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)
Proposal for a demonstration at ICMI Study 15
Grevholm & Bergsten
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).
Mediating artefact
Subject
Rules
Goal
Community
Result
Object
Division of labour
The modified activity system (From Postholm et al, 2004)
The development of a professional language
Outcome
Proposal for a demonstration at ICMI Study 15
Grevholm & Bergsten
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 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.
What will be demonstrated: The participants will work with 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 experience such work, write the report and reflect on the learning outcome
from the experience. Then they will take part of a video showing the work in
one such natural study group from the development project (Grevholm &
Holmberg, 2004). The 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 in strand
I to point e) the development of a professional language is a critical issue for
mathematics teacher education, and point f) 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 demonstrated crucial 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 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 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)
Proposal for a demonstration at ICMI Study 15
Grevholm & Bergsten
Capacity for participation in the session: 25 participants (working in 5 natural
study groups). It could of course be repeated if wanted.
Special requirements: Equipment 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.
Proposal for a demonstration at ICMI Study 15
Grevholm & Bergsten
Mediating artefact
Subject
Rules
Goal
Community
Result
Object
Outcome
Division of labour
Figure 1. The modified activity system (From Postholm et al, 2004)
References
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