The case and the context

Since a classroom has to be investigated in order to explore the mathemat- ics offered, the mathematics students’ experience, and how the classroom setting influence students’ experiences, it followed that the study would be a case study and that the methods would be qualitative methods. In this section, case study as such is discussed. Then the actual case and its con- text is presented.

7.2.1 Case study

In a case study the researcher has little control or no control of the factors influencing the events in the classroom. A case study is a “study of singu- larity conducted in depth in natural settings” (Bassey, 1999, p. 47).

Mertens (1998) discusses different definitions and views on case stud- ies and concludes that “the commonality in the definitions seems to focus on a particular instance (object or case) and reaching an understanding within a complex context” (ibid, p.166). She also referred to literature dis- cussing whether case study is a method or a research design. Yin (2009) claims that a case study is a method with its own research designs.

What according to Yin (ibid) decides if a case study is an appropriate method for research is the form of the research questions. The most ap- propriate questions are the ‘how’ and ‘why’ questions. In this thesis, the research questions involve also ‘what’ questions: ‘What mathematics …and what responses…’ Although ‘what’ questions, the answers searched for are descriptions of the mathematics and of the responses. Thus, the case study as a research method is seen to be appropriate.

In a case study, the theoretical framework and the research questions are the steering guides of how to define the case. Also Miles and Huber- mann (1994) give the advice to: “attend to several dimensions of the case: its conceptual nature, its social size, its physical location, and its temporal extent”.

In this thesis, the case is the specific class under observation. Accord- ing to the chosen theoretical framework, the class includes many sub cas- es, the individual students.

In following Miles and Hubermann’s (ibid) advice above, the bounda- ries for the case related to the social size, the physical location and its temporal extent was set. The specific class is a class located in one of the upper secondary schools participating in the LBM project described in appendix 2.4. The class had 27 students during the time of observation. The contact with the teacher started two weeks before the class started school, then the observation went on intensively in two periods in Sep- tember and November 2007 with some meetings in between. Then there was a new meeting with the class in May 2008. This means that this case study has boundaries when it comes to size, location and time.

The unit of analysis is the student within the classroom setting. This includes the didactical means: the textbook and its resources, the comput- er and the software in use, the teaching, the classroom interactions, and student’s mathematical activity working with mathematical tasks. 7.2.2 Participants and the classroom

To talk about a random sample of a population has no significance in my case; also it is not an extreme case. Working in the TBM-project entailed cooperating with someone within the project. I aimed to work with a teacher from upper secondary school. The teacher who accepted to join

this study is an experienced teacher, and she has worked in the same school for many years. When her school decided to participate in the pro- ject, she signed on as did four others in her school. As she said, she is used to working in projects since she, together with some colleagues, had recently worked out and set up a plan to use lap-tops in mathematics for all students in the “Programme for Specialization in General Studies” (see section 2.2.2).

The teacher was engaged in teaching many mathematics classes. The class in this study was a class in grade 11. This was the second year of the K06 curriculum (see section 2.2.2) which implied working with a new textbook and a new curriculum. The teacher expressed that the pressure of the lack of time weighed heavily as the new curriculum included more topics than the former curriculum.

The 75 students, attending the programme in this school, came from different schools and mostly they did not know each other. At the start, they made a judgement about their own abilities and goals in mathemat- ics. On the basis of those judgements, they were divided into three differ- ent groups. The observed group or class was seen as a high achieving group of students since all of them were aiming towards the highest math- ematical education in upper secondary school. In the class, 27 students started; two went to another group and two came as new students during the autumn.

All students had their own computer. The classroom was equipped with all facilities making it convenient for both teacher and the students to use their computers in their daily work. In addition, the technical support was reported by both teacher and students to function well. When I was there, they used their computers to write mathematics and to draw graphs. The programs were MathType and TI-interactive. All written tests includ- ing the examination were done on the computer. The classroom can be classified as a paperless classroom. The teacher, however, wrote mostly on the whiteboard during plenary sessions. Exceptions were when the technique of writing the tasks in MathType on the computer was intro- duced at the end of the plenary sessions.

More background information about the school, the classroom, the teacher, her practice and thoughts, the students and students’ use of, and opinions about the use of computers in mathematics lessons is to be found in appendix 2 and its sub-sections.