Challenges and choices in developing complete digital courses in upper secondary Mathematics education Cornelia Brodahl, University of Agder, Norway ICME11, Monterrey, Mexico, July , 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 pupils teachers Free and open learning and research in Norway University and colleges 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 % in 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 course author team for Mathematics 1-2 mathematicians: experienced educators, 1 with Flash competency The parAbel team 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 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 LO no. k Classification document version no. n Joint analysis Need for terms Joint discussion Classification document version n+1 LO no. k+1 Joint analysis Need for terms Joint discussion Classification document version n+2 Joint discussion  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 1.A photo collage 2.An animation, faithful to real data 3.An animation, traced and overdrawn by a curve 4.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 support from a teacher and fellow students? Multimedia and dynamic presentation of theory with 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 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 The Oracle Templates for reuse To provide a high proportion of interactivity Scoring and tracking Degree of difficulty Type of challenge …

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

14 The ParAbel Calculator

15 The ParAbel Calculator