‘lived resources’ and mathematics teachers professional development

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Salamanque, September 20 10 ‘Lived resources’ and mathematics teachers professional development Ghislaine Gueudet (IUFM de Bretagne-UBO, CREAD)

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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 - PowerPoint PPT Presentation

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Page 1: ‘Lived resources’ and mathematics teachers professional development

Salamanque, September 2010

‘Lived resources’ and mathematics teachers professional development

Ghislaine Gueudet (IUFM de Bretagne-UBO, CREAD)

Page 2: ‘Lived resources’ and mathematics teachers professional development

Outline

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

Page 3: ‘Lived resources’ and mathematics teachers professional development

Digital resources for mathematics teachers

A context of generalised availability of digital resourcesSoftwareDigital textbooksOnline exercisesForumE-mailInteractive Whiteboards...Official / personal websites

Page 4: ‘Lived resources’ and mathematics teachers professional development

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...

Page 5: ‘Lived resources’ and mathematics teachers professional development

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).

Page 6: ‘Lived resources’ and mathematics teachers professional development

Digital resources for mathematics teachers

Online teacher associationsIn France, Sesamath develops free online resources:Online exercises, lesson plans, a dynamic geometry environment (Tracenpoche), digital textbooks...

Page 7: ‘Lived resources’ and mathematics teachers professional development

Digital resources for mathematics teachers

The 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.

Page 8: ‘Lived resources’ and mathematics teachers professional development

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)

Page 9: ‘Lived resources’ and mathematics teachers professional development

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 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)

Page 10: ‘Lived resources’ and mathematics teachers professional development

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

Page 11: ‘Lived resources’ and mathematics teachers professional development

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

Page 12: ‘Lived resources’ and mathematics teachers professional development

Teacher documentation, a case study

Reflexive 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)...

Page 13: ‘Lived resources’ and mathematics teachers professional development

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

Page 14: ‘Lived resources’ and mathematics teachers professional development

Myriam: Schematic Representation of the Resource System

Page 15: ‘Lived resources’ and mathematics teachers professional development

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)

Page 16: ‘Lived resources’ and mathematics teachers professional development

Myriam, introduction of functions

Where 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...

Page 17: ‘Lived resources’ and mathematics teachers professional development

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 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”...

Page 18: ‘Lived resources’ and mathematics teachers professional development

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.

Set of resourcesTeachers (collective, community?)

InstrumentationInstrumentalization

Documents: combined resources + schemes of utilization

Special organization

For a given class of situations, through different contexts

Page 19: ‘Lived resources’ and mathematics teachers professional development

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)

Page 20: ‘Lived resources’ and mathematics teachers professional development

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 development

Pairform@nce, a French national project set up by the Ministry of Education

Page 21: ‘Lived resources’ and mathematics teachers professional development

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...

Page 22: ‘Lived resources’ and mathematics teachers professional development

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

Seven stages

Page 23: ‘Lived resources’ and mathematics teachers professional development

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…

Page 24: ‘Lived resources’ and mathematics teachers professional development

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

Page 25: ‘Lived resources’ and mathematics teachers professional development

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 traineesA trainee: « Maths are not physics! […] When I want them to investigate in geometry, I want deductions. »

Page 26: ‘Lived resources’ and mathematics teachers professional development

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.

Page 27: ‘Lived resources’ and mathematics teachers professional development

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 trainees

Example of a lesson: functions and optimizationGilda & Lauren, teachers in the same school, a lesson for grade 9

Page 28: ‘Lived resources’ and mathematics teachers professional development

-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

Lessons designed by the trainees

Page 29: ‘Lived resources’ and mathematics teachers professional development

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 »

Page 30: ‘Lived resources’ and mathematics teachers professional development

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)

Page 31: ‘Lived resources’ and mathematics teachers professional development

Conclusion

Need 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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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.

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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