Chap. 15 – Communities, documents and professional geneses: interrelated stories
Ghislaine Gueudet and Luc Trouche
Abstract
This chapter aims at deepening the documentational approach of mathematics didactics, whose main
concepts have already been presented (Chap. 2), in illuminating the importance of collective aspects
in teachers’ documentation work. Teacher’s work has always had, by nature, collective aspects, but
the development of digitalization fosters them. The chapter articulates the frames of communities of
practice and of documentational approach, defining the concept of community documentation genesis.
It evidences the interactions between community geneses, community documentation geneses and
professional geneses, in two contexts: a first one is the context of teachers’ associations on line,
making and sharing resources. A second one is a new teachers training organisation, based on a
collaborative way of designing resources.
Keywords
Collectives; Communities of practice; Community geneses; Community documentation; Professional
geneses; Resources; Teachers associations; Teachers education.
15.1 Introduction
We try in this chapter to deepen the documentational approach of mathematics didactics, whose main
concepts have already been presented (Chap. 2). We want here to illuminate the importance of social
aspects in teachers’ activity, in particular in their documentation work. Human work always takes place
in an institution (Douglas 1986), in a cultural, historical and social reality (Engeström 1999). At the
opposite of a common point of view (“a teacher, being in sole command in her classroom”), we will
enlighten that a teacher does not work alone, and that, according to the nice sentence of the French
Dictionary of Pedagogy1: “Teaching is collaborating” (our translation). In some cases, for example the
case of Japanese lesson studies (Chap. 14), collective aspects of this work clearly appear. In other
cases, such aspects are less visible, but they are always present: each teacher necessarily has
relationships with her colleagues, related with her documentation work. Each teacher takes part in a
variety of collectives: sometimes institutional compulsory (a teacher is involved in a classroom or
school teachers team) or institutional chosen (for example a training session, § 15.3); sometimes in
the frame of associations, large (for example a national association, opened to every mathematics
teacher), or more restricted to teachers sharing a same objective (for example Sésamath in France
§ 15.2). More generally, the teacher’s documentation work is both supported and constrained by a
working environment (Chap. 4), by curriculum resources (Chap. 5, Chap. 6) and more generally by a
resource system (Chap. 2, Chap. 4).
Alike Chapter 2, this chapter focuses on digital resources, particularly online resources, which both
modify some collective aspects of documentation and illuminate existing phenomena. Digitalization
sparks off various forms of collectives, more or less formal, as pointed out by Pedauque (2006, p. 12):
« That is actually what digitalization changes: it makes virtual, flowing, unlimited, elusive,
communities » (our translation). This phenomenon clearly appears in teaching: for example, an
institutional report of the French Ministry of Education (Pochard 2008) presents the « dynamic of
collective » as an effect of digitalization. Digitalization socializes what were, before, individual or
private activities, crucial for teacher’s documentation:
- It gives rise to large collectives, where private activities were predominant (for example for textbook
design, § 15.2);
- It socializes individual documentation work, as in the case of the digital homework notebook (Chap.
2) that makes available, for parents, some elements formerly restricted to the “private” classroom
space.
In this chapter, we look at the conditions of emergence of collectives, at the links between collectives
and documentation work, as well as the links between individual and collective documentation. The
point for us (Chap. 2) is that the documentation is both a question of resources and of teacher’s
knowledge. Looking at collective aspects of teachers’ documentation, we will be sensitive at this last
1
The « Nouveau Dictionnaire de Pédagogie », coordinated by Ferdinand Buisson, has been published in 1910. It is now online,
http://www.inrp.fr/edition-electronique/lodel/dictionnaire-ferdinand-buisson/. The given quotation can be found at the entry
“Conseil des maîtres”.
1
aspect, keeping in mind what are « the participants in mathematics teachers education: individuals,
teams, communities and networks » (Krainer and Wood, 2008).
First of all (§ 15.2), we precise our choices (theoretical choices, and, consequently, choices of
vocabulary and methodology), then we consider the case of a teachers’ association (§ 15.3). In the
third part we study the case of an institutional innovative teacher training program (§ 15.4), finally we
draw some conclusions (§ 15.5), pointing out elements requiring further research.
15.2 Collectives and documentation work
We have considered (Chap. 2) teacher’s activity related to her resource system. Our approach is
rooted in activity theory, as introduced by Vygotski (1978) and Leont’ev (1979). This theory has been
complemented by Engeström (1999), adding in particular a specific interest for communities. Focusing
on collective aspects of teachers’ documentation work brings up to distinguish a variety of collectives
involving a given teacher and to take into account different sets of collective resources linked to these
collectives. This study presents several levels of complexity:
- Complexity of the boundaries of each resources set (for a given collective, teachers’ resources are
more or less shared);
- Complexity of overlapping of collectives (a given teacher always participate in different groups: her
classes, teachers’ class group, school mathematics teachers group etc.);
- Complexity of time (time is not the same, for a teacher meeting her classes almost each day, and for
a collective of teachers working together in a not so regulated manner).
Mastering (as far as possible) this complexity leads us to do conceptual and methodological choices.
15.2.1 Community of practice and ‘lived’ resources
From a conceptual point of view, we have chosen, among some possible theoretical frameworks
(Gueudet & Trouche 2008; Sensevy Chap. 16), the concept of communities of practice, introduced by
Lave and Wenger (1991) to designate group of people sharing an interest, a craft, or a profession. Our
choice is coherent with a flow of current research on mathematics teachers professional growth
(Jaworski 2008, Lerman & Zehetmeier 2008). A community of practice (CoP) is not a congealed entity,
it evolves naturally because of its own dynamic. Each community of practice is a community of
learning: it is through the process of sharing information and experiences within the group that the
members learn from each other, and from their activity, and have an opportunity to develop
themselves personally as well as professionally. Wenger (1998) stated the concept of CoP, pointing
out three conditions for such a community: mutual engagement (members establish norms and build
collaborative relationships), joint enterprise (members create a shared understanding of what are the
common objectives) and shared repertoire (members produce resources, material or symbolic, which
are recognized as their own, by the group as well as by each of its members). Wenger underlines also
two interrelated processes, participation and reification, which seem crucial, for his theory, and for our
research:
- The participation supposes a personal contribution to the shared project, which is not a blind
contribution, but comes with a negotiation of what is to be done, how and why;
- The reification is the process supplying the shared repertoire of the community, result of the
engagement and the participation of each member.
Wenger shows the duality between participation and reification: reification results from participation,
and the shared repertoire supports each member’s participation to the shared objective. Reification
could certainly appear as an ambiguous word (from its etymology, reification = transformation into an
object; once made, an object does not evolve anymore). Nevertheless, for Wenger, reification is a
process, so the word has not to be understood as the crystallisation of complete objects, but as the
production of temporary objects, “lived” resources, always engaged in new developments.
Each group of teachers cannot of course be qualified of CoP: for example, the set of mathematics
teachers working in a same school do not, generally, gather the three features of mutual engagement,
joint enterprise and shared repertoire. But the conceptualisation of CoP is interesting for the dynamics
of human groups that it allows to grasp, the motor of this dynamics being the production of a shared
repertoire. That is exactly what we want to study in the context of teaching: the documentation work.
15.2.2 Towards a new model
The conceptualisation of CoP meets our objective of research: it allows to describe, through the
duality participation/reification, the documentational geneses occurring in a group of teachers engaged
in a common objective of designing resources for teaching. We had modelled (Chap. 2, Figure 1) a
2
documentational genesis as an interplay between a teacher and a set of resources, leading to a
document, mixed entity composed of resources and a scheme of utilisation. We propose here
(Figure 1) an extended model drawing on the conceptualisation of CoP: we consider the interactions
between a teachers’ community of practice of and sets of resources, mobilized for achieving common
goals.
Figure 1. A representation of a community documentational genesis
The duality participation/reification pointed out by Wenger allows to describe the interactions between
the community and what it has created. The duality instrumentation/instrumentalisation, already
defined in the case of one teacher (Chap. 2), allows to describe what happens on a more general
level: teachers, individually or collectively, are engaged in documentation work with new resources
exceeding the shared repertoire, these resources are proposed to the community, they contribute to
its instrumentation, and the community, in the reverse process of instrumentalisation, shapes these
resources, adapts them. The shared repertoire is a component of each member resource system (see
for example Figure 4).
We will name community documentation what is built, along the time, by the community, which is
deeper than the shared repertoire. It integrates also shared knowledge, as Lave and Wenger (above)
underline: each community of practice is a community of learning, and teachers involved in one
community develop professional knowledge. Therefore the community documentational genesis,
yielding the community documentation, includes, but exceeds the reification process.
Finally, interpreting the processes in terms of geneses, we will extend the duality
participation/reification by the duality between two geneses: the community genesis (emergence of
mutual engagement and joint enterprise), and the community documentational genesis (creation of
shared repertoire and building of shared knowledge).
There is an interplay between each teacher’s knowledge and the shared knowledge embedded in a
CoP she is part of. As Krainer (in Wood and Krainer, p. 1) states, « Teachers are active constructors
of their knowledge, embedded in a variety of social environments. These environments influence and
shape teachers’ beliefs, knowledge and practice; similarly, teachers themselves influence and shape
their environments ». There are thus strong interactions between each teacher’s documentation and
the community documentation, but the community documentation cannot be only defined by the
gathering of the documentation of its members:
- the community documentation exceeds what each teacher does for herself, for example the work in a
teachers association (§ 15.3) produces objects (mailing, webpage, workplace, tools) that a teacher
alone would not do;
- a teacher’s documentation (for example what she learns from her contacts with her students)
exceeds what she can share with her community.
Our theoretical perspective implies some methodological choices, that we precise in the following
section.
15.2.3 Methodological choices
We have chosen, in order to study the documentation occurring within teachers collectives, cases of
teachers communities of practice, or teachers collectives developing towards communities of practice.
We are aware that this is not the only case of collective teachers work, but our choice lies on an strong
hypothesis: studying teachers collective based on a mutual engagement and a joint enterprise – a
CoP – will allow a better understanding of what is in germ in more informal collectives.
3
We have also chosen cases where a single collective takes, for its members, a decisive place for their
documentation, either because it corresponds to a strong personal commitment (it is the case of
Sésamath, § 15.3), or because it corresponds to a strong institutional objective (it is the case of the
Pairform@nce program, § 15.4). We are aware that a same teacher could be involved in several
CoPs, influencing her documentation, but we assume that if a given CoP has a preponderant place for
a given teacher, we could neglect, in some sense, the other communities in which this teacher could
be involved.
The two cases we will study in the next section are not “representative” of an “average” teachers
association (for the first case), or of an “average teacher training organization” (for the second case). It
could be said that the two cases are advanced cases (for the design and usage of online resources):
another hypothesis is that these cases could be considered as laboratories for the future, good
representatives of what could happen, in the next years, within teachers communities of practice.
We have already presented (Chap. 2) a particular methodology of reflexive inquiry, aiming at analyze
teacher documentation work. We will extend in this chapter such a methodology to analyse community
documentation work (questionnaire, logbook, schematic representation of the resource system,
classroom observation, collection of resources).
15.3 Sésamath, individual and collective resources systems
The first case presented in this chapter, Sésamath, association created in 2001, is the largest
teachers online association in France; its growth has been very fast (one reason could be the
existence of the French network of IREM 2, which have, in some sense, prepared the way). In this
section, we will first describe its documentation work; then we will focus on one of its members.
15.3.1 Sésamath, a teachers association designing and sharing teaching resources
Sésamath (http://www.sesamath.net/) essentially gathers in service mathematics teachers (about one
hundred members), aiming to “freely distribute resources for mathematics teaching” (announced on its
website, see Figure 2).
Figure 2. Sésamath front page: “mathematics for everybody”, “working together”, “supporting one another”, “communicating”
It presents the features of a CoP: mutual engagement, joint enterprise, and a shared repertoire
consisting in resources for teaching: a base of online exercises (Mathenpoche), textbooks online (with
also printed copy available – very cheap), software under free license, for example a dynamic
geometry system, TracenPoche (TeP) and simulated geometry instruments InstrumenPoche (IeP) 3.
The audience of Sésamath is very large: about one million visits, each month, for its websites. The
community documentation exceeds this shared repertoire: Sabra (2009) evidences the knowledge,
which is produced, and generated, by the community documentation work, mainly knowledge on
mathematics, on mathematics teaching and on teaching.
Let us have a closer look at the documentation work in this community. It would be impossible, for a
hundred of members, to develop a so large repertoire of resources. What allows this productivity, and
fosters in the same time Sésamath genesis, is the development of tools favouring collaborative work.
The main tool consists in a platform for collaborative work (Sésaprof), which gathers thousands of
teachers, for achieving a given project (for example the design of a textbook). Each project concerns
about fifty teachers, a reasonable number for a real collaboration; we hypothesize that a CoP emerges
in the same time that its project takes form, but we did not study each of these numerous groups. The
development of Sésamath appears thus as strongly linked to the support and needs of digitalization
2
The IREM (Institute for Research on Mathematics Teaching) have been created, in 1970, in each French region to support
mathematics teachers for implementing the so called Modern Mathematics reform. Along the time, they enlarged their
objectives, and became a frame where teachers, from primary schools to universities, could reflect together, without any
hierarchy, to their professional questions.
3
Which means « Trace-in-the-Pocket » and « Instrument-in-the-pocket ».
4
(Gueudet & Trouche 2009). Borba and Gadanidis (2008) consider “virtual environments and tools both
as factors mediating teacher collaboration and as co-actors in the collaborative process” (p.182). In
the approach we develop, the perspective is slightly different; we do not consider resources as actors.
Nevertheless, the same duality is present: the use of digital tools permits collective documentation
work; it also shapes this work.
This opens a view on the community genesis, which seems to have common features with other
teachers online communities geneses: the more active members of these associations describe
(Gueudet & Trouche 2009) their genesis as a rolling stone (Figure 3); a group of pioneers meets for
sharing resources (first step) and constitutes a first kernel; then (second step), this initial group
deepens the documentation work in coopering4 (that is the beginning of a shared repertoire). In this
dynamics, it draws around it a crown5 of teachers interested only in using the resources of this shared
repertoire, eventually to give back some personal resources in it. Last step, the “cooperation kernel”
passes to a stage of collaboration, thinking together what is to make, which means a step of blooming
of the initial CoP; this dynamic draws the sharing crown to a stage of cooperation, and gathers a new
crown of “sharing teachers”.
Figure 3. The genesis of a teachers online association, seen as a rolling stone (Gueudet & Trouche 2009)
This dynamic is fostered by a permanent reflexion of the kernel about the organization and the ways to
develop it. It results in permanent proposals to the members of the successive crowns (Figure 3), to
encourage their progression towards the centre. Thus the kernel is neither closed, nor invariant: it is
always renewed (“old” members quitting, new members arriving). The development of an association
is probably linked to its openness6. To deepen this analysis, we need to focus on Sésamath members,
that is the purpose of the next section.
15.3.2 Pierre’ documentational genesis, Sésamath side vs school side
We met Pierre, a member of the kernel of Sésamath, in October 2008, at a training session managed
both by the association and INRP7. We had asked the president of Sésamath to find a member of the
association, member of its kernel since at least five years, between 30 and 40 years old, and actively
involved in a project. Pierre corresponded to this description, and accepted to participate in the
methodology of reflexive inquiry for two years, what allows us to have some elements on his
documentational geneses and the community documentational genesis seen “through his window”. In
this section, we describe the documentational “landscape” we discovered the first year, before
describing his work with his students, and then analyzing some evolutions between the first and the
second year.
As already mentioned in chapter 2, Pierre is 35 years old and teaches in a middle school (grade 6 to
9). His father had a passion for sciences; his mother and her parents were teachers (his grand father
had written textbooks). He started by studying physics, and has kept a vision of mathematics as “a tool
necessary for designing scientific models”. He has finally chosen mathematics due to their
ambivalence: “a world both formal and dream-like”. Solving problems constitutes for him the heart of
mathematics teaching. He describes a mathematics teacher as a real one man’s band: “artist, actor,
human resource manager, psychologist for individuals and groups, mathematician, cultural
reference…”.
4
Dillenbourg (1999) distinguishes cooperative and collaborative work: « In cooperation, partners split the work, solve sub-tasks
individually and then assemble the partial results into the final output. In collaboration, partners do the work 'together’ ».
5
This crown could be interpreted in term of periphery (Wenger 1998) of the community.
6
In this sense, the name itself of this association, Sésamath, is certainly revealing, as a wink to « Open sesame », the famous
phrase from the Arabian Nights.
7
INRP: National Institute for Pedagogical Research. The organisation of this joint training session, dedicated to the quality of
resources, is another evidence of the Sésamath care for support its members’ continuous education.
5
It evidences his strong involvement in his school: he is “teacher in charge of technology” 8, treasurer of
the household socio-educational, responsible of the school’s chess club… These activities are not
dedicated to mathematics. It clearly appears that all the collective aspects of mathematics teaching
are linked with Pierre’s involvement in Sésamath. He was, in 2008, member of the Sésamath board for
5 years (he spent one hour a day reading emails and participating to forum “that engage the
association life”); he was member of the project “grade 6 textbook”, in progress at this time. He was at
last the pilot of a new Sésamath project: “mathematics files for primary schools”.
Documentation work takes place within each of these collective involvements and each of them is part
of Pierre’s work, as he said: “Consuming time in collective activities is a component of my teaching
activity”. He particularly underlines the importance of the primary school project (Pierre said: “it gives a
better understanding of what my pupils know when arriving in the college”), the Sésamath board (“it
makes me aware of the questions asked to the profession as a whole”) and the “grade 6 textbook”. It
is actually this last project, which appeared as determining for Pierre’s documentation: for the time of it
(2 years), Pierre decided to have only grade 6 classes (three classes, for 6 hours teaching in it), to
“accord” his documentation work to the community documentation. Thus the documentation work that
Pierre accomplished in 2008-2009 for the grade 6 level concentrated his main efforts, and connected
individual and community documentation.
The interplay between Pierre’s and community documentation appears also through the schematic
representation of his resource system (SRRS, Chap. 2), see Figure 4. Sésamath repertoire
(textbooks, exercise books, software), constitute, for Pierre, the “horizon” of his system. What is
described as “personal resources” (down right) are archives and seem to be congealed (no arrow
comes to renew them): what seems to be ‘lived’ are resources of the shared Sésamath repertoire.
Different arrows allowing to distinguish different
types of activity:
- Thick for preparing lessons;
- Medium for preparing exercises;
- Thin for preparing activities.
Most of the arrows concern activities (i.e. problem
solving, open ended questions, which constitute
the heart of Pierre’ teaching).
Pierre does not renew his personal resources:
actually, he essentially contributes to feed
Sésamath repertoires.
Apparently no
colleagues.
interactions
with
his
own
Figure 4. Pierre’s schematic representation of resource systems (SRRS), Feb. 2009, handmade, our translation
Pierre’s explanations on “how it works” help to understand his documentation work:
- In the first direction (from Sésamath resources to his own resources), he “digs up” what he needs,
and “customizes” it (“generally, I pick up an exercise, I keep its main idea, and I rephrase its
questions”);
- In the second direction, Pierre acts as a “brocanteur” 9: he “bargains-hunts” resources (on the web as
well as in old books found on bookstalls), captures them in his computer. The space dedicated to his
documentation work on his computer has an important role. Pierre gave it a name, Piwosh, standing
for “Pierre’s workshop”10. Piwosh looks like an incubator of resources. Pierre jots down his ideas on
Piwosh as they come (Pierre has sometimes difficulties to find them again). He develops, shapes
them when the need occurs, tests them with his students. The resources thus follow a path, from test
phases to revision phases, until they are good enough (according to Pierre’s judgment) to be added in
the shared Sésamath repertoire.
What means: responsible for computer and software equipment, for giving his colleagues advice for use (website, software…).
Hard work (his logbook shows it is time consuming (6 hours in three weeks), for a limited gratitude of the institution (one hour
paid a month).
9
French word standing for « secondhand goods dealer ». The English expression is interesting, evidencing that a resource is
never a firsthand one, but always inherits from some older ones.
10
Our translation from French TafPi, literally “Taf de Pierre”; Taf is a slang French word, meaning “work”.
8
6
There is not only an interplay between Pierre’s and Sésamath resource systems: it is a more complex
interplay, where other members of the textbook project act as active partners: Pierre proposes his
ideas for discussion on Sésamath discussion lists, he discusses also the resources proposed by the
members of the project group, emerging community of practice. The Sésamath resources system
appears thus both as a result of Pierre’s documentation work, and as one of its essential sources. This
situation constitutes a culmination of the collaborative process within Sésamath: this is not only the
resource content that is shared (“sharing the same exercises”), this is not only the type of material
resources that is shared (“sharing the same type of textbook”), it is, physically, the same resources
which are shared, on the same remote host, and which are available, from anywhere, for each
member of the project.
To this collaborative way of this documentation work corresponds a collaborative way of teaching,
which we evidence in the following section.
15.3.3 Documentation work going on in Pierre’s class
Using online resources is an important feature of Pierre’s documentation work, out as well as within
his classes:
- Within his classroom, a connected computer, a projector and an interactive whiteboard (IWB) are
used to work with online resources (instrumentation). For example, at the beginning of each lesson,
the teacher opens Pronote (Chap. 2), an application allowing to display the students list, to note the
absentees, to memorize what has been done, and what remains to make… Another example of this
continuous Internet use: the teacher exploits Google to do any arithmetic operation exceeding
students’ capacities of mental computation (it is amazing to observe that handheld calculators remain
in students’ schoolbags!);
- For prolonging the work with his students out of the classroom, he develops a collaborative website
on which he regularly uploads mathematics enigma. Students can try to solve them and write their
solutions on a forum.
Sésamath resources are widely used during each lesson, and they contribute to Pierre’s
instrumentation processes. For example, the simulated geometrical instruments (Sésamath IeP) allow
to visualize, with a film in a loop, geometrical constructions to be done by students. It clearly
contributes to the development by Pierre of a scheme, for the class of situations “teaching how doing a
geometrical construction corresponding to a mathematical text”. Firstly, he proposes to his students to
do the work without any help; then, when the construction is almost complete for all the students, he
shows the construction process on the IWB, then plays the film in a loop, to help the students who
have not succeeded to complete their figure. Pierre explains why this method is important: “students
have to establish a direct relationship with the construction” (actually, when looking at the film, they
receive no scaffolding from the teacher), “geometry goes on as a film, not as a picture”, “repetition, in
pedagogy, is essential”, “students have to follow their own rhythm” (which is the case with the film: if
students are lost, they can always wait for the next passage of the film, thanks to the loop), etc. We
consider these declarations as operational invariants, components of this scheme, fostered by the
resource (IeP) involved in this situation.
Pierre has developed, within Sésamath, a strong professional knowledge: “learning is collaborating” 11,
which has evident consequences for the orchestrations (Chap. 13) of mathematical situations:
- What is in front of students (Figure 5), inside the classroom, is not the teacher, but the blackboard
and the IWB. Pierre permanently combines these two boards, essentially for using Sésamath
resources, expressing this idea: “Comparing different resources is the way to make his/her own idea”;
11
Which echoes our introductory quotation (§ 1) “teaching is collaborating”…
7
Figure 5. Pierre’s classroom configuration (drawn by Pierre), and Pierre in his classroom, showing something on the IWB
- Pierre explains that what he names the “chevron” configuration (Figure 5, Pierre’s classroom) of the
students’ tables fosters debate in the classroom, students facing the two boards and their colleagues
to discuss a given problem.
Problem solving is, for Pierre, the heart of learning mathematics: he privileges phases of joint
construction (geometrical figures, conjectures), more than phases of validation. For him, learning can
be viewed as a process of using, elaborating and sharing resources. Thus this process is dynamic,
collective, and cannot be fully planed by the teacher. Thus joint design of resources in Sésamath and
joint construction of knowledge (Chap. 10, Chap. 16) in the classroom seem to walk together.
It is to be noticed that Pierre and Myriam (Chap. 2), although they have a common interest for
Sésamath resources and for problem solving, seem to develop very different documentation systems.
For Myriam, the official texts are very important resources, intervening in many documents she
develops, providing problems texts. Pierre naturally also refers to the official texts, but does not look
for ideas of exercises in them. Myriam uses the Sésamath textbooks and Sésamath exercise sheets to
prepare her own sheets; but she does not use, for example, TeP (geometry software) and IeP
(simulated instruments). Sésamath is for her only one source, amongst others. She sometimes
projects in class online exercises, but does not often use the web connection during the lessons. One
can hypothesise than this difference is linked to the difference of position towards the association.
There is, in Pierre’s case (and not in Myriam’s), a strong interaction between community and individual
documentation system, between the documentation work for his association and for his own classes.
We should describe this situation as a symbiosis between two documentation systems. This can be
linked with two points: first of all, Pierre is member of the Sésamath kernel; secondly, his
documentation work for the association (making a grade 6 textbook) perfectly meets his
documentation work for himself (making the teaching of his own grade 6 classes). What will happen at
the end of these exceptional conditions – which mean the end of textbook elaboration? The second
year of Pierre’ following brings some information about, contrasting, both individually and collectively,
the documentation landscape,.
15.3.4 Association vs school, two faces of a same medal
One year after, Pierre’s situation within Sésamath has deeply evolved. The work on the grade 6
textbook is finished, and Pierre is no more member of the Sésamath board. He explains: “After a
strong investment, it is necessary to take a step back”. It is certainly an effect of the completion of the
textbook (“the work has been done”), but also a consequence of a personal event (Pierre has had a
new child): in a certain sense, new decisive steps of two geneses... Pierre is still a Sésamath member,
but involved in a single project (mathematics files for primary school), which is not as time consuming
as the previous one (instead of 10 hours a week for the association the previous year, he now spends
about one hour a week). This enlightens the possible trajectories (Wenger 1998) inside the
association’s rolling stone (Figure 3), both towards the interior and towards the exterior. Even in the
association’s kernel, complex trajectories take place due to both community documentation geneses
and personal stories.
This evolution goes with a greater care by Pierre about what could be collectively done within the
school: for example, the website that Pierre developed for communicating with his students migrated
from a private host to the school common website, for sharing with colleagues. The new SRRS (Figure
6) that Pierre draws evidences this phenomenon.
8
Pierre’s wordings:
“I use more personal resources
(actually Sésamath resources that I
modify to adjust to my needs) […]
My work for Sésamath concerns now
levels that I do not teach myself
(mainly primary school level).
Since the last year, and after our
reflection [Pierre means: the reflexion
with the researchers], I thought about
documents I got back from my school’
colleagues. Finally I found some, and
some of them have been used without
modifications. I displayed this on my
drawing…”
Figure 6. New schematic representation of resource systems (SRRS) made by Pierre in Feb. 2010 (our translation)
When discussing with Pierre about the data collected one year before, he precises also the interest of
the classroom arrangement (Figure 5) in relation with this collaboration with his colleagues: he
sometimes exchanges his classroom with his neighbour’s one, for organizing small groups work,
which fits well in this room. This exchange induced to introduce this neighbour (who teaches French)
to the interest of IWB, then to give him some ideas about how to use it, etc. This re-evaluating of the
existing collaboration within the school is certainly a consequence of Pierre’s refocusing on his school,
but also an indirect effect of our methodology of reflexive inquiry (Chap. 2) itself: working with
researchers (Figure 6: “after our reflection, I thought…”) on his own documentation work makes
necessarily Pierre more aware of his colleagues as part of “the sources of his resources”. Pierre
distances also himself from Sésamath resources (Figure 6 is to be compared to Figure 5 from this
point of view):
- Sésamath is not the only Pierre’s horizon: through his new SRRS appears the importance of
external resources (films, readings…);
- the textbook design is complete, Pierre takes up a more critical stance: the whole Sésamath
resources are no more directly applied from the association’s website. When they seem to be not
enough relevant, they are modified, and saved in Pierre’s personal repository for future usages.
There is a sort of balance between Pierre’s investment, in his association and in his school, not only
as communicating vases (less in the association, more in his school and vice versa): the various types
of community documentation work feed each other. We could say, extending a formula we met twice
in this chapter: documenting is collaborating. The case of Pierre evidences also the interplay between
documentation geneses and professional geneses. Pierre’s drawings (Figure 7), representing the
evolution of his classroom configurations, are very interesting from this point of view:
Figure 7. Evolution of equipment and classrooms configurations (drawings from Pierre)
9
- First configuration: the beginning (four years ago), when the IWB entered the classroom, he “put it in
a corner, on its feet”, and the students “in front of the boards, as looking at a film”;
- Second configuration: this new tool, and the discussions in Sésamath about the resources to be
designed for this purpose (Pierre wrote, with a colleague, a paper on this theme, for the journal of the
association12) led him to a new configuration. The IWB is now installed on a wall (“it is now part of the
classroom”), the students’ desks faced both the blackboard and the IWB (necessary to compare the
information “without privileging one of them”). Implementing new resources creates new needs for
writing: a white board appears on the side of the blackboard, to keep the memory of what appears on
the IWB without changing its current display;
- Last configuration: the “chevrons” (already seen Figure 5) appearing for encouraging debates around
problem solving.
We conceptualize this professional growth as a professional genesis, encompassing several
documentational geneses. The collectives, under various forms, foster these processes. This occurs in
the context of associations, and in the context of “natural life” of schools. Is it possible that the
schooling institution takes profit also of this dynamic of collectives for teacher professional
development programs? ? We examine this question in the next section.
15.4 Pairform@nce, training paths, collective aspects of documentation and professional
development
The French national professional develoment program Pairform@nce13 is aiming to develop in-service
teachers’ skills in using ICT in class with their students. We present in this section its principles, then
the research we have developed in this frame, related to teachers’ collective documentation, and
illustrate our approach through a case study.
15.4.1 Pairform@nce principles and associated research
Pairform@nce is a professional development program intertwining face-to-face and online activities,
for teachers intervening at all class levels, from primary to secondary, and all topics (Gueudet et al.
2009). It lies on two main principles: (i) collaboration among teachers: professional development,
especially concerning ICT, cannot be only an individual process, it results from the collective activity
and experience of peers (ii) co-design of lessons with ICT and implementation in class: the program
sets up the collective design of a teaching sequence, its test in class and an afterwards shared
reflection. Its main assumption is thus that the collaborative process of designing and experimenting
lessons is a mean of professional growth, meeting on this point the experience of Lesson Studies
(Winslow, Chap. 14; Lerman & Zehetmeier 2008).
The Pairform@nce program is structured around training paths available on an online platform. Each
training path gathers resources on a certain topic (for example “Individualisation with online exercises”
§ 15.4.3) and tools for collaboration, enabling trainers to set up training sessions. A path is structured
in seven stages: 1) Introduction to the training session, 2) Selection of teaching contents and
organisation of teachers teams, 3) Collaborative and self-training, 4) Collaborative design of a lesson,
5) Test of this lesson in each trainee’s class, 6) Shared reflection about feedbacks of class tests, 7)
Evaluation of the training session. The training paths are elaborated by designers, which are most of
the time expert teacher trainers. Once a training path is available on the platform, it can be chosen by
teacher trainers to set up sessions with a support (organisational and financial) from the regional
school authority. Thus, the Pairform@nce program involves multiple agents, at least path designers,
teachers trainers and trainees.
Our research team has set up a methodology enabling to study the different documentation processes
involving these various agents, lying on some principles:
- being both actor and observant of the program itself, to deeply understand its springs;
- studying the development of paths from the very beginning, i.e. from their design;
- aiming to find some general results, studying thus a variety of paths;
- keeping in mind that a path, as any resource, evolve through usages, that implies a principle of
design-in-use (Rabardel & Bourmaud 2003): training path design is initiated by designers and pursued
by trainers while there are using it;
12
http://revue.sesamath.net/spip.php?article21
The word “Pairform@nce” is a modification of the French word “performance”, where the first part “per” has been replaced by
the word “pair”. Per and pair have the same pronunciation in French but “pair” means peer. An English translation could be
“Peerform@nce”, pointing out the principle of collaboration among teachers.
13
10
- designing path anticipating their further enrichment by trainers, which means: rather flexible in order
to facilitate instrumentalisation processes, including “assistants” in order to facilitate documentational
geneses, including also tools to collect trainers reactions and propositions for path evolutions;
- favouring, at each stage of the work, collective processes, for the designers as well as for the
trainers and the trainees (in this last case, it is a natural feature of the Pairform@nce program).
Following theses principles, we have engaged the design of four training paths, regarding two different
subject matters (mathematics and geography-geology), for a variety of training themes and ICT tools,
at the secondary school level. Each path (Figure 8) was designed by a path design group (PDG, four
persons) constituted by teacher trainers and researchers using to work together before 14. Each
training path was tested throughout an experimental training session (ETS) managed by its designers,
in the course of its design, following the design-in-use principle. Following the collective work principle,
the methodology included continuous collaboration (online and with regular face-to-face meetings)
between the different PDG, constituting a design and research team15.
Figure 8. The implementation of the methodology principles
A large number of questions can be studied about this program, from various points of view that our
implication allows to develop. We will focus here on the trainees, looking at the relations between
community geneses and documentation geneses, and at the consequences in terms of professional
growth, in the frame of one experimental training session.
15.4.2 Presentation of an experimental training session
We focus here on an experimental training session (ETS), corresponding to a path in mathematics,
devoted to the use of online exercises for organising various forms of individualised work in class. In
what follows we shorten it as « individualisation ». We consider here the trainees’ documentation work
and the emergence of trainees communities during the ETS. For this training, we were involved as
trainers and have thus observed the work in presence; we have collected all the resources designed
by the trainees, and their answers to an initial and a final questionnaire about the training. We also
have followed a given team of two trainees, and have observed them in class.
The ICT tools involved in the « Individualisation » path are e-exercises bases, that propose interactive
exercises, but also possibilities for the teacher to choose amongst these exercises and program
specific sessions for individual students or groups of students. The training addresses secondary
school mathematics teachers, teaching from grade 6 to 9. It proposes the design of a lesson by each
trainees’ team, to be tested by one or several members of the team. Workshops in presence (three
days) alternate with distant training (during 13 weeks). During the distant training, the platform permits
communication between trainees, and between trainees and trainers on an online forum.
14
Several institutions were involved in the research, particularly two IREM (Institute of Research on Mathematics Teaching) and
one IUFM (Academic Institute for Teachers Education)
15
The authors of this chapter were amongst these pilots.
11
Forum
Step 4
Collective,
lesson
design
Space to
download
the trainees’
productions
Figure 9. « Individualisation » path, example of a screen for step 4
The designed lessons are tested at least twice, by two different members of the team. A crossobservation is organized within the team: one trainee observes at least one session while another
teaches. Suggestions of modifications of the lesson follow the observation, and are included in a new
version of the lesson for the second implementation. Several resources are proposed in the path to
support the lesson design by the trainees, in particular three grids: grid of lesson description, grid for
session observation, and final report grid. Examples of lessons described by using the three grids are
proposed on the platform, with various articles, and quickstart guides for the software.
Six teams of trainees were involved in the ETS, with between two and four teachers in each team. All
of them were experienced middle-school teachers; some of them were acquainted with the use of eexercises, and others were discovering this use. Concerning individualisation, all of them declared
before the training that they were not used to implement it in classes. Teachers of a given team were
all working in the same school; they were used to work together to design assessment texts, but none
of them has been engaged in the collective design of a lesson before.
All the teams strongly committed in the collective lesson design work. The trainees, in their collective
documentation work, have developed common resources: students’ sheets, lesson plans, lists of
exercises chosen in the online resource etc. These outcomes of the documentation contribute to build
a shared repertoire, and indicate the emergence of communities of trainees. We will now consider
more precisely the case of one team of trainees of the ETS, Clarisse and Chantal.
15. 4. 3 The case of a team: Clarisse and Chantal
Clarisse and Chantal work in the same college since 2005; sometimes they write together assessment
texts; but the « Individualisation » training was their first opportunity to design a lesson together. As
mentioned above, we have followed the work of this team by collecting the resources they elaborated,
their initial and final questionnaires; we also met them at their college, where they presented us their
choices for the lesson, and we observed one classroom session. The lesson concerns angles and
circles, and more precisely the theorems about the angle at the centre and angles subtended by the
same arc; it is given in grade 9 (students aged 14-15). In Clarisse’s and Chantal’s school, pupils in
grade 9 are provided with laptops, lent for one year.
Clarisse is a confirmed user of e-exercises. The e-exercise basis she uses is called “Mathenpoche 16”.
It can be used online; it can also be downloaded (in this case the teacher looses the access to the
registered activity of the students). Mathenpoche is downloaded on the laptops of all Clarisse’s
students. She has developed a fluent use of it: after the introduction of notions or methods, the
students turn their laptop on, and work for 10-15 minutes on e-exercises she has chosen. She
chooses quite large lists of such exercises, for all the students to stay busy during the 10-15 minutes,
even if her objective is more focused on the two first exercises, that she wants all the students to
succeed.
At the beginning of the training, Chantal did not develop such a use of Mathenpoche; she only used it
online in a computer lab. During the design of their common lesson, Clarisse has suggested to follow
16 “Maths in the pocket”, http://mathenpoche.sesamath.net, see chapter 2.
12
her usual classroom use of Mathenpoche for one of the sessions. Chantal has agreed, has asked her
students to download Mathenpoche on their laptops, and has used it as planned during the lesson.
This experience has been successful: the students have appreciated it and were commited in the
mathematical work. Thus Chantal has generalized this use for other mathematical contents. In this
case, one trainee proposed a resource, coming from her own resource system: short periods of work
on Mathenpoche exercises in the course of an ordinary classroom session. This resource was
accepted by the other trainee, and has become a shared object in their common repertoire.
Clarisse and Chantal have also used a dynamic geometry software, GeoGebra 17, for another lesson. It
was used for the proof of the angle at the centre theorem. They planned that the pupils work on
GeoGebra, downloaded on their laptops, and used dynamic diagrams prepared by the teachers. The
first diagram was intended to be used to formulate an hypothesis about the angles (given two points
on the circle, link between the measurement of the angle with vertex at the centre and the
measurement of the angle with vertex on the circle). The second diagram, which is in fact an
animation with 11 successive states, was presenting the different stages of the proof of the theorem.
Clarisse and Chantal have expected the pupils to find these stages by observing and manipulating the
figure. Clarisse has implemented it first in her class. The students have found the hypothesis, but
stayed unable to find the proof, despite the animation. They were not able to interpret the construction
they observed neither to translate it into a mathematical reasoning. Chantal has observed this session;
thus she has decided to handle herself the proof when she implemented the session, still by using the
same animation. It has turned out to be difficult too: the proof is very long (11 stages!) and the
students quickly loosed their concentration.
In this case, the team has developed a common document. It comprises a resource including the
GeoGebra diagrams, the lesson plan etc. This resource, composed by the team, is associated to
professional knowledge. At the beginning of the training, Clarisse and Chantal shared knowledge
about the usefulness of a dynamic geometry software for students to formulate hypotheses about
geometrical properties. Their experience confirmed and probably reinforced this knowledge. On the
opposite, for the first time, they have tried to use a dynamic diagram to support the search for a proof.
After their two experiments in class, they retain that such a use is not appropriate: a dynamic diagram
designed by the teacher is not enough for the students to find or even to understand a proof. This
professional knowledge has developed during the training, in the course of their common
documentation process.
Clarisse and Chantal were clearly engaged in a common documentation work; they have shared
resources, elaborated new resources together, but also developed common professional knowledge.
At the same time, their team became a community of practice.
We have observed similar phenomena among the other trainees teams. We retain thus that the
principles of the Pairform@nce program support, under certain conditions, the emergence of teachers
communities of practice, and these communities documentation. It fosters, this way, professional
geneses.
15.5. Discussion
We have evidenced, in this chapter, that the collective is everywhere in teachers’ documentation work,
and that it takes very different forms that the concept of communities of practice allows to analyze. We
illustrated it with two case studies, a teachers association and a teacher development program.
About communities, our study contributes to evidence several results, in particular:
- Each community is both spontaneous and cultivated (Wenger 1998). It is often said that teachers
association are quite spontaneous: we have showed how the board of Sésamath takes care of its
development. It is often said that a teacher development program gathers in a quite artificial manner
teachers: we have showed how the relationships between teachers involved in such programs are
important for the success of the development program. Finally, it is a subtle mixture of nature and
culture, which allows the emergence and the development of a CoP;
- Each community is a tumultuous aggregation of members, tumultuous in a different senses: some
teachers enter the community while other ones get out; teachers’ roles inside the CoP permanently
change, sometimes suddenly; as a rolling stone, a community gathers in successive crowns various
groups attracted in some way by the practice of the community and its shared repertoire;
17
http://www.geogebra.org/cms/en/community
13
- No community is an isolated one. Pierre, for example, is member of Sésamath, member of various
collective within his school. These collectives are not acting as communicating vases, but as costimulating agents;
- Paraphrasing Lave and Wenger (op. cit.), saying that each community of practice is a community of
learning, we could say that each teachers community of practice is a community of documenting,
which means that community geneses and documentation geneses act in concert. The
documentational approach takes place in the thread of the theory of community of practice.
We assume that these phenomena are not specific to local situations (associations, or development
programs), but concern, at different levels, each teacher, involved in various collectives. Following the
work of a teacher means following interrelated stories: stories of the collectives she is part of, stories
of their documents, stories of her professional growth. Instead of story, we have used, both in chapter
2 and chapter 15, the term genesis to underline the idea of development boosted by itself, fed by an
environment, directed towards a higher level of organisation.
Our study proceeded by successive zooms out. We evidenced (Chap. 2) how studying teacher’s
activity requires to encompass documentational geneses, considering out and in school activity, and
sets of resources intervening in her documentation work. This “resources” point of view led us to
situate the teacher within a set of collectives where these resources are living. It would certainly be
necessary, this time by successive zooms in, to more precisely study what is at stake inside these
collectives, along the time. We are aware that the understanding of community documentational
geneses requires a refinement of methodology and new tools, allowing to collect and to analyse new
types of data (extracts of online forum, emails, verbatim of communities meeting – online or face to
face – annotations of resources…). We are now developing these new tools, towards a methodology
of community reflexive investigation (Chap. 2).
We have for sure studied, in this chapter, extraordinary communities. But something extraordinary lies
also under the ordinary course of each teacher’s work. This is what the deep study of the individual
and collective documentation work gives access to.
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