1. Thinklets and TI; Technology for Learning and Doing Mathematics Martin van Reeuwijk Freudenthal Institute Utrecht University, Netherlands

2. RME technology examples the future …

3. Freudenthal Institute (FI) Research and Development of Mathematics Education Research institute at Utrecht University About 30 fulltime positions actually working about 50 staff members

4. Core activities of the FI Macro- and micro-didactic research; Curriculum development; Assessment development, comparative achievement studies (e.g. PISA); Research on and development of educational technology (ICT); Professional development and teacher education (bildung); Organization of and participation in national and international networks, conferences

5. Features and Focus Primary, secondary, and vocational education national and international projects Integrating research, development and teacher education activities Working for and with teachers: journals, conferences, courses, websites Philosophy/theory: Realistic Mathematics Education (RME) Methodology: Developmental Research back

6. The Dutch Math Ed Microworld student teacher math teachers teacher training preservice teacher training in service research curriculum development examination board ministry of education publishers politicians school inspectors university higher vocational back

7. Realistic Mathematics Education a short introduction …

8. Start with a context. Realistic Mathematics Education in short

9. Breaking leads to fractions … 4 24 Realistic Mathematics Education in short

10. Chocolate pieces become model for fractions … 4 24 2 24 + Realistic Mathematics Education in short

11. Rectangle model for operating with fractions … 3434 1414 Realistic Mathematics Education in short

12. Contexts, problem situations, concrete, realistic Model of, informal, intuitive Model for, pre-formal, Vertical mathematization Horizontal mathematization Solving problems Guided reinvention Formal mathematics, abstract,

13. Characteristics of RME Starting in contexts Building on preformal knowledge Different strategies and answers ‘Guided reinvention’ From “model of” to model for” Horizontal & vertical mathematization Intertwining learning strands Practical value Meaningful and sense making back

14. Technology in Mathematics Education different kinds different purposes

15. Technology in Mathematics Education Tools Models Games For Practice For concept development For testing, assessment Learning Environment

16. Technology in Mathematics Education Tools Graphing, solving, calculating Graphing calculator APPS (applications), TI Navigator (network of calculators) Real data collection (sensors) (e.g. EasyData for real measurements) Thinklets On-line web based, user friendly Many variations possible

17. Technology in Mathematics Education Graphing calculator APPS (applications), TI Navigator (network) Real data collection (sensors) (e.g. EasyData)

18. Technology in Mathematics Education

20. Models and Games Concept building, insight, didactical Thinklets (Electronic) Learning Environment Registration, integration, combination TI Interactive (or Maple, …)

21. Mathematics as an human activity; learning and doing …thinklets Building houses

22. What are Thinklets small computer programs that run over the internet (aka applets) can make learning mathematics more fun, more sense making, and more efficient. Easy, simple to use, user friendly Interactive, visual, dynamic Fit a mathematical topic Tested in class and improved Thinklets

23. Easy, small, feedback Frog Solving Equations Thinklets

24. Use of Thinklets Supporting instructional materials can be used, on screen or paper (worksheets) Used in various moment in the teaching- learning process: exploration, a tool, concept development (model), practice, assessment,... Thinklets

25. One or many Thinklets … Algebra arrows Thinklets

26. Add-on value of thinklets Fun and motivate students Work at own level of thinking, possible to address differences between students Visual, interactive, dynamic Focus on concept and model, applet does calculations Promotes creativity and self esteem Provides a model students can fall back on Feedback and practice are powerful Webbased: Always and everywhere available back Thinklets

27. a Future of Technology in Mathematics Education (actual) conditions future device

28. Continuous development and research Alternatives for (commercial) publishers paper with textbook series are becoming available Students want to move faster than teacher and textbook, generation gap Hardware (Internet connection) is no problem any more, always available Still transition to ICT-integrated math ed is hard Future of technology in mathematics education The conditions

29. The challenge … Handheld, easy to use On-line, web based Tool and model Multi purpose (reference guide, calculator, word processor, PDA, browser, phone, music player, camera, …) For fun (games) and school (also fun) (for TI, Casio, …) is to develop a device that is: Future of technology in mathematics education

30. My telephone Future of technology in mathematics education

31. More about FI, RME, Thinklets, TI www.thinklets.nl www.fi.uu.nl www.rekenweb.nl www.wisweb.nl education.ti.com