Cornelia Brodahl, University of Agder, Norway cornelia.brodahl@uia.no

1. Challenges and choicesin developing complete digital courses in upper secondary Mathematics education Cornelia Brodahl, University of Agder, Norwaycornelia.brodahl@uia.no ICME11, Monterrey, Mexico, July 6 - 13, 2008

2. A Strategy of Joint Promotion MST of Mathematics, Science and Technology Facts on education in Norway • 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 life’s 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 mathematicians:experienced educators,1 with Flash competency The project’s 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. Jointdiscussion Classificationdocumentversion no. n Needfor terms LOno. k Jointanalysis Jointdiscussion Classificationdocumentversion n+1 LOno. k+1 Jointanalysis Needfor terms Classificationdocumentversion n+2 Joint discussion 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 sun’s 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 learner’s 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 learner’s 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 -> 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