thinklets and ti; technology for learning and doing mathematics martin van reeuwijk freudenthal...
TRANSCRIPT
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Thinklets and TI; Technology for
Learning and Doing Mathematics
Martin van ReeuwijkFreudenthal Institute
Utrecht University, Netherlands
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RMEtechnology
examples
the future …
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Freudenthal Institute (FI)
• Research and Development of Mathematics Education
• Research institute at Utrecht University
• About 30 fulltime positions actually working about 50 staff members
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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
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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
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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
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Realistic Mathematics Education
a short introduction …
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Start with a context.
Realistic Mathematics Education in short
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Breaking leads to fractions …
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Realistic Mathematics Education in short
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Chocolate pieces become model for fractions …
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224 +
Realistic Mathematics Education in short
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Rectangle model for operating with fractions …
34
14
Realistic Mathematics Education in short
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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
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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
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Technology in Mathematics Education
• different kinds• different purposes
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Technology in Mathematics Education
• Tools• Models• Games• For Practice• For concept development• For testing, assessment
• Learning Environment
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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
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Technology in Mathematics Education
• Graphing calculator APPS (applications),
TI Navigator (network) Real data collection (sensors)
(e.g. EasyData)
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Technology in Mathematics Education
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Technology in Mathematics Education
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Technology in Mathematics Education
Models and Games Concept building, insight,
didactical• Thinklets
(Electronic) Learning Environment
Registration, integration, combination
• TI Interactive (or Maple, …)
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Mathematics as an human activity;
learning and doing …thinklets
• Building houses
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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
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Easy, small, feedback
• Frog • Solving Equations
Thinklets
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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
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One or many Thinklets …
• Algebra arrows
Thinklets
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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
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a Future of Technology in
Mathematics Education
• (actual) conditions• future device
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• 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
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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
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My telephone
Future of technology in mathematics education
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More about FI, RME, Thinklets, TI
•www.thinklets.nl•www.fi.uu.nl•www.rekenweb.nl •www.wisweb.nl
•education.ti.com
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