Thinklets and TI Technology for Learning and Doing

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

RME technology examples the future …

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

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

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

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

Realistic Mathematics Education a short introduction …

Realistic Mathematics Education in short Start with a context.

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

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

Realistic Mathematics Education in short 1 4 3 4 Rectangle model for operating with fractions …

Realistic Mathematics Education in short Vertical mathematization Formal mathematics, abstract, Model for, pre-formal, Model of, informal, intuitive Guided reinvention Horizontal mathematization Contexts, problem situations, concrete, realistic Solving problems

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

Technology in Mathematics Education • different kinds • different purposes

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

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

Technology in Mathematics Education • Graphing calculator n APPS (applications), TI Navigator (network) n Real data collection (sensors) (e. g. Easy. Data)

Technology in Mathematics Education

Technology in Mathematics Education

Technology in Mathematics Education Models and Games Concept building, insight, didactical • Thinklets n (Electronic) Learning Environment Registration, integration, combination • TI Interactive (or Maple, …) n

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

Thinklets 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 Easy, small, feedback • Frog • Solving Equations

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

Thinklets One or many Thinklets … • Algebra arrows

Thinklets 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

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

Future of technology in mathematics education The conditions • 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 challenge … (for TI, Casio, …) is to develop a device that is: 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) • •

Future of technology in mathematics education My telephone

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