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‘Lived resources’ and mathematics teachers professional development

Ghislaine Gueudet (IUFM de Bretagne-UBO, CREAD). ‘Lived resources’ and mathematics teachers professional development. Outline. Digital resources for mathematics teachers A documentational approach Teacher’s documentation: a case study

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‘Lived resources’ and mathematics teachers professional development

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  1. Ghislaine Gueudet (IUFM de Bretagne-UBO, CREAD) ‘Lived resources’ and mathematics teachers professional development Salamanque, September 2010

  2. Outline • Digital resources for mathematics teachers • A documentational approach • Teacher’s documentation: a case study • Collaborative lesson design and professional development • Conclusion

  3. Digital 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

  4. Digital 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...

  5. Digital 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).

  6. Digital 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...

  7. Digital 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.

  8. A documentational approach, origins • a conceptualisation of resources as anything re-sourcing the teacher’s 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)

  9. A 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)

  10. A 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 teacher’s choices and knowledge

  11. 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

  12. Teacher 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)...

  13. 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 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

  14. Myriam: Schematic Representation of the Resource System

  15. Myriam, distant work with the students Myriam’s 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)

  16. Myriam, introduction of functions Where on [AB] should be M to obtain Perimeter (CNMP)=9? Objective: introducing p(x)=x+6 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...

  17. Myriam, 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 daughter’s 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”...

  18. Individual 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.

  19. Teachers’ 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)

  20. Collaborative lesson design and professional development Pairform@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.

  21. Collaborative 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...

  22. Example of a training path: inquiry in mathematics with a DGE Seven stages

  23. 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…

  24. Example of a training path: inquiry in mathematics with a DGE

  25. A black-box example, reaction of the trainees Find 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 trainees A trainee: « Maths are not physics! […] When I want them to investigate in geometry, I want deductions. »

  26. Lessons 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.

  27. Lessons 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.

  28. Lessons 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

  29. Gilda 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 »

  30. Conclusion 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)

  31. Conclusion 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/recherche/approche_documentaire/lived-resources Need for further theoretical and methodological developments, in the documentational perspective, an ongoing work

  32. References Adler, J. (2000). Conceptualising resources as a theme for teacher education. Journal of Mathematics Teacher Education, 3(3), 205–224. 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@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.

  33. References 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-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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