Overview of the study and role of the researcher

The purpose of the study was to understand the use of collaborative metacognition during problem solving. Data collection took place in a primary school in Scotland, where a primary school was chosen as most studies which have considered group metacognition have either occurred in high school or pre-school/infant school. There is relatively little information regarding metacognition during group work in mathematics at primary school level. Three data sets were generated during the study : content analysis of student

interactions; transcripts from critical recall interviews; and transcripts from teacher focus groups.

Students were videotaped during their weekly problem solving sessions in their normal classroom. The sessions lasted approximately ninety minutes during which times students were in groups of four. The teacher grouped the students based on her assessment of the likelihood of them working well together. She also grouped them in terms of their ability in mathematics as measured by the standard assessments used by the teacher. Each group had a mixture of students whom the teacher knew to find mathematics relatively easy and those who found it more challenging. Equal numbers of boys and girls were participating

in the study and so two boys and two girls were in each group.

The problems on which the groups worked were mathematical problems which did not necessarily fit with the area of mathematics which was being covered in the curriculum at that time. The problems were chosen by the class teacher, who followed three criteria which I will now outline. The problems were ones which required metacognitive thinking. Previous research suggests that not all problems require such an approach and therefore might result in no metacognitive interactions (e.g. Georghiades 2004). Secondly, the problems, although potentially difficult for all class members, were not beyond their capabilities. Again, research has shown that when students work with more difficult problems, metacognitive thinking is more likely to result (e.g. Georghiades, 2004). The final criterion was that the problems were ones which would lend themselves to group interaction. The teacher used existing school resources to identify such problems. Students were filmed during three sessions and during each session they worked on a different problem. The first problem was about measurement, the second one about area and the final one about sequential patterning. The problems can be found in Appendix B.

The duration of the study was 15 weeks, the students were videotaped at three points: Once at the beginning of the study, once in the middle and once at the end. This approach was adopted because it was congruent with an Activity Theory perspective which suggests that researchers should spend enough time in the research situation in order to gain an understanding of that situation. The data from these videotapes were then transcribed and content analysis was performed in order to understand the use of collaborative

metacognition. More detailed information regarding this can be found in the section below entitled content analysis.

As previously mentioned, in order to gain a richer understanding of the use of

metacognition, I employed an Activity Theory perspective. Within Activity Theory, the principle of contradictions allows researchers to uncover potential issues which might impact the activity. In order to understand these issues I employed a critical recall method. Students were shown a point in their problem solving session which was important to the outcome of the session. The students were asked to talk about that point in the session in order to highlight any potential contradictions. The students who participated in these interviews were the same students as those who were videotaped. Further details are presented in the section critical recall interviews.

The final data set came from teacher focus groups. In order to further understand the impact of the presence of the teacher on collaborative metacognition I conducted a focus group. I chose to interview a number of teachers rather than only the class teacher. This was for two reasons. Firstly, by the time students reach primary five they have had a number of class teachers. Although students have one specific teacher for the year, classes are often taken by other teachers as cover for absence, training, etc. Therefore many teachers had an impact on each learner’s experience of collaborative problem solving during mathematics. In order to understand the historical perspective of teacher influence in this area, it was necessary to understand multiple perspectives. Secondly, interpretation of findings is more valid if a number of teachers report similar experiences, rather than only one teacher. Further details of the focus group are contained within the section focus

group.

5.2.1 Ethical Considerations

This research was subject to the rigorous ethical procedures employed by the University of Glasgow. The research study was reviewed and approved by the School of Education’s Ethics Committee. In line with the guidelines provided by the University of Glasgow, informed consent was sought from all those who participated in the study. Participants were provided with an overview of the aims of the study, together with details regarding the procedures and the type of data which would be collected. All participants were informed that they would be able to withdraw from the study at any point during data collection. They were also informed that once the data collection phase was complete, they could ask for their data to be withdrawn, without the need to provide any reason for this. For the students in the study, parental consent of the same nature was also obtained.

Throughout the study I ensured that students continued to be happy to be filmed and that none were feeling uncomfortable with the video cameras. Furthermore the teacher also ensured that students were able to communicate directly with her regarding any issues which may have arisen due to the research study

Confidentiality and security of data is paramount in a research study with human data, but even more so when dealing with children. All videotapes were kept in a securely locked cabinet, along with consent forms. In order to protect the identity of those involved, pseudonyms have been used throughout this thesis. Further ethical considerations are addressed in the following sections, where appropriate.

5.2.2 Sampling

Access to primary school classrooms poses certain ethical considerations. Due to these it is neither easy nor guaranteed. Non-probability sampling (Cohen et al 2007) was the appropriate method to adopt since I was looking for a specific age group of children. However, there were many other factors which I had to take into consideration. Firstly, the methods which I had chosen for my study required that I would be in the classroom during the course of the study. Furthermore, I would be required to transport and use a lot of recording equipment. I therefore adopted a convenience sampling approach in order to ascertain if there were any schools in the local area willing to participate. A number of negative responses led me to widen my search and engage teachers whom I knew personally to ascertain if it would be possible to gain access to their schools. Only one positive response was given and so I chose to go to that school.

There are drawbacks to such an approach. Generalisation to the wider population might not be possible (Cohen et al 2007). However, as I noted in the previous chapter,

generalisation is problematic within case studies. The focus, rather then being on generalisation is to provide a rich detailed account of a situation.

Sampling is an important consideration in research concerning children within their school environment. The process by which we are able to learn more about real classroom learning is research. However, there is no compulsion to allow such research and access will only occur if it is accepted at school and local authority level. The growth of

methodologies such as action research, where the teacher is also the researcher addresses this issue to a certain extent. However, teachers are afforded a maximum of thirty five hours per year for continued professional development (CPD). This CPD should consist of:

“an appropriate balance of personal professional development, attendance at nationally accredited courses, small scale school based activities or

other CPD activity”

(Donaldson, 2011)

The thirty five hours per year afforded to teachers is not sufficient to be engaged in projects of the size contained within this thesis and would require teachers to be removed from the classroom for long periods of time.

This issue of sampling is not an easy one to overcome. However, when interpreting

findings, it is worth bearing in mind the overall purpose of the study which is to understand a very specific situation from the perspective of those who are involved in that situation.

5.2.3 The impact and role of the researcher

Engestrom (2009) suggests that the researcher should participate in the activity which is being studied. As such, my role was as participant observer. I participated on a level similar to that of the teacher. The students regarded me in the same way they would regard another adult helper in the classroom, such as a classroom assistant. However, this raised an important issue of reactivity effects (e.g. Cohen et al 2007) where behaviour was potentially changed due to my presence. For example, students may have been less attentive, or they may not have accepted me as a teacher figure. Students might also have felt that if they were being observed that they should work hard. The teacher might also be influenced by the presence of another adult. For example, she may have spent more time on lesson preparation or paid more attention to particular aspects of classroom

management. All of these issues might have in turn influenced the use of collaborative metacognition.

In order to reduce the reactivity effect as much as possible, I worked with the teacher and the students in the classroom for some time before the commencement of the study. I contacted the teacher during the school year prior to the one in which the study was conducted. At that time, the teacher was working with a primary five class (age 8-9). Each week for one hour, the students engaged in collaborative problem solving in mathematics. The problem solving sessions took place in the morning and I spent each morning with the class during their sessions. I worked with the teacher for three months during that school year prior to the one from which the data were collected. Although there were different students during this time it was important to understand the approach that the teacher took during her problem solving sessions. It was also important to understand general classroom and school rules regarding behaviour.

Although the data collection for the study took place over two school terms, I worked with the class for the whole of the school year. This meant that the students were introduced to me at the same time as their new class teacher. It also meant that the problem solving sessions were always the same, with both the class teacher and I present. By working closely with the teacher and students for a significant period of time prior to the study, I

was able to assess what was “normal” classroom behaviour as compared to classroom behaviour which was influenced by the presence of others.

Students often encounter other adults in their classroom such as classroom assistants, pre- service teachers and parent helpers. All of these might impact behaviour. It is reasonable to assume that the regular presence of another adult over the course of the entire school year would not influence behaviour greatly. However, the possibility of this occurring should not be ignored and so remained a potential issue.

One other element of the study which had the potential to influence behaviour was the presence of the video recording equipment. The presence of the cameras produced a lot of interest from all of the students in class, even those who were not being filmed. In order to reduce the impact, the recording equipment was taken into the class on a number of

occasions prior to the collection of data. By the time the data collection started, the students were used to being recorded. However, it was evident that they were still aware of the cameras, particularly at the beginning of sessions. Often, students would make faces into the camera, or say something silly. However, this generally occurred at the beginning of sessions and behaviour settled during the session.

It is difficult to assess the impact of the cameras on the work of the students and specifically their impact on the measured variables. However, the large proportion of social interactions recorded suggest that the cameras did not encourage students to be more focussed on the task than they would normally be. As with the presence of the researcher, it is an issue which should be borne in mind when interpreting the data.