absent on days when I was due to visit. I therefore chose to work with groups of 3 so that an absence would not preclude a session and so that group members would be unlikely to fail to

participate.

The class teacher was asked to provide a list of groups of 3 children (for whom consent had been given) who she thought would co-operate and would be supportive of each other. She was asked to exclude any

children who would “find it extremely difficult to talk about their ideas and their thinking”.

I did not ask the teacher to consider ability when grouping children. She provided me with a list of 9 groups of 3. At that time she explained that she had considered that children should work with others with whom they

are used to “doing maths”. This meant that all 3 children within each group were from the same maths set – that is, each group of 3 comprised children who had been assessed by teachers as being of similar ability. Once I realised this, although initially disappointed because I had expected to work with mixed ability groups, I could see that there would be advantages to this approach:

• that the pace of each activity would match more closely the needs of every child in the (similar ability) group, rather than a “best-fit” match that would be necessary for a mixed ability group;

• that this approach would afford me the opportunity to consider “ability” differences when constructing and developing new

concepts, more reliably than I would have been able to do (or had previously intended to do) with mixed ability groupings.

I therefore took the decision to embrace this unforeseen differentiation of my sample groups, rather than re-group them. I selected 3 groups of 3 children – one from each of the 3 ability sets. Gray et al (2000) had focused on ability differences and reported some interesting findings. I considered that their research might support me in analysing and

comparing the progress of different groups. It is important to note, at this point, that ability is not here defined but is some construct in the mind of the teacher who made the decision when populating the groups. There was no methodological intention to relate findings to ability since my interest is in the changing thinking of individuals.

At this stage I did not choose the particular children who would become the focus for individual case studies. This decision was made much later, after all sessions with children had taken place and after preliminary analysis of the data.