Proposal for a demonstration at ICMI Study 15
Grevholm & Bergsten
The development of a professional language
in mathematics teacher education
Barbro Grevholm & Christer Bergsten
Summary
The demonstration aims at examining and critically discussing the value of a practice developed in a Swedish project in mathematics teacher education, aimed at developing a professional language. In addition, the usefulness of the framework of cultural historical activity theory for the interpretation of the intervention project, and as a theory and method for change and development will be investigated.
The participants will work with one example of tasks created for student teachers’ work in natural study groups. The aim is to support the development of the ability to communicate mathematics with pupils and develop a professional language, while working with core concepts in mathematics. Participants will experience such work in natural study groups, write the report and reflect on the learning outcome from the experience, and take part of a video showing the work in one such natural study group from the development project. The group reports will be compared. Based on this shared experience the value of the practice will be discussed and critically investigated using the framework of cultural historical activity theory.
The demonstration relates to Strand I points e) and f), where the latter is related especially to the theoretical framework and the question of how to create educational change in a wanted direction. For Strand II it is especially points e) and f) that are relevant.
Plan for the session (in all 3 hours):Introduction and creation of “natural study groups” (15 min), Work in natural study groups and writing a report of how the group solved the task (60 min), Looking at a video clip from one group of student teachers, the transcript of this clip and the report from that group (30 min), Introduction to Postholm’s modified activity system as theoretical framework (15) min, Discussion, critique, investigation and work on the interpretation of the activity in the theoretical frame and summary (60 min)
Background and theoretical framework:To develop a professional language and the ability to communicate mathematics includes to reason mathematically, argue, explain, deduce, prove and convince one-self and others. The teacher educators in the project wanted to expose the student teachers explicitly to those aspects of the core concepts that were considered important. The project wanted to try out if it is possible to create open, explorative tasks with focus on core concepts that promote mathematical discussion and reasoning in the group work of student teachers, and if student teachers’ development of a professional language will be supported through use of such group work. In the creation of natural study groups and specially designed tasks for discussions the teacher educators are using social constructivist perspectives for analysing learning and development. As a framework for analysing the activities of the student teachers we use the cultural historical activity theory (CHAT, see figure below for the unit of analysis).
The modified activity system (From Postholm et al, 2004)
The development of a professional language
in mathematics teacher education
Barbro Grevholm & Christer Bergsten
Goal of the session: The demonstration aims at examining and critically discussing the value of a practice developed in material from a Swedish project in mathematics teacher education for teachers in years 4-9 in compulsory school, aimed at developing a professional language.. In addition, the usefulness of theThe framework of cultural historical activity theory as modified by Postholm et al (2004) will be discussedThe questions are is it useful for the interpretation of the intervention project in question and what it can contribute to our understanding of learning from the student teachers’ perspective, and as a theory and method for change and development will be investigated.
What will be demonstrated: The participants will work with one example of tasks created for student teachers’ work in natural study groups. The aim of the tasks is to support the development of the ability to communicate mathematics with pupils and develop a professional language, while working with core concepts in mathematics. A natural study group consists of 4-5 student teachers working without a teacher (Tresman, 1992) with a common task to produce a shared and agreed result in written form based on the discussions in the group. Participants will first experience such work in natural study groups, then write the report and reflect on the learning outcome from the experience. The session can be videoed if the participants agree to do this. After thatThen theyparticipants will take part of a video showing the work in one such natural study group from the development project (Grevholm & Holmberg, 2004). The group reports produced will be compared. Based on this shared experience the value of the practice will be discussed and critically investigated using the framework of cultural historical activity theory (Postholm et al, 2004).
The relation to the foci of the ICMI study: The demonstration relates to several foci of the study. in Sstrand I1to point e) the development of a professional language is a critical issue for mathematics teacher education, and point f) history and change of teacher preparation is related especially to the theoretical framework and the question of how to create educational change in a wanted direction. For strand II it is especially points e) and f) that are relevant:. Is the practice demonstrateda crucial practice for learning from practice? How does language play a role in learning from practice? The demonstration also relates to questions about curriculum in teacher education,core concepts in content and the role of professional language in the curriculum.
Plan for the session (in all 3 hours):
Introduction and creation of “natural study groups” (15 min)
Work in natural study groups and writing a report of how the group solved the task (60 min)
Looking at a video clip from one group of student teachers, the transcript of this clip (in English) and the report from that group (30 min)
Introduction to Postholm’s modified activity system as theoretical framework (15) min
Discussion, critique, investigation and work on the interpretation of the activity in the theoretical frame; summary (60 min)
Capacity for participation in the session: 25 participants (working in 5 natural study groups). It could of course be repeated if wanted.
Special requirements: Video camera and opportunitiesEquipment to show a video.
Background for the session: The demonstration builds on a development project initiated and inspired by research results from a study on student teachers’ concept development in mathematics and mathematics education (Grevholm, 2000, 2004ab). Most curricula for mathematics teacher education programmes seem to lack explicit aims concerning the development of a professional language. The research study revealed the need for more active work on the development of a professional language for student teachers to be able to communicate with their future pupils. “The importance of developing a rich mathematical language” (Bergsten & Grevholm, 2004, p. 135) has also been shown in other studies on student teachers in Sweden.
To develop a professional language and the ability to communicate mathematics includes to reason mathematically, argue, explain, deduce, prove and convince one-self and others (Mason et al, 1982; Schoenfelt, 1992; Stacey, 1988). The teacher educators wanted to expose the student teachers explicitly to those aspects of the core concepts that were considered important. “If it is something we want our students to know, understand or manage, we have to make this the object of explicit and carefully designed teaching” (Niss, 2001, p 43). Two questions were asked in the project:
1)Is it possible to create open, explorative tasks with focus on core concepts that promote mathematical discussion and reasoning in the group work of student teachers.
2)Will student teachers’ development of a professional language be supported through use of such group work?
In the creation of natural study groups and specially designed tasks for discussions the teacher educators are using social constructivist perspectives for analysing learning and development (Björkqvist, 1998). As a framework for analysing the activities of the student teachers we use the cultural historical activity theory (CHAT) (Engeström, 1987). In the modified activity system introduced by Postholm et al (2004) the node or factor object has been expanded to goal – result – object – outcome (see figure 1), which opens for a more fine grained analysis of the object of the activity. In the developmental project the subject is the group of student teachers and the object is relevant knowledge and abilities for a mathematics teacher. The interpretation of other nodes and the use of the model will be discussed in the demonstration session.
Figure 1. The modified activity system (From Postholm et al, 2004)
References
Bergsten, Christer & Grevholm, Barbro (2004). The didactic divide and the education of teachers of mathematics in Sweden. Nordic Studies in Mathematics Education9(2), 123-144.
Björkqvist, Ole (1998). Mathematics teaching from a constructivist point of view. Åbo Akademi University: Reports from the Faculty of Education, no. 3, 1998.
Engeström, Yrjö (1987). Learning by expanding. Helsinki: Orienta-Konsultit Oy.
Grevholm, Barbro & Holmberg, Inger (2004). To develop the ability of teacher students to reason mathematically. Final report on project number 026/00 to the Council for Higher Education from Department of Mathematics and Science, Kristianstad University. Kristianstad: Kristianstad University College.
Grevholm, Barbro (2000). Research on student teachers’ learning in mathematics and mathematics education. Research report. Kristianstad: Kristianstad University.
Grevholm, Barbro (2004a). Mathematics worth knowing for a prospective teacher. In B. Clarke, D. Clarke, G. Emanuelsson. B. Johansson, F. K. Lester, D.V. Lambdin, A. Wallby, & K. Wallby (Eds.). International Perspectives on Learning and Teaching Mathematics. (pp. 519-536) Göteborg. National Center for Mathematics Education.
Grevholm, Barbro (2004b). Research on student teachers’ learning in mathematics and mathematics education. In Hiroshi Fujita, Yoshihiko Hashimoto, Bernhard Hodgson, Peng Yee Lee, Stephen Lerman & Toshio Sawada (Eds.), Proceedings of the Ninth International Congress on Mathematical Education (pp. 131-132). Dordrecht: Kluwer.
Mason, John, Burton, Leone & Stacey, Kaye (1982). Thinking mathematically. Wokingham: Addison-Wesley Publishing Company.
Niss, Mogens (2001). Den matematikdidaktiska forskningens karaktär och tillstånd. In B. Grevholm (Ed), Matematikdidaktik i Norden (pp 21-50). Lund: Studentlitteratur.
Postholm, May-Britt, Pettersson, Tove, Gudmundsdottir, Sigrun, & Flem, Annlaug (2004). The need for Structure and guidance when ICT is used in project work. Trondheim, Norwegian University of Technology.
Schoenfeld, Alan H. (1992). Learning to think mathematically: Problem solving, metacognition and sense making in mathematics. In D. A. Grouws (ed), Handbook of research in mathematics thinking and learning. New York: Macmillan.
Stacey, Kaye (1988). Describing, explaining, convincing. An introduction to proof for Students. Shell Centre for Mathematical Education, University of Nottingham.
Tresman, P. Uri (1992). Studying students studying calculus: A look at the lives of minority mathematics students in college. The College Mathematics Journal, 23 (5), 362-372.