The pilot and main study

In this section I first (4.5.1) briefly describe the pilot study. In Section 4.5.2, the main study is described including selection of teachers and schools involved and the three main teachers in my study.

4.5.1 The pilot study

Towards the end of the first year of my Ph.D. study, I considered use of case study design as an appropriate choice based on the possibility to follow a number of teachers quite closely during the three years of the developmental projects. Thus, in the spring 2005 I conducted a pilot study. The pilot study was supposed to serve several objectives:

• Be a possibility to get some experience in being a researcher within the developmental projects. Get some practical experience, included use of methods like interviews and participant observa- tions during teaching in classrooms and computer labs.

• Get some indications as to whether the methodology and theoreti- cal framework were feasible or not for the analysis and consider adjustments.

• Be an important source in the further development of my research questions, theoretical framework and methodology.

• Build confidence and trust among the teachers in the project and their students in order to carry out the main field work in

2005/2006.

The field work related to the pilot study highlighted two mathematics teachers working at Grade 9 at Vestpark, one of the schools in the

ICTML project. I participated in their planning phase of a number of les- sons in school team meetings and observed three lessons. I had a conver- sation with one of the teachers who was available for a conversation af- ter two of the lessons. I also conducted a focus group interview with the two teachers using video recording from one of their common lessons as a resource.

I visited the other three schools and teachers in the ICTML project as well in order to prepare for field work in 2005/2006. I transcribed data from the mentioned sessions at Vestpark and analysis of these data con- tributed to a conference research paper: “Teachers reflections on the use of ICT tools in mathematics: Insights from a pilot study”. The paper was reviewed and published in the conference proceedings (Erfjord & Hun- deland, 2007).

4.5.2 The main study

Use of Excel and Cabri was considered in workshops in the ICTML pro- ject which started in August 2004. As mentioned, I had a research inter- est in teachers’ implementation and orchestration of use of such com- puter software tools in their mathematics teaching. I had visited several

teachers at the four schools in the ICTML project, Austpark, Dalen, Fjel- let and Vestpark, and continued in autumn 2005 to visit these four

schools more regularly. This was also part of the agreement in the pro- jects that I, as a didactician, was supposed to have contact and support teachers at the schools, which for me particularly was expected to be support related to the ICTML project. As part of the agreement in the projects, there were meetings between didacticians and teachers in schools as well as workshops at UiA.

In a school team meeting at Austpark in October 2005, two of the teachers exposed a plan to use Cabri for the first time in their teaching careers. The teaching was accomplished in their classes at Grade 8 in January 2006. In a workshop session early in January 2006, one of the teachers at Fjellet informed didacticians that she too, five days earlier, for the first time in her teaching career, had started to use Cabri in her class at Grade 8. Hence, three teachers at two of the schools in the pro- jects, Austpark and Fjellet, implemented and started to orchestrate use of Cabri in their mathematics teaching in January 2006. The two teachers at Austpark, Jakob and Frode, and Trude at Fjellet eventually constituted what I, in Section 4.2.2, described as my case study.

Jakob, Frode and Trude

Jakob entered the projects in their second year for schools when he got a temporary full teaching position at Austpark. During his two years at Austpark, from August 2005 till June 2007, he mainly taught mathemat- ics and natural sciences. In June 2005 he had completed the first of two years in a master programme in mathematics didactics at UiA. He com- pleted his final year of the master program during the two years he par- ticipated in the projects and worked at Austpark. His earlier educational programme included a subject teacher education programme in natural sciences, ICT and mathematics. Consequently, Jakob was a newcomer as teacher when entering the projects. Although he started his participation in the projects one year later than most of the other teachers, he had some experience with the LCM project as a master’s student responsible for video recordings in two of the workshops. He participated in the pro- jects until the schools’ participation in the projects was finished in June 2007. Jakob left Austpark and got a new position as teacher at another school in Norway where he started to work in August 2007.

Frode participated in the LCM project from the start in August 2004 until January 2007 when he got a leader position at another school. He had his first job as teacher in 1997, and he worked at Austpark from 2000 till 2007. His educational programme ahead of 1997 included the four year General Teacher Education programme. Like many teachers accomplishing this programme, Frode’s work involved teaching most of the school subjects at lower secondary school including mathematics,

Norwegian, social studies, physical education, English and natural sci- ences. As well as the General Teacher Education programme, Frode had accomplished a study in informatics and a course in school development and management at UiA alongside his job as teacher at Austpark. He also worked as a practice teacher for teacher students in their General Teacher Education programme at UiA. During his career as mathematics teacher ahead of the projects, the only computer software he had used in his teaching was Excel.

Trude participated in both of the projects from the start in August 2004 but stopped her participation in March 2006 when she took a break from teaching for the rest of the school year. Trude had been a teacher since 1974 after finishing a three year General Teacher Education pro- gramme which at that time approved teachers to teach in primary and lower secondary school (Grade 1-9). Her educational programme also included half a year with mathematics as well as half or one year pro- grammes in other school subjects such as Christianity, physical educa- tion and history. Trude had also worked as a practice teacher for teacher students in their General Teacher Education programme at UiA for ten years. Alongside her participation the first year of the projects, she had a full time job as vice principal substitute. Trude had started her teaching career as a teacher in primary schools, worked two years at an interna- tional school in Asia and from 1991 in lower secondary school.

Ahead of the projects, all the teachers at Austpark and Fjellet re- ported minimal use of spreadsheets as the only mathematics related computer software tool used in their mathematics teaching. The teachers at Austpark reported that their use of Excel had been organised as a course, not particularly mathematics related, which I have described as a frequent used approach with spreadsheets in Norwegian schools (see Section 2.2.2, p. 35). Trude argued that her use of spreadsheets had been very limited in the past. This illustrates that Jakob, Frode and Trude and their students had quite limited experience in use of computer software tools in mathematics teaching.

At Austpark they had a big computer lab with modern computers, a room with older computers and a set with approximately 12 portable ma- chines and a portable projector to be shared between 15 classes. Most of Jakob and Frode’s teaching with computer software occurred in the big computer lab quite a distance from their classrooms. The computer lab had 28 computers and a mounted projector connected to a computer in front of the room. Jakob also used the portable machines and projector in some lessons occurring either in a classroom or in another available room. Fjellet had a computer lab with 20 computers and a set with ap- proximately 15 portable machines and a portable projector to be shared between ten classes. The computer lab was upgraded and unavailable

during Trude’s teaching period with Cabri. Thus, Trude’s Cabri teaching occurred in her classroom with the school’s set with portable machines. Trude never used any video projector but portable video projectors were available at the school.

Other teachers and another case

The two schools, Fjellet and Austpark, participated with respectively three and five teachers at lower secondary grades in the two develop- mental projects. Some of the teachers participated in both projects, some only in one of the projects, and four mathematics teachers at Austpark (Eivind, Sigurd, Robin and Runar) did not participate in any of the pro- jects. The situation in Year 2 of the projects, the main period for my data collection, is illustrated below in Table 4.1. The table also illustrates that some of the teachers participated all three years and others not. The rea- son why they did not participate all three years was that these teachers did not work all the three years at Austpark or Fjellet either because of changes in teaching positions or a break from teaching:

Table 4.1: Mathematics teachers, Grades 8-10 2005/2006, at Austpark and Fjellet and their extent of participation in the developmental projects

2005/2006 Austpark Fjellet

Mathematics teachers at Grade 8

Jakob: (LCM and ICTML, Year 2 and 3) Frode: (Only LCM, Year 1,2 and half of 3) Eivind: (None of the projects)

Trude: (LCM and ICTML, Year 1 and ¾ of Year 2) Mathematics teachers at Grade 9

Harald: (LCM and ICTML, Year 1, 2 and 3) Gunnar: (LCM and ICTML, Year 1, 2 and 3) Sigurd (None of the projects)

Markus: (LCM and ICTML, Year 1, 2 and 3)

Mathematics teachers at Grade 10

Elise: (Only LCM, Year 1, 2 and 3) Robin: (None of the projects) Runar: (None of the projects)

Ludvig (only ICTML, Partly Year 1 and 2) In addition to Jakob, Frode and Trude, four other teachers at the schools implemented Cabri during the school year 2005/2006: Eivind, Harald, Gunnar and Markus. The contributions from Harald and Gunnar are con- sidered most important in my case since they contributed in school team meetings with Jakob and Frode while Eivind obviously was not part of these since he did not participate in the projects. Markus did not inform didacticians about his use of Cabri, which occurred many weeks after the other teachers’ use of Cabri, neither in school team meetings nor work- shop sessions.

Findings in Chapter 5 indicate that Jakob and Frode considered Eivind’s use of Cabri as important in their own implementation process with Cabri. Since Eivind was not part of the projects, he never attended any sessions in the projects and I did not observe his teaching. Alto- gether I argue that in addition to Jakob, Frode and Trude, the case needed to take into consideration contributions from:

• the other participating teachers in the projects at the two schools; • their non-project participating colleagues;

• school leaders;

• teachers at other schools in the project;

• didacticians at UiA in workshops, meetings and interviews. Vestpark was central in the pilot study and I had expectations for the school’s contribution to my research study. However, the school had ac- cess problem to Cabri and the teachers chose to use computer software very little. Since I wanted to consider teachers’ implementation and or- chestration of computer software use, such limited use would offer little contributions apart from emphasising lack of use of computer software in teaching. These kinds of limitations are well documented like in the quoted research papers and surveys in Section 2.2.1.

Similar to Fjellet, Dalen was a school with only one class and thus only one mathematics teacher at each grade. Nevertheless, Dalen was in another position than the three other schools in the ICTML project. Be- fore entering the ICTML project, the mathematics teachers at Grade 8-10 at Dalen, Otto, Rikard and Viktor, were already experienced with use of computer software. Otto was at the time the most experienced mathemat- ics teacher with many years experience of using computer software in teaching. He also had a part time job in the ICTML project as a resource teacher, both for didacticians during planning and accomplishing the workshops and to support teachers in the project. A school team with the three teachers and two didacticians, Aud and I, was established already the first autumn of the project where the teachers had an aim of develop- ing a bank of ICT resources for mathematics teaching at their school. For a long period I planned to design my study with two cases. The second case; “Design and use of own computer software tasks” considered how this team with teachers and didacticians planned, designed, orchestrated use of the tasks in teaching and talked about experience in using com- puter software tasks in mathematics teaching. Although this case was excluded as a case in this thesis, it was central throughout my data col- lection which included Austpark, Fjellet and Dalen. I also made some analysis of this case but later decided to omit the case from my thesis since I experienced the nature of the cases to be so different. Instead I aimed to deepen the analysis of the case with Jakob, Frode and Trude in the thesis, and possibly return later to the Dalen case.