Summary of the key theoretical concepts

In the following table (Table 3.1) I illustrate a summary of the key theoretical concepts that I employed in the theoretical framework and their meaning.

Concept Meaning

Classification Shows the power relations between categories and sets the limits of the discourse. Strong classification entails strong boundaries (which I will represent with ‘+’), weak classification entails weak boundaries (which I will rep- resent with ‘-’).

Framing Shows the control relations on communications and sets the form of realisation of the discourse (who can control the selection, sequencing, pacing and evaluation of the communicated knowledge). Strong framing (which I will represent with ‘+’) means that the control is with the transmitter, weak framing (which I will represent with ‘-’) means that the control is with the acquirer.

Positional Identity Shows how individuals identify their position in relation to others according to the ways that make them feel comfortable or constrained.

Comfort Zone This zone consists of the things that students know al- ready from school regarding the learning of mathemat- ics (both mathematical knowledge and pedagogical ap- proaches).

Transitional Zone In this zone students can grasp new meanings, adjust to the new context and expand their ways of learning mathematics.

Discomfort Zone This zone includes the things that students find com- pletely different in the university context, regarding the learning of mathematics, from those experienced at school.

CHAPTER

4

Methodology

In this study I took an interpretivist paradigm and I used qualitative methods to analyse my data. With the use of this paradigm researchers reveal the interpretations of a phenomenon by the social actors; in order to understand the phenomenon under investigation the researcher has to see things from the view point of the people who are involved in it (Pring, 2004). In this sense, the truth does not lie “out there”, expected to be discovered, it lies in how the researcher interprets the phenomenon by interacting with the actors involved in it. This interpretation is acquired in a clear, open and systematic way. Similarly, for this study I interacted with the students and their lecturers in order to understand in depth the effect of the transmitted messages on their transitional experience. By using this paradigm, I was able to investigate the phenomenon in great depth and collect honest and trustworthy accounts from the participants, something that enhanced the validity of the collected

data.

Although for me as a researcher elements of the truth can be revealed by both qualitative and quantitative research methods the time restrictions that a PhD programme imposes and some practicalities did not let me em- ploy both. In the context of my study I would have liked to have a bigger cohort of participants and include also other variables that would help me to understand students’ transitional experience. For instance, it would have been helpful to include a quantitative analysis of the data that I collected from the first questionnaire. The time limitations did not allow me though to take further actions. Because of the nature of the study I had to follow students during the first semester of the studies, hence all the data collection needed to finish during a very restricted time window. Therefore, I had to make a choice about what methods I would use in order to be both consistent with the time schedule of the programme and to give also a good account of the secondary-tertiary transition. This is why I chose to employ only qual- itative methods. In this way I attempted to understand in depth what the lecturers and students have to say and explore how the teaching-learning interactions between them at this phase can influence students’ transitional experience. The methods I chose to employ were appropriate for this work and good for the purpose of the study in general. Of course every method- ology has its limitations but at the end of the day there is no such thing as “perfect” methodology.

4.1

Pilot study

During the spring semester of the academic year 2014-2015 I conducted the pilot study of my research project. My main motivations for the implemen-

tation of the pilot study were to design and evaluate a research protocol, to test whether or not the research instruments were appropriate, to identify barriers that arise during the implementation of a study, to develop a re- search plan, to reflect on my role as a researcher by analysing a small data set, to explore the potential of the theoretical/methodological framework and to familiarize myself with the various stages of a research process.

In this pilot study I investigated the different kinds of messages that a mathematics lecturer sent out to his students through the discourses and the practices he used in the lectures. I followed ten students who were in the second semester of their studies for a joint degree in Mathematics during the attendance of a Multivariate Calculus module. The research was conducted through observations of the lectures and focus groups with the students. The observations and the focus groups were preceded by an informal discussion with the lecturer at the beginning of the semester; the lecturer referred to his teaching plan and the ways he expected students to work for this module. A sequence of observations of the lectures followed. During the observations I focused on the messages that the lecturer transmitted to his students and kept a record of them. Subsequently the focus groups were formed. In the focus groups I brought up for discussion some of the messages that I observed during the lectures and the students discussed and commented on them.

For the categorisation of the transmitted messages that I identified during the lecture observations I used aspects of grounded theory (Strauss & Corbin, 2008). I classified the messages in the following distinct categories:

• Messages about learning habits in university mathematics • Messages about the learning resources

• Messages about what students should do when they feel stuck

After the identification and categorisation of the messages, I employed Bernstein’s (2000) concepts of classification and framing to analyse each mes- sage separately. These two concepts contributed to the creation of bound- aries between the different practices that took place in the lecture theatre and created a picture of the control that the messages had on students’ in- terpretations. The findings of this study provided some indications about the extent to which the different kinds of messages sent out by the lecturer are important. They began to reveal the ways in which these messages can shape students’ conception of university mathematics and thereby affect their transitional experience.