The Transition to Graduate Studies in Terms of Students Motivation
BERA Conference 2006 Geraniou, E. & Simpson, A
University of Warwick
THE TRANSITION TO GRADUATE STUDIES IN TERMS OF STUDENTS’ MOTIVATION
Eirini Geraniou and Adrian Simpson
University of Warwick
Paper presented at the British Educational Research Association Annual Conference, University of Warwick, 6-9 September 2006
The results presented here belong to a broader study on the Transition from an undergraduate to a postgraduate degree in Mathematics. One main issue that emerged from the data, among others, was the importance of motivation for the long term goal of writing an original thesis. Two kinds of motivation were identified in the data, internal motivation and external motivation. Moreover, the data revealed the existence of three transitional stages within the PhD degree, Adjustment, Expertise and Articulation. Based on the first two transitional stages, three types of students were identified. Overall, twenty-four students participated in this study and their responses were analyzed using a grounded theory approach.
INTRODUCTION
Every mathematics studentin his/her academic life goes through a series of transitions in order to succeed in becoming a mathematician. These transitions require reconstructions and reconceptualizations of the mathematical knowledge of the student/learner, in the same way as Piaget claimed that new knowledge is reconstructed by the learner through the use of “active methods” so as to be acquired. Many researchers have investigated such transitions, like the transition from counting to number (Cobb, 1987), from number to arithmetic (Fuson, 1990, Steffe and Cobb, 1988) and from arithmetic to algebra (Davis, 1985). Further research has been done on the transition from primary to secondary education (Galton & Willcocks, 1983; Anderson, et.al., 2000) and even more from secondary to higher education (Tall, 1991, Alcock & Simpson, 1999, Daskalogianni & Simpson, 2000). However, there are indications that students who wish to continue their studies and obtain a postgraduate research (PhD)degree, face difficulties as well (Pole et al., 1997; Ford, 1985; Herzig, 2002; Duffin and Simpson, 2002, 2005, in press). The difference between the nature of a taught degree, and a research degree, requires significant changes on behalf of the students in terms of how they deal with the subject.
As revealed by the data, the major issue concerning students who undergo the transition from a taught to a research degree is motivation. In fact, two types of motivation were identified, internal motivation, which is motivation caused by the individual, and external motivation, which is motivation caused by external factors. Both types of motivation proved to be crucial for the students’ successful transition to a PhD degree. Moreover, it was implied that the transition to graduate studies occurs in three separate stages, Adjustment, Expertise and Articulation. Since the collected data focuses on the first two years of a PhD degree, based on the first two transitional stages, three types of students were identified. These types of students differ in terms of the types of motivation that students used so as to survive each of the first two transitional stages. Students who used an internal survival strategy, which was based on internal motivation, in the Adjustment and the Expertise stage are called II students. Students who used an external survival strategy in both stages are called EE students and finally students who used an external survival strategy in the Adjustment stage and an internal survival strategy in the Expertise stage are called EI students.
This paper is based on the data acquired as part of the first author’s research towards obtaining a PhD in mathematics educationand aims at revealing the importance of motivation in the process of the PhD degree in mathematics as described by the students themselves and the ways in which students using any of the two identified types of motivation handled the transitional stages and therefore moved one step closer towards the successful completion of their PhD degree. Moreover, the importance of each of the three transitional stages and their role towards students’ efforts of becoming independent mathematicians will be discussed.
THEORETICAL FRAMEWORK
The transition from school to university, i.e. the transition to advanced mathematical thinking has been widely investigated (e.g. Tall, 1991, Alcock & Simpson, 1999, Daskalogianni & Simpson, 2000). This transition, though, is not the final one for all students. Some of them decide to move on to a graduate degree and there is evidence that there are issues regarding this further transition, which could be described as the transition to graduate studies.
Pole et al (1997) investigated this transition by focusing on doctoral students and their supervisors in the areas of physics, mathematics and engineering science. They concluded that due to the nature of the undergraduate studies, students begin their PhD degrees looking for instruction and direction from members of staff, mainly supervisors, and don’t enjoy autonomy which characterises the nature of a research degree. This agrees with Duffin and Simpson’s (2002; 2005; in press) argument that the difference between undergraduate and graduate studies, according to the mathematics PhD students in their research, was the lack of an external authority to provide them with validated results. For graduate studies, theonly external authority is the supervisor. This means that those who are used to relying on others in order to learn would have to change their attitude towards learning in the graduate degree. There were other authors (Burgess et al, 1994; Hockey, 1994; 1995; Wright and Lodwick, 1989, Wright, 2003) who investigated the role of the supervisor. They all agreed that not only students, but also supervisors face difficulties and argued that the relationship between student and supervisor changes over time. Furthermore, Wright (2003) argued that the first year of the PhD degree is a year of judgement for the students, during which the supervisor’s role is crucial since it will play an important role in the students’ future progress and therefore the successful completion of their PhD degree.
Duffin and Simpson (2002; 2005, in press), based on their theory of natural, alien and coherent learners (Duffin and Simpson, 1993), investigated these three learning styles for PhD mathematics students during the transition to graduate studies. They concluded that alien learners are unstable whereas natural learners are stable during the transition to independent graduate study. Moreover, they claimed that alien learners have to adopt a different route so as to adjust (Duffin and Simpson, 2005). They should change to a natural or a coherence stance. Duffin and Simpson (2005) introduced a new term based on the students’ opinions towards others. They built the term ‘cognitive empathy’ to describe how students conceive the mental statesof others. As they claimed, the students they interviewed seemed to be comparing themselves to authors of research papers, supervisors, other researchers, other PhD students or even undergraduate students whom they are teaching.
Herzig (2002) proposed a model of PhD mathematic students’ persistence and attrition, “in which student participation in the life of the department and discipline lead to increased student integration which is crucial for students’ success” (p. 1). In his model, Herzig (2002) argued that students have to adjust, or become integrated, in two distinct stages. The first stage is the ‘course-taking community of practice’ and the second one is the ‘research community of practice’. This first stage is compulsory for PhD students in the United States. They have to pass qualifying exams before starting their research projects. The start of their research project is the beginning of the process of adjustment in the second stage. Herzig commented on the issue of isolation, since “mathematics is a highly specialized discipline and many graduate students have few peers with whom to collaborate (National Research Council, 1992)” (p. 4). In this case, the relationship between student and supervisor is crucial (Tinto, 1993).
Other research regarding the transition to graduate studies was conducted by questionnaires given to doctorate students in the disciplines of mathematics and mathematics education in New Zealand by Morton and Thornley (2001). They found out that the most common motives for pursuing a doctorate were the students’ interest in their subject which resulted in them wanting to learn more and improve their career opportunities. Other motives were personal satisfaction, encouragement by first degree lecturers to continue into research and limited job opportunities with only a first degree.
Similarly to other authors’ results (Duffin and Simpson, 2002, 2005, in press; Pole et al, 1997; Herzig, 2002, etc.), Morton and Thornley (2001) argued that the main reason for dissatisfaction regarding the interaction with other research students was isolation from other research students in their particular research area.
Carlson’s (1999) study investigated the behaviour of PhD students and their development and success through mathematical tasks. These graduate students proved to have strong persistence and strong confidence. They expected difficult mathematical tasks to require a lot of time and seemed to enjoy tasks that require mathematical reasoning. This investigation proved that these beliefs are common among successful graduate students and important for the continuation of their studies.
Most of the research projects mentioned above were formed based on graduate students in various disciplines and were carried out in different universities around the world. Apart from the above mentioned studies, there are not many other research projects that were carried out in the UK aiming at revealing more issues concerning the graduate study of mathematics. This study was designed in an effort to fill this gap and reveal more issues regarding the transition to independent graduate studies in this discipline. In more detail, the research questions that guided the study were:
- Which are the main issues concerning students who start a PhD degree?
- How do students deal with the transition to graduate studies in mathematics?
METHODOLOGY
Since this research field is a growing onein mathematics education, a grounded theory approach (Strauss and Corbin, 1998) was suitable for the research so as to develop a new theory which describes the transition in question. 24 students were interviewed and some of them more than once so as to examine their development over time.
Most of the students had completed a MMath degree and the rest had completed either a first degree or a master’sdegree, either at the University of Warwick or some other UK or European university and then started a PhD in mathematics.
The groups of students interviewed are:
Group A: MMath (2) 1st year PhD (2+4) 2nd year PhD (6)
Group B: 1st year PhD (4) 2nd year PhD (4+1) 3rd year PhD (5)
Group C: MMath (6) 1st year PhD (6)
Group F: Finalists (7)[1]
The interviews consisted of open-ended questions and gave the researcher the ability to clarify issues not very well covered by the students. All of the interviews were taken in 2002-2003 and were fully transcribed and analyzed. The data discussed in this paper is based on and guided by the students’ responses. The style used was the “conversational technique” introduced by Burgess (1985). The purpose of this technique is to avoid leading questions and to seek amplification of the students’ responses to allow the conversation to follow the students’ thought processes.
The data analysis was carried out based on the grounded theory approach as discussed by Strauss and Corbin (1998). Two processes were mostly used, the constant comparative method and memo writing. Memos were written for all the transcripts. By constantly comparing the data and the memos, certain themes emerged and they were named in an effort to describe them in the most suitable way. Those derived themes served to form a theory grounded in the data, which was generated to describe and explain patterns of behaviour students followed in order to have a successful transition to graduate studies.
INTERNAL AND EXTERNAL MOTIVATION
The central theme that was derived from the data was motivation. Motivation for this study describes the force, influence, enthusiasm, drive or incentive that directs one’s actions towards completing a PhD.
It is not easy during such a long degree, which is based on a specific area of mathematics, to always feel passionate for your work. Sometimes it is tiring to work on the same thing for a long period of time. Therefore finding the dedication that is required to do a PhD is hard. Motivation seemed to be needed not only for the long-term goal of obtaining the PhD, but also for the short-term goal of doing a piece of work towards a PhD degree. Motivation seemed to appear as a prerequisite to success when doing a PhD.
It is worth mentioning that there was an obvious distinction between forms of motivation. Motivation was either caused by an external or an internal factor. By external factors we describe motivation that is achieved with the mediation of somebody or something else, whereas by internal factors we describe motivation that is originated from oneself. Internal motivation could be achieved through personal achievement, personal interest or determination and external motivation could be achieved through obligation, application or others.
THE THREE TRANSITIONAL STAGES
Students talked about their PhD degree in connection with past experiences from previous degrees and valuable information came out about the nature of the PhD degree. Three transitional stages were identified based on the students’ claims: Adjustment, Expertise and Articulation. These stages stretch across the whole process of the PhD degree and are strongly connected with its nature.
By looking at the data from each group of students at each stage, some issues arose for each year of study. By comparing them, the natural processes were visible of coming into terms with what a PhD degree is like and adjusting to its nature (Adjustment phase), applying the background knowledge obtained at the beginning of the PhD degree so as to solve the research problem (Expertise phase) and writing down the results and the whole thesis (Articulation phase).
In more detail, a PhD is almost completely different to what the students were used to as undergraduates and therefore, they have to go through the process of becoming accustomed to its nature. This process is defined as Adjustment.
As it was described by the students, the 1st year is mainly covered by reading and gaining enough background knowledge so as to start their research. Afterwards, the students attempt to apply their knowledge so as to tackle their research problem. This process is defined as Expertise.
Finally, after reaching a result, the student is ready to undertake the necessary step of putting his/herresults into words. This process of writing-up the thesis is defined as Articulation.
Students had to go through all these stages. In order to overcome possible difficulties that arose, they formed ways of dealing with them. These are described as Survival Strategies and will be defined in the next paragraph.
SURVIVAL STRATEGIES
A survival strategy is a method that a student uses when the levels of his/her motivation are decreased or even when there is a complete loss of motivation (internal or external), so that he/she can get back on track and regain it. This could be described as an action – reaction process, action being the loss or decline of motivation and reaction being the survival strategy.
One has to bear in mind that the choice of a survival strategy depends on the specific situation, that the student experiences. There are cases when the reasons are external in the sense of losing some external motivating factors. For example, students get stuck and no one is around to offer assistance. On the other hand, there are internal reasons for losing motivation that are buried deep inside every student’s character. For instance, students get bored or are unable to see the point in what they are doing. In any case, the studentseither need to rely on internal motives and thus an internal survival strategy is needed, or they need to look for an external motive and thus an external survival strategy is needed.
EXTERNAL SURVIVAL STRATEGY: When students rely on external factors to regain or strengthen their motivation, we will say that they are using an external survival strategy. This strategy can be identified through two parameters: Discussion and Application. For example, the student may seek advice from a peer, another researcher or the supervisor when his/her levels of motivation drop (Discussion). The student might decide to apply what he/she has read, to give a talk or to do a presentation (Application).
INTERNAL SURVIVAL STRATEGY: When students rely on internal factors to regain or strengthen their motivation, we will say that they are using an internal survival strategy. This strategy can be identified through three parameters: Self-reliance, Interest and Achievement. In more detail, the student may feel less motivated from time to time, but he/she convinces himself/herself that he/she can do it (Self-reliance). The students may lose the drive to do their work, but then out of their initiative, look for a personal interest in their work (Interest). The student may find the motivation he/she was missing by having the desire to achieve or finish what he/she has started (Achievement).