Table Of ContentAdvances in Mathematics Education
Luc Trouche
Ghislaine Gueudet
Birgit Pepin E ditors
The ‘Resource’
Approach to
Mathematics
Education
Advances in Mathematics Education
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More information about this series at http://www.springer.com/series/8392
Luc Trouche • Ghislaine Gueudet • Birgit Pepin
Editors
The ‘Resource’ Approach to
Mathematics Education
Editors
Luc Trouche Ghislaine Gueudet
Institut Français de l’Education CREAD, ESPE Bretagne
Ecole Normale Supérieure de Lyon Université de Bretagne Occidentale
Lyon, France RENNES, France
Birgit Pepin
Eindhoven School of Education- ESoE
Eindhoven University of Technology- TU/e
Eindhoven, The Netherlands
ISSN 1869-4918 ISSN 1869-4926 (electronic)
Advances in Mathematics Education
ISBN 978-3-030-20392-4 ISBN 978-3-030-20393-1 (eBook)
https://doi.org/10.1007/978-3-030-20393-1
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Foreword
In the past two decades we have witnessed an enormous growth of interest in and
development of the relationship between teachers and the resources they use. The
Re(s)sources 2018 conference that was organized to give collective and cumulative
voice to this work, to identify progress and forge a research agenda that lies up
ahead, thus comes as no surprise. What is significant about this volume is that it is
not simply a record of the conference. The collection of chapters in this book take a
step beyond the conference. The invited talks, invited plenary panel as area for
debate (represented in Chaps. 1, 2, 3, 4, 5, 6 and 7), the working groups where the
substantive interaction and discussion among participants took place within the
conference (represented in Chaps. 8, 9, 10 and 11), and the deep reflection on the
documentational approach to didactics (DAD), on its “missing resources” and then
a suggested research program going forward (Chap. 12) have been coordinated into
a substantial work resulting in a significant contribution to the field at this
juncture.
So, what then is this accumulation and its sources? The impetus for the interest
in and development of the field of teachers’ activity with resources converges into
three spheres of influence. First is the spread of reform initiatives in mathematics
education and the introduction of new curriculum texts of various kinds. With this
came the rapid appreciation that teachers interpret texts. Implementation of reform
with curriculum texts is thus a complex phenomenon and a challenge for research.
Second is the increase in digital resources. There is now, indeed, an explosion of
information available to teachers. Here too there is a need to understand the selec-
tion and integration of such resources in teachers’ practice. Linked to both, yet sepa-
rate is the third influence: the field of teacher development wherein teachers interact
with and produce related resources – what in key chapters in this book is called their
documentation – and research on this interaction. These three themes are identified
and described in a similar way in the introduction to this volume, and elaborated
through the various chapters. Each of these themes articulates a problem of practice
in mathematics education, and all are related to some form of change impacting on
or being impacted by teachers’ work. A fourth thread lies in a number of chapters
v
vi Foreword
that give serious attention to the evolution of various aspects of the field, and so a
capturing of change and its processes.
There is a great deal of rich and reflective writing in this book, providing readers
with insights into progress in the field and ways of moving the field forward. I note
just a few examples. There is deep reflection through the chapters, and then compre-
hensively in Chapter 1, on the variety of concepts and constructs that have come to
frame the domain, with debate on which might be considered “solid,” with others
needing to be more firmly established through research. The notion of a “pivotal”
resource, for example, is argued as “solid,” with some suggesting that “resource
system” requires further work. There is discussion on resource as process and/or
product and arguments for a focus on both if teachers’ activity with resources is to
be fully described and understood. There is an interesting reflection on the impor-
tance of teachers’ planning with resources, and how this occurs in different ways in
China and Japan where teachers’ collective work not only has a long history, but has
also taken place inside and outside of the school. A more recent and, in my view,
critical focus of attention has been on the resource itself, and a concern with the
quality of its mathematical and/or pedagogical affordances. In other words, a
resource is not a benign “object” with which teachers interact. It itself shapes teach-
ers’ work and its effects. The editors together with all authors have produced a text
worth reading!
My own interest in resources has a resonant yet different location in a problem of
practice, going back some two decades to my work researching a professional
development program with mathematics, science, and English language teachers in
South Africa (see Adler & Reed, 2002). This was a program in the early post-
apartheid context and so also concerned with change. More specifically, it was a
formalized upgrading program, making available both knowledge and material
resources for teaching these key subjects to teachers in urban and rural school con-
texts. I was challenged by teachers’ constant refrain “we have no resources.” At face
value, this was completely understandable. Their conditions of work were struc-
tured by varying levels of poverty, and hence limited material and infrastructural
resources. At the same time, while teachers lamented their “lack” I was struck by
what they did do with the little that was available. Other “resources” became visible
in that they were impacting teachers’ work. Time, for example, and how it is demar-
cated, structures formal schooling, yet the affordances and constraints of how time
is punctuated and used was seemingly taken for granted. Was time, then, not a “cul-
tural” resource, a function of the particular socio-economic school context, and the
context of schooling? How teachers interacted with colleagues in their schools and
in the project was an obvious social resource. In South Africa’s multilingual con-
text, language is a critical resource, here both in terms of which languages are used
and valued, and then how these languages are used. There was also a range of physi-
cal and material resources in the classroom (number of desks, state of the chalk-
board and available chalk, and curriculum materials like textbooks, new and old, to
name a few). Curriculum resources also ranged from the more physical, like a geo-
metric peg board, to the more ideational, like a designed task and worksheet. In
addition to the consideration of what might be a resource in teaching, it was also
Foreword vii
apparent in our observations of teaching that the insertion of new curriculum
resources did not equate their productive use. A need emerged for a broader concep-
tualization of resources in and for teaching, and in two ways. Firstly it was impor-
tant to expand a conceptualization of resources beyond the physical and material to
include social and cultural resources. Secondly, and there is now wide appreciation
of this, it became apparent that while an important question in contexts of poverty
must be on what and whether resources are available, a critical question is how what
is available is used. And hence the emphasis on resource, not only as a noun but also
a verb, and thus the refocusing on the teacher-working-with-resources.
Looking back and having had the privilege of reading the chapters in this vol-
ume, I have been reflecting on the question of what makes something a resource?
Using the notion of variation in some of my current work, the answer to this ques-
tion must include a reflection, then, on what is not a resource? My earlier view
described above was that a resource lay in its use, and use included all that was
available in the cultural, social, and physical/material domains. I extended my ear-
lier work to include teachers’ knowledge as a resource in and for teaching, studying
domains of knowledge teachers drew on in their practice, distinguishing between,
for example, principled mathematical knowledge, procedural knowledge, everyday
and practical knowledge. So what then is not a resource? As the field has grown so
have the distinctions and deliberations around boundaries of what is/is not a
“resource,” with arguments against knowledge being considered a resource, for
example, and thus the earlier conceptualization too wide. And as with other fields,
boundaries are broken and re-figured as a shared language is refined and
“solidified.”
The book itself creates a boundary around the notion of resources in terms of
what is and is not reflected on, and a comprehensive overview of chapters is pro-
vided in the introductory chapter. Coming from a multilingual context, I was struck
by an apparent absence of reflection on language as a resource or concern across
many chapters. For those working in multilingual contexts in particular, language is
a critical resource, and a substantial focus of attention in research on language and
mathematics education – a large research domain in itself. Here “language as a
resource” is a discursive move against “language as a problem” and so an orienta-
tion to learners in multilingual classrooms being not what they “lack” in relation to
the language of instruction, but to the range of linguistic resources they bring and
use (e.g., Setati Phakeng, 2012; Planas, 2018; Barwell, 2018). How is teachers’
documentation related to the language used and the way it is used, by teachers,
learners, and in texts? Does this matter? As intimated, I refer here not only to the
language (i.e., French, English, Japanese) in which teacher-resource interaction
occurs, but also to the way in which language is used, and hence discursive acts in
mathematics teaching and learning activity. Chapter 12 confronts this issue, engag-
ing with some ways in which issues of language use (in both senses) can and should
frame research up ahead.
Less conspicuous in its absence, but also worth thinking further about, is how the
notion of resources has entered research on identity. Nazir and Cooks (2009) talk of
practice-linked identity resources, and distinguish ideational, material, and r elational
viii Foreword
resources. Together with a colleague we have explored teachers’ learning and iden-
tity formation through a study of the practice-linked identity resources made avail-
able in a professional development program, and teachers “take-up” (use) of these
in their talk and in their practice (Ntow and Adler, 2019). We suggest that the notion
of ideational resources is particularly productive in studying take-up from profes-
sional development in that much of what is offered in professional development is
ideational, carried either in mediated activity or texts. There is perhaps overlap here
with the call for more reflection on the affordances of a resource and concern with
the quality of teachers’ interaction with resources.
In raising language and identity resources, I point to how widely the notion of
resource has come to be used in our field. And hence, again, the question, what then
is not a resource? In the introductory chapters, the editors point to the intention of
the book, and so the boundary it creates, “not to circumscribe” but to rather push
towards operational invariants, and regularities of practice that take the field for-
ward in a rigorous way. There is deep appreciation of the dialectic at play as the
book pulls together diverse elements of an emerging field, it simultaneously
becomes part of this emergence. It is a substantial contribution!
University of the Witwatersrand Jill Adler
Johannesburg, South Africa [email protected]
References
Adler, J., & Reed, Y. (2002). Challenges of teacher development: An investigation
of take-up in South Africa. Pretoria, South Africa: Van Schaik.
Barwell, R. (2018). From language as a resource to sources of meaning in multilin-
gual mathematics classrooms. Journal of Mathematical Behavior 50. doi:
10.1016/j.jmathb.2018.02.007
Ntow, F., & Adler, J. (2019 online first). Identity resources and mathematics teach-
ing identity: an exploratory study. ZDM – Mathematics Education. https://doi.
org/10.1007/s11858-019-01025-z
Planas, N. (2018). Language as resource: A key notion for understanding the com-
plexity of mathematics learning. Educational Studies in Mathematics 98(3),
215–229.
Setati Phakeng, M. (2012). Mathematics in multilingual classrooms in South Africa:
from understanding the problem to exploring possible solutions. In B. Herbel-
Eisenmann, J. Choppin, & D. Wagner (Eds.), Equity in Discourse for Mathematics
Education: Theories, Practices and Policies (pp. 125–145). Switzerland:
Springer.
Contents
1 Introduction ............................................................................................. 1
Ghislaine Gueudet, Birgit Pepin, and Luc Trouche
Part I Framing the Field of Research
2 Studying Teachers’ Documentation Work:
Emergence of a Theoretical Approach .................................................. 17
Ghislaine Gueudet
3 The Construct of ‘Resource System’ as an Analytic
Tool in Understanding the Work of Teaching ....................................... 43
Kenneth Ruthven
4 How Did Mathematics Masters Work Four Thousand Years Ago?
Curricula and Progressions in Mesopotamia ....................................... 61
Christine Proust
5 Reflecting on a Theoretical Approach from a Networking
Perspective: The Case of the Documentational
Approach to Didactics ............................................................................ 89
Michèle Artigue
Part II A Comparative Perspective
6 Mathematics Teachers as Curriculum Designers:
An International Perspective to Develop a Deeper
Understanding of the Concept ............................................................... 121
Birgit Pepin, Michèle Artigue, Verônica Gitirana,
Takeshi Miyakawa, Kenneth Ruthven, and Binyan Xu
ix
