Lived resources and mathematics teachers professional development Ghislaine Gueudet (IUFM de Bretagne-UBO, CREAD)
Salamanque, September 2010
Outline Digital resources for mathematics teachers A documentational approach Teachers documentation: a case study Collaborative lesson design and professional development Conclusion
Digital resources for mathematics teachersA context of generalised availability of digital resourcesSoftwareDigital textbooksOnline exercisesForumE-mailInteractive Whiteboards...Official / personal websites
Digital resources for mathematics teachersDevelopment of new forms of collaboration, the GeoGebra community: a world-wide network, communication between users, sharing resources supporting the use of GeoGebra...
Digital resources for mathematics teachersIntergeo: 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).
Digital resources for mathematics teachersOnline teacher associationsIn France, Sesamath develops free online resources:Online exercises, lesson plans, a dynamic geometry environment (Tracenpoche), digital textbooks...
Digital resources for mathematics teachersThe issue of technology integrationA 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 softwareDevelopment of new, holistic perspectives on technology integration, considering the structuring features of the classroom context (Ruthven 2007)New aspects of digital resourcesDesign 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.
A 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)
A documentational approach, originsResearch 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 utilisationScheme : a cognitive construct, comprising rules of action and structured by operational invariants
Extension of the approach: development of a documentational approach (Gueudet & Trouche 2009)
A documentational approachDocumentational 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
A 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
Teacher documentation, a case studyReflexive investigation (Gueudet & Trouche 2010): a methodology to follow teacher documentation.Long-term follow-up, collection of resourcesFollowing the teacher in-class and out-of-classThe teacher as partner in the research: logbook, representation of the resource system (SRRS)...
Teacher 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 resourcesNon digital: textbooks, overhead projector, professional papers, students productions...Digital: laptop, software, online exercises, websites, e-mail...Involvement in collectivesLocal reflection group, In-service teacher trainingPersonal environmentDiscussions with her husband (physics teacher) about the articulation between maths and physicsHer daughter in grade 10 works with the calculator, with GeoGebra
Myriam: Schematic Representation of the Resource System
Myriam, distant work with the studentsMyriams 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)
Myriam, introduction of functionsWhere on [AB] should be M to obtain Perimeter (CNMP)=9?Objective: introducing p(x)=x+6Use 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...
Myriam, introduction of functionsIntroduction 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 GeoGebraMyriam 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...
Individual and collective documentationTeachers belong to many 'collectives' (Gueudet & Trouche 2009), where documentation work takes placeUnder 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.
Teachers collective work and professional developmentTeachers 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)
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. Collaborative lesson design and professional developmentPairform@nce, a French national project set up by the Ministry of Education
Collaborative lesson design and professional developmentA 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...
Example of a training path: inquiry in mathematics with a DGESeven stages
Example of a training path: inquiry in mathematics with a DGE Seven stages (like all the Pairform@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
Example of a training path: inquiry in mathematics with a DGE
A black-box example, reaction of the traineesFind the point R on D (the river) such that PR+RG is minimal. (The solution is given by the point L)A black box example, presented to foster the debate between traineesA trainee: Maths are not physics!  When I want them to investigate in geometry, I want deductions.
Lessons designed by the traineesThe 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.
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. Lessons designed by the traineesExample of a lesson: functions and optimization Gilda & Lauren, teachers in the same school, a lesson for grade 9
A paper-and-pencil workA geometrical modelling with GeoGebra, the area of a rectangle ABCDA geometrical modelling with GeoGebra + the trace of a point M with coordinates (AB, area(ABCD))A proof on paper
Lessons designed by the trainees
Gilda and Lauren, documentation work and teacher knowledgeThe 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
ConclusionFrom 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)
ConclusionNeed for further theoretical and methodological developments, in the documentational perspective, an ongoing work
Mathematics Curriculum Material and Teacher Development: from text to lived resources
G. Gueudet, B. Pepin & L.Trouche (eds.)
Springer 2011Mathematics Education Library
Table of contentshttp://educmath.inrp.fr/Educmath/recherche/approche_documentaire/lived-resources
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ReferencesJaworski, 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-paris8.fr/Site/default.asp?Act_group=1 ). 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
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