Thinklets and TI; Technology for

Learning and Doing Mathematics

Martin van ReeuwijkFreudenthal Institute

Utrecht University, Netherlands

RMEtechnology

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 Researchback

The Dutch Math Ed Microworld

student

teacher

math teachers

teacher training preservice

teacher training in service

research

curriculumdevelopment

examination board

ministry of education

publishers

politicians

school inspectors

university

higher vocational

back

Realistic Mathematics Education

a short introduction …

Start with a context.

Realistic Mathematics Education in short

Breaking leads to fractions …

424

Realistic Mathematics Education in short

Chocolate pieces become model for fractions …

424

224 +

Realistic Mathematics Education in short

Rectangle model for operating with fractions …

34

14

Realistic Mathematics Education in short

Realistic Mathematics Education in short

Contexts, problem situations, concrete, realistic

Model of, informal, intuitive

Model for, pre-formal,

Vert

ical

math

em

ati

zati

on

Horizontal mathematization

Solving problemsGuided

reinvention

Formal mathematics, abstract, bd

bcad

d

c

b

a

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 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

Technology in Mathematics Education

• Graphing calculator APPS (applications),

TI Navigator (network) Real data collection (sensors)

(e.g. EasyData)

Technology in Mathematics Education

Technology in Mathematics Education

Technology in Mathematics Education

Models and Games Concept building, insight,

didactical• Thinklets

(Electronic) Learning Environment

Registration, integration, combination

• TI Interactive (or Maple, …)

Mathematics as an human activity;

learning and doing …thinklets

• Building houses

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 teaching-learning 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

Thinklets

a Future of Technology in

Mathematics Education

• (actual) conditions• future device

• 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

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

My telephone

Future of technology in mathematics education

More about FI, RME, Thinklets, TI

•www.thinklets.nl•www.fi.uu.nl•www.rekenweb.nl •www.wisweb.nl

•education.ti.com