the dme, designing mathematics education in a digital ... · the dme, designing mathematics...
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The DME, designing mathematics education in a
digital environment
From tools to rich integrated digital learning environments
Peter Boon
Freudenthal Institute
Faculty of Science
Utrecht University
Netherlands
04.03.10
www.fi.uu.nl/en/
Central question in the DME-project (and former projects on digital
education):
How can digital resources improve mathematics education?
How can digital resources improve mathematics education?
Research Design
How can digital resources improve mathematics education? A Design-Research approach
Design of tools and activities
Research
Research
research
research
20002000 20112000 11 years
Technology
New possibilities
Math education
Existing practiceLearning objectives
How to use?
Video / audio
Animations
Feedback features
Game features / scores
Dynamic interactions
Constructions possibilities
“Virtual reality”
…….
Technology
New possibilities
Math education
Existing practiceLearning objectives
Educational Software design
• to serve existing practice
• to inspire with new ideas
Technology
New possibilities
Math education
Existing practiceLearning objectives
Educational Software design
• to serve existing practice• to inspire with new ideas
Aiming on add-on value compared with other resources
Important Choices for Math Education in the Netherlands (Freudenthal, 1970’s):
Mathematics is a Human Activity and should not be
presented to learners as a finished, formal construct.
Math Education should go the way of (guided) re-
invention and re-construction
Own productions (strategies) of students are important
indicators for teaching and do stimulate a problem
solving (and posing) attitude
activities
(x-2)2 = x2 - 4x + 4
2 + 3 = 542 : 7 = 62/5 + 2/7 = 24/35
Meaningfull situations/problems
Formalmathematical
language
Models/reprentations
Iceberg Metaphor
Equations
3x+1=x+5
Quadratics
3x(x+2)=2x2+6x
Functions
x (x-3)2
Derivative
Separate concepts, or…..
… a connected body of knowledge.
Connections
We started with (small) applets
Technical viewpoint:
Internet-based Java programs,
Java is an advanced programming language
User viewpoint
Accessible software
No installation needed
Educational designer viewpoint:
Flexible ICT units for educational materials,
can be combined with other e-content
Can relatively easy be adapted in the design
process
Applets
Applet-worksheets
Applet sequences
Lessons
Digital modules
Digital curricula?
Applets
Applet+task
Applet sequences
Lessons
Digital modules
Digital curricula?
Applets
LMS-software
CMS-software
Authoring-software
Software needed Intended educational unit
Applets
Applet+task
Applet sequences
Lessons
Digital modules
Digital curricula?
Applets
LMS-software
CMS-software
Authoring-software
Software needed Intended educational unit
DME
June 8, 2011
Research
Embedded technological tools for mathematics: the Digital Mathematics Environment
June 8, 2011
Research
Embedded technological tools for mathematics: the Digital Mathematics Environment
June 8, 2011
Research
Embedded technological tools for mathematics: the Digital Mathematics Environment
June 8, 2011
Research
Embedded technological tools for mathematics: the Digital Mathematics Environment
June 8, 2011
Research
Teachers’ access to student work and results
June 8, 2011
Research
Authoring and educational design possibilities in the Digital Mathematics Environment
Applets
Applet-worksheets
Applet sequences
Lessons
Digital modules
Digital curricula?
How can digital resources improve mathematics education?
Research Design
How can digital resources improve mathematics education?
Research Design
How can digital resources improve mathematics education? A Design-Research approach
Design of tools and activities
Research
Research
research
research
2000 201010 years2000 201010 years2000 201010 years
Funds for running the project
Funded projects
Subscriptionsschools
Funded projects
Textbookpublishers
2000 201010 years
Technology
New possibilities
Math education
Existing practiceLearning objectives
How to use?
Video / audio
Animations
→ Feedback features
→ Game features / scores
→ Dynamic interactions
→ Construction possibilities
“Virtual reality”
…….
Applets sequences Modules worksheets Lessons
10 years10 years2000 201010 years
10 years10 years2000 201010 years
Applets
LMS
CMSAuthoring tools
Realistic Mathematics Education (RME)
Students can build up their own math. knowledge,
starting with meaningfull problems
instead of
Learning algoritmes and rules without
connections with students present knowledge
New possibilities
Design:
Ed. materials (educ. software)
• technology
• didactics
Interaction
Design of tools and activities
Research
Research
research
research
Knowledge
Impact on Educational
practice
Knowledge
Knowledge
Knowledge
Design of tools and activities
Research
Research
research
research
Knowledge
Products
Knowledge
Knowledge
Knowledge
SUMMARY
This presentation is about designing internet-based software for mathematics education, especially the use of the internet as a mature and versatile environment for learning mathematics.
We will start by looking at features and principles that make digital learning activities stand out in comparison with paper materials. We will consider not just feedback issues, but will also focus on design principles for activities that offer students help in discovering and visualizing mathematical concepts. In addition we will focus on requirements and design issues that make a digital environment a true working environment for studying and teaching longer learning trajectories or even curricula.
New possibilities
Visualisations / audio
Animations
Directe feedback
Game features / scores
All kind of interactions
Constructions possibilities
“Virtual reality”
…….