Theory-enriched practical knowledge in mathematics teacher education
Oonk, W.
Citation
Oonk, W. (2009, June 23). Theory-enriched practical knowledge in
mathematics teacher education. ICLON PhD Dissertation Series. Retrieved from https://hdl.handle.net/1887/13866
Version: Corrected Publisher’s Version
License: Licence agreement concerning inclusion of doctoral thesis in the Institutional Repository of the University of Leiden
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1 General introduction
1.1 Background and context
Since the 1980s, teacher training colleges have gradually come to realize that prescriptive transfer of theory is unsatisfactory. This was partly due to the fact that theory was insufficiently in step with reality and with the complexity of action in practice (e.g., Corporaal, 1988; Verloop, 2003). Furthermore, the observation was made that student teachers do encounter different types of ‘theory’ in their practice schools through the model function of the mentors. These theories are colored by various views (Zanting, 2001).
It is clear that the tension between theory and practice is an important factor in the practical training of student teachers. On the one hand both teacher educators and student teachers consider practical training as an effective way to acquire (practical) knowledge, on the other hand it is argued that the realization of teacher training goals is occasionally impeded by the conformist and conservative influence that practical training can have on student teachers (Zeichner, Tabachnick & Densmore, 1987).
Over the last few years, research on the relationship between theory and practice in teacher training has focused on the question of how student teachers can integrate theory and practice and what the relationship between the two components should be, or which of the two has to be the point of departure when designing the learning environment (Eraut, 1994a,b; Leinhardt, McCarthy Young & Merriman, 1995; Ruthven, 2001). There is no unambiguous conception of theory, nor of practice or the relationship between the two.
Little is known of how student teachers construct professional knowledge; this is particularly true in relation to primary teacher education in the Netherlands.
With respect to primary mathematics teacher education in the Netherlands, in the 1990s new developments were initiated by a group of twelve expert educators. This resulted in a book that became a standard work for teacher educators (Goffree & Dolk, 1995). This publication was also a reason for developing the Multimedia Interactive Learning Environment (MILE) for primary mathematics teacher education, as a medium between theory in teacher training colleges (Pabos) and student teachers’ training practice (Dolk, Faes, Goffree, Hermsen & Oonk, 1996). MILE is a digital representation of primary school practice for mathematics, which enables student teachers to intensively study authentic practice within the primary school (see chapter 3). Research relating to the new learning environment from the very beginning targeted student teachers’ ways of constructing knowledge, with teaching practice as the starting point for the student teachers’ learning process.
Research into student teachers’ knowledge construction is of vital importance for the current and future curriculum development of primary mathematics teacher education.
General introduction
Such research can be considered in the context of at least three current issues.
First, there are complaints from inspectors, managers, teacher educators as well as from student teachers about the level of the programs offered by teacher training colleges (e.g., Inspectie van het Onderwijs, 1998; Onderwijsraad, 2005). Beyond organizational conditions (such as no time for developing deeper understanding; overloaded programs), there are ‘content-dependent’ reasons for this superficial level of programs.
One is the nature and the content of the learning environment for student teachers, which often lacks a well thought-out strategy for linking theory and practice. Another reason is the problem of how to gauge student teachers’ level of reflecting on practice, particularly in relation to their use of theoretical knowledge.
Second, student teachers do not automatically appreciate theory (Lampert &
Loewenberg Ball, 1998). They often have their doubts about the point of (formal) theory (e.g., Clark & Peterson, 1986).
Third, the age-old ‘gap’ between theory and practice exists in different forms and on different levels. Although Freudenthal contended already in 1987 (p. 14) that “a gap is not necessary”, recent researchers and teacher educators still refer – directly or indirectly – to the existence of that phenomenon (e.g., Ball & Cohen, 1999; Jaworski, 2006; Van Zanten & Van Gool, 2007; see section 2.4).
1.2 Purpose and relevance
The importance of integrating theory and practice by (future) teachers is acknowledged everywhere. Very little is known even now about the character of that process of integration. The complexity of behaviour in practice and a lack of clarity about the concepts of theory, practice and the relationship between the two, complicates the discussion about the subject. This study intends to contribute to that discussion and to the development of theory regarding the relationship between theory and practice.
The purpose of the present study was to gain insight in the student teachers’ process of integrating theory and practice, and particularly to find out how they relate theory and practice and to what extent they are competent to use theoretical knowledge in multimedia educational situations.
It demands a huge effort of (future) teachers and their educators to become familiar with the idiosyncratic and complex reality of teaching. In an elaborated model of teaching practice, Lampert designed an image of the ‘Complicated Terrain of Teaching’ (Lampert, 2001). Practice and theory as well as the relationship between the two are a part of this complicated terrain (Eraut, 1994b; Leinhardt et al., 1995; Jaworski, 1999).
The developments over the last thirty years in the area of Dutch primary mathematics teacher education (Pabo), led to an approach of integrating subject matter, pedagogical content matter and school practice. However, such an approach does not in itself lead
automatically to student teachers’ integration of theory and practice. Acquiring a teacher’s professional knowledge base in primary mathematics teacher education, the area in which this study takes place, requires a constructive commitment and much effort to become
‘owner’ of the specific insights and procedures. Further research should show how student teachers link theory and practice in an adequate – for example multimedia – learning environment and should also express the quality of these activities.
The major scientific relevance of this research lies in its contribution to gaining an insight in the student teachers’ process of integrating theory and practice and to find out to what extent they are competent in relating the two. Insight in that relationship can lead to a better understanding of the complexity of acting in practice.
The societal relevance of this research is twofold. First, (future) teachers’ use of theory is part of the ‘linking process’ between theory and practice, particularly in the way that theory supports observing and analyzing practice, and can therefore lead to improving (future) teachers’ practice. Theories can provide an instrument for teachers to recognize more quickly and adequately all kinds of aspects of the teaching-learning process.
Teachers that can handle such an instrument are able to see more in the same situation and therefore can think, speak and act more effectively (Fenstermacher & Richardson, 1993). Second, establishing a knowledge base that underlies teachers’ practice is a condition for improving the status of teaching as a profession (Booth, Hargreaves, Bradley & Southworth, 1995). Theoretical knowledge as part of practical knowledge (see section 2.3) is considered to form a part of the professional knowledge base of teachers (Verloop, Van Driel & Meijer, 2001). Prospective teachers should provide the experience that using theory is interesting and will gain a profit for one’s practice as a professional teacher.
The present research might be a contribution to avoiding the gap between theory and practice.
1.3 Research questions
The research questions described below are related to the consecutive research phases of this thesis.
The first exploratory study (section 3.5) focused on knowledge construction and on investigation processes experienced by student teachers in the Multimedia Learning Environment MILE. In total, 15 meetings with two student teachers were held, eight of which were two-hour sessions with participation of the researcher. The culmination of the student teachers’ investigations consisted of an oral exam, a written report, and a presentation. Audio recordings during the discourse, e-mail communications, and written reflections documented the collaboration and the individuals’ learning and thinking processes.
General introduction
The underlying research question was:
What is the character of the investigation process of student teachers in MILE and what is the output of their learning process in terms of knowledge construction?
The second exploratory study (section 3.8) was designed to find out how prospective teachers made connections between theory and practice in MILE. Ten two-hour meetings were held in two classes of 25 student teachers. Four pairs of student teachers were observed and interviewed, and a participating study of the group work was conducted with two student teachers. A list of possible signals of theory in action (‘Signals of use of theory’) was generated to support and analyze the observations of student teachers at work (cf. appendix 1).
The research question in this context was:
Which signals of utilizing theory do student teachers show in their reflections on studied practices of MILE?
The small scale study (chapter 4) targeted student teachers’ use of theory in a more structured and ‘theory-enriched’ learning environment. The research procedure consisted of eight components for triangulation. Five meetings were held in Amsterdam (6 student teachers) and Alkmaar (8 student teachers). All meetings were videotaped by the researcher. In the first meeting student teachers were given an initial assessment and a written numeracy test. After the third meeting, a 45-minute stimulated recall interview was held with each student teacher. In the fourth meeting student teachers made a concept map. In the last meeting there was a final assessment and a (anonymous) questionnaire. Shortly after the course each student teacher was interviewed.
The research question for this phase was:
In what way and to what extent do student teachers use theoretical knowledge when they describe practical situations, after spending a period in a learning environment that invites the use of theory?
A sub-question to this question in the small scale study was:
To what extent is there a relationship between student teachers’ use of theory and their level of numeracy?
The main goal of the large scale study (chapter 5) can be described globally as gaining insight into the phenomenon of ‘theory use’ by students in teacher training colleges for primary school teachers. Two dimensions are distinguished. On the one hand theory use manifests itself in the way students describe situations with the aid of theory; this is called the nature of theory use. This may occur for example in a factual description of a teaching situation or by responding to a situation. On the other hand, theory use is expressed by the degree to which the students use the theoretical concepts meaningfully, the level of theory use.
The large scale study was performed on 269 students from 11 different teacher training colleges. The learning environment of the student teachers was a more sophisticated version of the learning environment from the small scale study. The research procedure consisted of four components: the initial assessment, the final assessment, followed by an anonymous questionnaire and a written numeracy test after the course for the participating student teachers. The emphasis of the data-analysis was on the student teachers’ reflective note in the final assessment.
The large scale study focused on three main questions, with the third question split into two sub-questions:
1. In what way do student teachers use theoretical knowledge when they describe practical situations, after spending a period in a learning environment that invites the use of theory?
2. What is the theoretical quality of statements made by the student teachers when they describe practical situations?
3a. Is there a meaningful relationship between the nature and the level of theory use? If so, how is that relationship expressed in the various components of theory use and in various groups of students?
3b. To what extent is there a relationship between the nature or the level of the student teachers’ use of theory and their level of numeracy?
1.4 Nature of the study
The research approach of the whole study – comprising the four sub-studies – can be considered as an amalgam of exploratory research, qualitative research (Denzin &
Lincoln, 2000), empirical research (Richardson, 2001) and design research (Gravemeijer, 1994). The design research emerges especially in the way in which the teacher education curriculum – in particular the student teachers’ learning environment – for this research was constructed, both in the way that it was formed and in its use by pre-service teachers.
The learning environment – necessary to develop for elaborating and answering the research questions – was gradually refined in accordance with the developmental research or educational design research approach (Gravemeijer & Cobb, 2006; section 2.7.2).
1.5 Outline of the thesis
In chapter two the theoretical foundation for this thesis is worked out. First, in the context of the discussion about relating practical and propositional knowledge, it is necessary to know in which way teacher education programs are different. Section 2.2 distinguishes ways in which teacher training colleges attempt to come to a balanced view of both theory and practice and, as a consequence, to a view of the relationship between those two components of the knowledge base of teaching. After discussing the concepts of theory and practice in teacher education (2.3), we focus on that relationship
General introduction
(2.4) finally pointed specifically to the situation in primary mathematics teacher education in the Netherlands (2.5). Section 2.6 aims at gaining insight in characteristics of a domain-specific instructional theory, which insight will lead us to qualifying focal points for theory in teacher education, derived from the characteristics that have been found. These points of interest are important for designing the learning environment (2.7) for the student teachers involved in this research.
Chapter three continues with a description of the (making of the) multimedia learning environment MILE. Next, we address the question – in the first exploratory study (3.5) – of how student teachers do their investigations in MILE and which knowledge they acquire from their particular way of studying and learning. In section 3.8, on the second exploratory study, the main question is how prospective teachers make connections between theory and practice. The focus is particularly on signals of utilizing theory that student teachers show in their reflections on studied practices in MILE. The results of the second exploratory research provided us with tentative evidence that the intended learning by student teachers in the digitized learning environment could not be realized without theoretical enrichment. The study raised questions concerning quality, namely the depth of learning from practice. Among other things it was established that good practice of primary mathematics teaching in MILE – indicated as practice that is theoretically founded and observable in classrooms – does not naturally lead to good practice for primary mathematics teacher education.
Chapter four describes the small scale study in the adapted ‘theory-enriched’ learning environment for the student teachers involved. We address the question of how, and to what extent, student teachers use theory when they describe practical situations after spending a period in this learning environment. A sub-question focuses on the relationship between the use of theory and student teachers’ level of numeracy. The small scale research provided insight into the thinking and learning processes of student teachers – particularly their reasoning – and also provided elements for refining the design of the learning environment in the large scale study.
The fifth chapter, on the large scale research, addresses the issues of the nature and the level of use of theory. The questions in this research were about the way that prospective teachers used theory when they described practical situations, about the quality of their reflections on the (multimedia) practice situations, and the possible link between the nature and the level of use of theory. A reflection-analysis instrument was developed for analyzing the data of the student teachers’ reflections of the final assessment. As in the small scale study, one question focused on the relationship between the use of theory and student teachers’ level of numeracy. The instrument for the last question was a refined version of the one that was used in the small scale study.
Chapter six concludes this thesis with a general conclusion and discussion.
