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Title: Challenges and choices in developing complete digital courses in upper secondary Mathematics education


1
Challenges and choicesin developing complete
digital courses in upper secondary Mathematics
education
  • Cornelia Brodahl, University of Agder,
    Norwaycornelia.brodahl_at_uia.no

ICME11, Monterrey, Mexico, July 6 - 13, 2008
2
Facts on education in Norway
A Strategy of Joint Promotion MST of
Mathematics, Science and Technology
  • Failing interest and recruitment to university
    studies of mathematics, science and technology
    (MST)
  • Recruitment to MST is a major challenge
  • Need of
  • Covering the society and working lifes needs
    strengthened.
  • MST Competency in primary and lower secondary
    education.
  • More students choosing depth studies in upper
    secondary education.
  • More students in MST programmes in higher
    education.
  • Researchers and developers with necessary
    competency.

The percentage of graduates from upper secondary
education with a MST orientation in 1994 and
2003 Published by The Ministry of Education and
Research, 2006.
3
Facts on education in Norway
  • Population
  • 4.5 mill.
  • Ongoing education
  • 0.9 mill. young
  • 1.0 mill. in adult education courses
  • Educational level
  • 45 have upper secondary education
  • 26 have higher education
  • Upper secondary level
  • 550 schools
  • 164 200 pupils
  • 22 100 teachers
  • Free and open learning and research in Norway
  • University and colleges
  • 170 000 students
  • ICT in Education
  • By 2008, ICT shall be an integrated tool at all
    levels in Norwegian education
  • The use of ICT resources is one strategy to
    achieve recruitment to MST

4
The resources
  • Set out from the mathematics to be learned and
    presents it in a logical and accessible fashion
  • Are organized as interactive textbooks in a LMS
  • Provide chapters and sections with
  • theory and examples
  • small exercises
  • simulations
  • extension exercises
  • summary
  • Promote subjects in different and interactive
    ways
  • learning objects
  • step-by-step-explanations/instructions
  • formative assessment exercises
  • animations providing links to real life

Registered schools 30 in 2005 50 in 2008
www.parabel.no
demo
5
Why parAbel?
  • The use of ICT resources is one strategy to
    achieve recruitment to MST
  • To meet the claim of using digital tools in
    education (new curriculum)
  • Uses ICT-medium where it is suitable for learning
    through interactivity and visualization.
  • Pupils can work with Mathematics at their own
    level and at their own pace.
  • Adapted teaching - differentiation through
    exercises with different degree of difficulty
  • Use in classroom
  • animations to illustrate mathematical ideas and
    concepts
  • extra exercises, workbook
  • motivation, variation
  • individual or group work

6
The parAbel team
  • The course author team
  • for Mathematics
  • 1-2 mathematiciansexperienced educators,1 with
    Flash competency

The projects development and administration model
7
The constructivist principle
  • Cognitive and social constructivist thinking
  • Embracing new possibilities for making subjects
    attractive and engaging.
  • Creating learning objects to motivate
  • engagement
  • activity
  • reflection
  • sustained engagement

8
Developing Learning Objects (LO)
  • Starting point is the Mathematics Curriculum
  • Brainstorming for ideas to learning objects
  • Studying the literature for mathematical teachers
  • Studying the material of examples
  • Frequently evaluating learning objects
  • in a symbiotic activity related to research in
    the field of learning objects
  • Synopsis / functional specification
  • Cycle of programming

9
Example The suns path
  • Wanted visualizing the sine function by a real
    life graphic
  • From idea to realization
  • A phenomena well known to Norwegian students
  • Discussed in a Norwegian journal for Mathematics
    Education
  • A photo collage
  • An animation, faithful to real data
  • An animation, traced and overdrawn by a curve
  • A function plotter for sine curves to model the
    curve
  • The ideal use of the learning object
  • to experience and discuss aspects of the sine
    function concept

10
Serving different types of learners
  • Learners in classroom
  • Good teachers would carefully prepare for
    demonstration and dialogue with the students
  • Lone learners and distributed learners
  • How to compensate for the lack of supportfrom a
    teacher and fellow students?
  • Multimedia and dynamic presentation of
    theorywith graphical animations
  • Multi-step interactive explanations and exercises
  • High ratio of self-assessment exercises intended
    to challenge the learners beliefs
  • Non-trivial choices
  • Relating algebraic theorems to geometry
  • The Binomial theorem for n equal to 2
  • Development of a formula

11
Extending interactivity
Templates for reuse
  • Goal Rich and complex interactive learning
    objects
  • Concern for quantity and developmental effort
  • A balance between
  • Developing one-of-a-kind artifacts
  • pedagogical interactivity
  • providing content dialogue and interaction on
    the learners initiative
  • Using built-in learning templates in LMS
  • Using built-in learning templates in Flash
  • Reuse of user-made Flash templates/elements

To provide a high proportion of interactivity
The Oracle
Degree of difficulty
Type of challenge
Scoring and tracking

12
Further work
  • Make the resources richer
  • More courses. Vg1P primo January
  • Teacher courses
  • Formative evaluation (en extensive work to do)
  • Pedagogical and mathematical didactical analysis
  • LMS -gt Web 2.0
  • Collaboration with Chinese developers

13
Hilsen
Thank you for your attention
http//home.uia.no/cornelib/icme11
14
The ParAbel Calculator
15
The ParAbel Calculator
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