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

Tools & Teachers

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Tools & Teachers. Paul Drijvers Freudenthal Institute Utrecht University The Netherlands Fibonacci, 22-09-2010 www.fi.uu.nl/~pauld. The Freudenthal Institute. Aims at developing, investigating and improving mathematics education at primary, secondary and tertiary level - PowerPoint PPT Presentation

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Page 1: Tools & Teachers

Tools & Teachers

Paul DrijversFreudenthal Institute Utrecht UniversityThe Netherlands

Fibonacci, 22-09-2010www.fi.uu.nl/~pauld

Page 2: Tools & Teachers

• 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., Primas FP7-Science-in-society, Edumatics)

• www.fi.uu.nl/en/

The Freudenthal Institute

Page 3: Tools & Teachers

TOOLS & TEACHERS

DME

Orchestration

Page 4: Tools & Teachers

TOOL: FI’S DME

Page 5: Tools & Teachers

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/

Page 6: Tools & Teachers

Content: Activities Tasks Animations Links Pictures Video SCORM-

export

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Content: range of math levels

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Content: animations

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Content: online courses

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Authoring environment

Two (or more)design levels

Page 11: Tools & Teachers

Feedback: example

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

Page 13: Tools & Teachers

Monitoring: access to student work

Show

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DME qualities DME scores good on feedback facilities

Bokhove, C. & Drijvers, P. (2010). Digital Tools for Algebra Education: Criteriaand Evaluation. International Journal of Computers for Mathematical Learning, 15(1), 45-62. Online First.

Page 15: Tools & Teachers

TEACHER: ORCHESTRATING TOOL USE

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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?

Page 17: Tools & Teachers

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

Didactical configuration

Exploitation mode

Didactical performance

Page 18: Tools & Teachers

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.

Page 19: Tools & Teachers

Questions

1. Which types of instrumental orchestration emerge in technology-rich classroom teaching?

2. To what extent are teachers’ repertoires of orchestrations related to their views on mathematics education and the role of technology therein?

Page 20: Tools & Teachers

Two studiesI. Tool Use in an Innovative Learning Arrangement for

Mathematics• NWO-granted small-scale design and evaluation of

an instructional sequence on the concept of function in grade 8, using an applet embedded in the electronic learning environment DMEwww.fi.uu.nl/tooluse/en

II. EPN-pilot Algebraic Skills through ICT• Publisher initiated bigger-scale pilot on algebraic

skills in grade 12, using applets in the DME, and replacing a textbook chapterhttp://www.fi.uu.nl/dwo/gr-pilot/

Both studies use the Digital Mathematics Environment

Page 21: Tools & Teachers

Case Teacher C: grade 8

Page 22: Tools & Teachers

Case Teacher C [clip]

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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

Page 24: Tools & Teachers

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 ”

Page 25: Tools & Teachers

Orchestration types Seven orchestration types identified through theory-

driven (1,3,6) as well as bottom-up analysis (2,4,5,7):1. Technical-demo2. Explain-the-screen3. Link-screen-board4. Discuss-the-screen5. Spot-and-show6. Sherpa-at-work7. Work-and-walk-by

1-2-3 teacher-centred: teacher dominates communication

4-5-6-7 student-centred: interactive communication, student input

Page 26: Tools & Teachers

Orchestration table from study I

Page 27: Tools & Teachers

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.

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Conclusion1. Which types of instrumental orchestration emerge in

technology-rich classroom teaching?

Seven orchestration types are identified, as well as their frequencies.

2. 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.

Page 29: Tools & Teachers

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?

Page 30: Tools & Teachers

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.

Page 31: Tools & Teachers

Thank you!

Paul [email protected]

www.fi.uu.nl/~pauld