Title:
1Lived resources and mathematics teachers
professional development
- Ghislaine Gueudet
- (IUFM de Bretagne-UBO, CREAD)
2Outline
- Digital resources for mathematics teachers
- A documentational approach
- Teachers documentation a case study
- Collaborative lesson design and professional
development - Conclusion
3Digital resources for mathematics teachers
- A context of generalised availability of digital
resources - Software
- Digital textbooks
- Online exercises
- Forum
- E-mail
- Interactive Whiteboards
- ...
- Official / personal websites
4Digital resources for mathematics teachers
- Development of new forms of collaboration, the
GeoGebra community a world-wide network,
communication between users, sharing resources
supporting the use of GeoGebra...
5Digital resources for mathematics teachers
- Intergeo European research project about
interactive geometry. A platform offering
resources, tested and evaluated by users. A
central questioning about the quality of
resources (Soury-Lavergne et al. 2010).
6Digital resources for mathematics teachers
- Online teacher associations
- In France, Sesamath develops free online
resources - Online exercises, lesson plans, a dynamic
geometry environment (Tracenpoche), digital
textbooks...
7Digital resources for mathematics teachers
- The issue of technology integration
- A gap between the institutional expectations and
the actual use of software a gap between the
extensive use of digital means, of some online
resources, and a sparse use of software - Development of new, holistic perspectives on
technology integration, considering the
structuring features of the classroom context
(Ruthven 2007) - New aspects of digital resources
- Design and use are strongly intertwined
- Teachers do not work alone, they interact with
various groups with teachers of the same
school, with distant teachers on a forum, with
their students ... - Evolutions, and new perspectives on old facts,
requiring new approaches.
8A documentational approach, origins
- a conceptualisation of resources as anything
re-sourcing the teachers practice (Adler 2000)
material and socio-cultural resources - studies of curriculum material focusing on the
interactions between the teacher and the
curriculum material, central in the professional
development (Remillard 2005)
9A documentational approach, origins
- Research about students working with technology,
the instrumental approach (Rabardel 1995, Guin
et al. 2005) - An artefact an outcome of human activity,
designed for a specific aim. - An instrument developed by a subject from the
artefact, in a goal-oriented activity. - Instrument artefact scheme of utilisation
- Scheme a cognitive construct, comprising rules
of action and structured by operational
invariants - Extension of the approach development of a
documentational approach (Gueudet Trouche 2009)
10A documentational approach
- Documentational genesis
- a teacher develops a document from a set of
resources - the document associates resources, and a scheme
of utilization, in particular professional
knowkledge - a double instrumentalization/instrumentation
movement the teacher shapes the resources, and
the resources frame the teachers choices and
knowledge
11A documentational approach
- Geneses develop across different contexts for
the same objective they are ongoing processes a
given document yields resources that can be
engaged in further documentation work. - Teachers develop coherent and structured
resources systems and documentation systems - Documentational geneses are central in teachers
professional development
12Teacher documentation, a case study
- Reflexive investigation (Gueudet Trouche 2010)
a methodology to follow teacher documentation. - Long-term follow-up, collection of resources
- Following the teacher in-class and out-of-class
- The teacher as partner in the research logbook,
representation of the resource system (SRRS)...
13Teacher documentation, a case study
- (A focus on evolutions, and on digital resources)
- Myriam (aged 51), teaching grade 6 to 9. Followed
in 2008-2009 and 2009-2010. - Material resources
- Non digital textbooks, overhead projector,
professional papers, students productions... - Digital laptop, software, online exercises,
websites, e-mail... - Involvement in collectives
- Local reflection group, In-service teacher
training - Personal environment
- Discussions with her husband (physics teacher)
about the articulation between maths and physics - Her daughter in grade 10 works with the
calculator, with GeoGebra
14Myriam Schematic Representation of the Resource
System
15Myriam, distant work with the students
- Myriams grade 9 students are equiped with
laptops her school has a virtual learning
environment. - In 2009-2010, the school is blocked by the snow
during two weeks. Myriam uses a mailing list of
the class to send homework an exercise about
functions, using a spreadsheet to build a
graphic. (Instrumentalisation) - Some students send back a spreadsheet file
others copy the graph in a word processing,
Myriam can not see how it has been built. - She decides to go on sending distant homework,
but retains to precise carefully the form of the
work to send. - (development of teacher knowledge,
instrumentation)
16Myriam, introduction of functions
- Where on AB should be M to obtain Perimeter
(CNMP)9? - Objective introducing p(x)x6
- Use of a diagram (Laborde et al. 2001),
displaying the length AM and the perimeter. The
teacher pilots the computer, the students
observe. - The students formulate the conjecture, but can
not find the proof...
17Myriam, introduction of functions
- Introduction of functions a new theme in the
grade 9 curriculum (2008-2009) - First uses of GeoGebra other colleagues in the
reflection group use it her daughters math
teacher uses GeoGebra - Myriam professional knowledge, developed along
her professional practice, and her use of a DGE
(Geoplan) The students must be actively
involved in the building of new knowledge
Using a DGE diagram supports the formulation of
conjectures by students guides her choices for
this new topic and software. - The proof is too difficult the students consider
that the function is not necessary... - Myriam decides to propose a more concrete
situation the following year building
rectangular boxes with maximum volume. - Development of new knowledge observing the
joint evolution of two measures is not enough to
justify the introduction of functions...
18Individual and collective documentation
- Teachers belong to many 'collectives' (Gueudet
Trouche 2009), where documentation work takes
place - Under specific conditions, communities of
practice (Wenger 1998) emerge in these
collectives. - A community of practice develops a resource
system (development of the community and
development of the resource system are
simultaneous). - A complex articulation between individual and
collective geneses.
19Teachers collective work and professional
development
Teachers groups and in-service training
(Krainer Wood 2008) teams (purposely
designed), communities (self-selected), networks
(informal). Possible evolutions, from teams to
communities, from networks to communities (Wenger
1998)? Inquiry communities, gathering teachers
and didacticians (Jaworski 2004, 2008 Fuglestad
2007). Professional development, sustainable
evolutions Use of networking possibilities, to
develop distant collective work (Goos Bennison
2008, Borba Gadanidis 2008 ), to permit the
up-scaling of training programs (Cobb Smith
2008)
20Collaborative lesson design and professional
development
Pairform_at_nce, a French national project set up by
the Ministry of Education
- All disciplinary fields, primary and secondary
school - Integration of ICT following the German project
Intel Lehren - Design of training paths, providing the structure
of training device to be carried out across the
country - These training device are blended, using a
distant platform they are grounded in
collaborative lessons design.
21Collaborative lesson design and professional
development
A research and development project (Gueudet et
al. 2009, project coordinated by Luc Trouche at
INRP) Designing training paths and investigating
the collective documentation work - of training
path designers - of trainers - of
trainees. Focus on the trainees, use of elements
of the 'reflexive investigation' methodology
(logbooks, collection of resources, classroom
videos, interviews) complemented by elements
collected on the platform teachers discussions,
successive versions of files...
22Example of a training path inquiry in
mathematics with a DGE
Seven stages
23Example of a training path inquiry in
mathematics with a DGE
- Seven stages (like all the Pairform_at_nce paths)
introduction, choice of a theme, self and
co-training, design of the lesson, test of the
lesson, reflection on the lesson, evaluation of
the training. - A training over thirteen weeks, with three
face-to-face days introduction, constitution of
teams, work on the software (day 1) discussion
on inquiry in maths, preparation of the lesson
(day 2) presentation and discussion of the
lessons (day 3). - Teams with 4 teachers 2 in one school, 2 in
another. The lesson is tested and observed at
least one time. - Resources on the platform lessons examples
(studied in presence), description grid,
observation grid, software guides, research
articles - Communication via the platform forums, folders
24Example of a training path inquiry in
mathematics with a DGE
25A black-box example, reaction of the trainees
- Find the point R on D (the river) such that PRRG
is minimal. - (The solution is given by the point L)
- A black box example, presented to foster the
debate between trainees - A trainee Maths are not physics! When I
want them to investigate in geometry, I want
deductions.
26Lessons designed by the trainees
- The 9 teams (in 2008-2009) designed lessons where
the students worked on the DGE. - For 2 teams the diagram has been built by the
teacher, the students drag and observe - For 5 teams the diagram must at least be
completed - For 2 teams, the diagram intervenes in the
proof. - A shared operational invariant the dragging
of a dynamic diagram is helpful to formulate
conjectures . - The teams appreciate the cross observation, and
the observation grid provided by the trainers.
27Lessons designed by the trainees
Example of a lesson functions and
optimizationGilda Lauren, teachers in the same
school, a lesson for grade 9
- A lifeguard uses a rope and two buoys (B and C)
to form the boundary of a swimming zone. He forms
this way a rectangular zone. The length of the
rope is 160 m 16 dam. He wonders where to place
the buoys B and C to obtain a swimming zone with
the largest possible area. The point A is fixed.
28Lessons designed by the trainees
- A paper-and-pencil work
- A geometrical modelling with GeoGebra, the area
of a rectangle ABCD - A geometrical modelling with GeoGebra the trace
of a point M with coordinates (AB, area(ABCD)) - A proof on paper
29Gilda and Lauren, documentation work and teacher
knowledge
The students responsibility with the computer,
with the mathematics, stay limited. Professional
knowledge intervening in the teachers choices
(intrumentalisation) connecting different
dynamic representations supports the learning of
the concept of functions by the
students . Professional knowledge developed
during the training (beginning of a genesis)
observing the dynamic evolution of values,
while dragging a figure on a DGE helps to
conjecture properties of the figure measures
30Conclusion
- From a new context of generalized availability of
online resources to a new perspective on the
interactions between teachers and resources - - The features of the resources influence
teachers work (instrumentation), but teachers are
not passive resources users, aligning with the
designers intentions. - - Teachers develop their own documentation work,
they are the designers of their teaching
(instrumentalisation). - Along these interactions, teachers develop new
professional knowledge (geneses). - Collective lessons design a productive mode of
in-service teacher training, likely to contribute
to sustainable evolutions. - Online material to support lessons design
methodological assistance (Gueudet et al. 2008)
31Conclusion
Mathematics Curriculum Material and Teacher
Development from text to lived resources G.
Gueudet, B. Pepin L. Trouche (eds.) Springer
2011 Mathematics Education Library Table of
contents http//educmath.inrp.fr/Educmath/recherch
e/approche_documentaire/lived-resources
Need for further theoretical and methodological
developments, in the documentational perspective,
an ongoing work
32References
Adler, J. (2000). Conceptualising resources as a
theme for teacher education. Journal of
Mathematics Teacher Education, 3(3),
205224. Borba, M.C., Gadanidis, G. (2008).
Virtual communities and networks of practising
mathematics teachers, in K., Krainer T. Wood,
T. (Eds.) Participants in Mathematics Teachers
Education Individuals, Teams, Communities and
Networks (Vol. 3, pp. 181-206). Rotterdam/Taipei
Sense Publishers. Cobb, C., Confrey, J., diSessa,
A., Lehrer, R., Schauble, L. (2003). Design
Experiments in Educational Research, Educational
Researcher, 32-1, 9-13. Fugelstad, A.B. (2007).
Developing tasks and teaching with ICT in
mathematics in an inquiry community, In D.
Pitta-Pantazi G. Philippou (Eds.), Proceedings
of the Fifth Congress of the European Society for
Research in Mathematics Education (pp.1409-1418),
Larnaca, Cyprus. Gueudet, G., Soury-Lavergne, S.,
Trouche, L. (2009). Soutenir l'intégration des
TICE quels assistants méthodologiques pour le
développement de la documentation collective des
professeurs ? Exemples du SFoDEM et du dispositif
Pairform_at_nce, in C. Ouvrier-Buffet M.-J.
Perrin-Glorian (Eds.), Approches plurielles en
didactique des mathématiques (pp. 161-173).
Paris Laboratoire de didactique André Revuz,
Université Paris Diderot. Gueudet, G., Trouche,
L. (2009). Towards new documentation systems for
mathematics teachers? Educational Studies in
Mathematics 71, 199-218. Gueudet, G., Pepin, B.,
Trouche, L. (to appear). Mathematics Curriculum
Material and Teacher Development from text to
lived resources. York Springer. Guin, D.,
Ruthven, K., Trouche, L. (eds.) (2005). The
didactical challenge of symbolic calculators
turning a computational device into a
mathematical instrument. New York
Springer. Krainer, K., Wood, T. (Eds.). (2008).
Participants in Mathematics Teachers Education
Individuals, Teams, Communities and Networks
(Vol. 3). Rotterdam/Taipei Sense Publishers.
33References
Jaworski, B. (2008). Building and Sustaining
Inquiry Communities in Mathematics Teaching
Development, in K. Krainer T. Woods (Eds.),
Participants in Mathematics Teachers Education
(pp. 309-330). Rotterdam/Taipei Sense
Publishers. Rabardel, P. (1995). Les hommes et
les technologies, approche cognitive des
instruments contemporains. Paris Armand Colin
(english version at http//ergoserv.psy.univ-paris
8.fr/Site/default.asp?Act_group1 ). Remillard,
J.T. (2005). Examining key concepts in research
on teachers' use of mathematics curricula. Review
of Educational Research, 75(2), 211-246. Ruthven,
K. (2007). Teachers, technologies and the
structures of schooling. In D. Pitta-Pantazi G.
Philippou (Eds.), Proceedings of the Fifth
Congress of the European Society for Research in
Mathematics Education (pp. 52-67). Larnaca
CERME-5. Vergnaud, G. (1998). Toward a cognitive
theory of practice, in A. Sierpinska J.
Kilpatrick (eds.), Mathematics education as a
research domain a search for identity
(pp.227-241). Dordrecht Kluwer Academic
Publisher. Wenger, E., McDermott, R.A., Snyder,
W. (2002). Cultivating communities of practice a
guide to managing knowledge. Havard Business
School Press