Tools & Teachers Paul Drijvers Freudenthal Institute Utrecht University The Netherlands Fibonacci,

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)Primas The Freudenthal Institute

TOOLS & TEACHERS DME Orchestration

TOOL: FI’S DME

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)   

Content: Activities  Tasks  Animations  Links  Pictures  Video  SCORM- export

Content: range of math levels

Content: animations

Content: online courses

Authoring environment Two (or more) design levels

Feedback: example

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

Monitoring: access to student work Show

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

TEACHER: ORCHESTRATING TOOL USE

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?

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

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.

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?

Two studies I. 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 DME 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 chapter Both studies use the Digital Mathematics Environment

Case Teacher C: grade 8

Case Teacher C [clip]clip

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

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 ”

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

Orchestration table from study I

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.

Conclusion 1. 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.

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?

Literature  Bokhove, C. & Drijvers, P. (2010). Digital Tools for Algebra Education: Criteria and Evaluation. International Journal of Computers for Mathematical Learning, 15(1), 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.

Thank you! Paul Drijvers