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  1. Tools & Teachers Paul Drijvers Freudenthal Institute Utrecht University The Netherlands Fibonacci, 22-09-2010 www.fi.uu.nl/~pauld

  2. The Freudenthal Institute • Aims at developing, investigating and improving mathematics education at primary, secondary and tertiary level • Aims at intertwining research, design, professional development and implementation • Is the Dutch National Expertise Centre of Mathematics Education • Has wide international scope, including FP7 (e.g., PrimasFP7-Science-in-society, Edumatics) • www.fi.uu.nl/en/

  3. DME Orchestration Tools & teachers

  4. Tool: FI’s DME

  5. Tools: the digital math environment • FI’s Digital Mathematics Environment DME: • Content (applets, SCORM) • Authoring environment (including design of Feedback) • Monitoring and administration system (LMS, CMS, including log facilities) • www.fi.uu.nl/dwo/en/ • www.wisweb.nl • www.fi.uu.nl/dwo/prootool/en/

  6. Content: Activities • Tasks • Animations • Links • Pictures • Video • SCORM- export

  7. Content: range of math levels

  8. Content: animations

  9. Content: online courses

  10. Authoring environment Two (or more)design levels

  11. Feedback: example

  12. Feedback: design • Design choice: use built-in feedback or customize/design

  13. Monitoring: access to student work Show

  14. DME qualities • DME scores good on feedback facilities • Bokhove, C. & Drijvers, P. (2010). Digital Tools for Algebra Education: Criteria • and Evaluation. International Journal of Computers for Mathematical Learning, 15(1), 45-62. Online First.

  15. Teacher: orchestrating tool use

  16. Teachers are crucial! • High expectations concerning the integration of technology into mathematics education have not yet come true. • Growing awareness that teachers are crucial in the integration of technology into mathematics education (Gueudet & Trouche 2009, Lagrange & Monaghan 2009, Lagrange & Ozdemir Erdogan 2009, Maracci & Mariotti 2009, Pierce & Ball 2009, Ruthven, Deaney & Hennessy 2009) • Issue at stake: what do teachers do when they integrate technology in their teaching and why do they do so?

  17. Didactical performance Exploitation mode Didactical configuration Theoretical lens: orchestration • Instrumental orchestration as a model for analysing teacher activity (Trouche, 2004) • An instrumental orchestration: the teacher’s intentional and systematic organisation and use of the various artefacts available in a learning environment in a given mathematical task situation, in order to guide students’ instrumental genesis. • An instrumental orchestration: • a didactical configuration • an exploitation mode • a didactical performance

  18. A symphony orchestra conductor? Rather a jazz band leader... Trouche, L. & Drijvers, P. (2010). Handheld technology: Flashback into the future. ZDM, The International Journal on Mathematics Education. Online First.

  19. Questions Which types of instrumental orchestration emerge in technology-rich classroom teaching? To what extent are teachers’ repertoires of orchestrations related to their views on mathematics education and the role of technology therein?

  20. Two studies • Tool Use in an Innovative Learning Arrangement for Mathematics • NWO-grantedsmall-scale design and evaluation of an instructionalsequence on the concept of function in grade 8, using an applet embedded in the electronic learning environment DMEwww.fi.uu.nl/tooluse/en • EPN-pilot AlgebraicSkillsthrough ICT • Publisher initiatedbigger-scale pilot on algebraicskillsin grade 12, using applets in the DME, and replacing a textbookchapterhttp://www.fi.uu.nl/dwo/gr-pilot/ Both studies use the Digital Mathematics Environment

  21. Case Teacher C: grade 8

  22. Case Teacher C [clip]

  23. Case Teacher C • Orchestration type: Technical-demo • Didactical configuration:Teacher computer connected to the interactive whiteboard. Students in ‘traditional setting’ • Exploitation mode: Students listen and watch the teacher’s demonstration of applet technique • Didactical performance:Teachers remains seated and does not use the facilities of the IAW

  24. Teacher C’s profile Teacher C... • prioritizes teacher-centred orchestrations • finds clear explanations and instructions important • has a concern for student difficulties when learning mathematics, and when using technology ”As a teacher, one has to tell students clearly what they should do with ICT”

  25. Orchestration types • Seven orchestration types identified through theory-driven (1,3,6) as well as bottom-up analysis (2,4,5,7): • Technical-demo • Explain-the-screen • Link-screen-board • Discuss-the-screen • Spot-and-show • Sherpa-at-work • Work-and-walk-by • 1-2-3 teacher-centred: teacher dominates communication • 4-5-6-7 student-centred: interactive communication, student input

  26. Orchestration table from study I

  27. Orchestration table from study II Drijvers, P. (submitted). Teachers transforming resources into orchestrations. In Gueudet, G., Pepin, B., & Trouche, L. (Eds.), Mathematics Curriculum Material and Teacher Development: from text to lived resources? (pp. - ). New York/Berlin: Springer.

  28. Conclusion • Which types of instrumental orchestration emerge in technology-rich classroom teaching? Seven orchestration types are identified, as well as their frequencies. • To what extent are teachers’ repertoires of orchestrations related to their views on mathematics education and the role of technology therein? The teacher profiles suggest a clear relationship between orchestrations and views.

  29. Reflection • How general are the orchestration types, to other topics, to other types of technology, to other forms of teaching, to other pedagogical paradigms such as IBsme, … ? • Why such a preference for individual orchestrations in Study II? Do teachers feel that they should step back as soon as technology enters the classroom? • What are possible implications for teachers’ professional development concerning ‘TPACK’? And for ‘T-IB PACK’ • What does the model of instrumental orchestration offer? A fruitful framework for analysing teachers’ practices when teaching mathematics with technological tools?

  30. Literature • Bokhove, C. & Drijvers, P. (2010). Digital Tools for Algebra Education: Criteria and Evaluation. International Journal of Computers for Mathematical Learning, 15(1), 45-62. Online First. • Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool: whole-class teaching behavior in the technology-rich mathematics classroom. Educational Studies in Mathematics. Online First. • Drijvers, P. (submitted). Teachers transforming resources into orchestrations. In Gueudet, G., Pepin, B., & Trouche, L. (Eds.), Mathematics Curriculum Material and Teacher Development: from text to lived resources? (pp. - ). New York/Berlin: Springer. • Trouche, L. & Drijvers, P. (2010). Handheld technology: Flashback into the future. ZDM, The International Journal on Mathematics Education. Online First.

  31. Thank you! Paul Drijvers p.drijvers@uu.nl www.fi.uu.nl/~pauld