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 educationwith 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 course author teamfor 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 CurriculumStarting point is the Mathematics Curriculum

Brainstorming for ideas to learning objectsBrainstorming 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

LOno. k

Classificationdocument

version no. n

Jointanalysis

Need

for terms

Jointdiscussion

Classificationdocument

version n+1

LOno. k+1

Jointanalysis

Needfor terms

Jointdiscussion

Classificationdocument

version n+2

Jointdiscussion

Synopsis / functional Synopsis / functional specificationspecification

Cycle of programmingCycle 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 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

• 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 reuseTemplates for reuse

To provide a high proportion of interactivity

Scoring and tracking

Degree of difficulty

Type o

f ch

alle

nge

…

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 attentionThank you for your attention

http://home.uia.no/cornelib/icme11

14

The ParAbel Calculator

15

The ParAbel Calculator