1. Mathematics Department Marianne Moormann EDUCATIONAL FOUNDATIONS OF LEACTIVEMATH Presentation at the Kick-off meeting of the ActiveMath-EU project, Saarbrücken, 29/01/07

2. Overview Marianne Moormann, 29.01.20071 Overview Educational goals of ActiveMath Theoretical foundations Examples of the ActiveMath content

3. Educational goals of ActiveMath Marianne Moormann, 29.01.20072 Goals Learners’ autonomy Active and situated learning This is realized in ActiveMath by various interactivity options and the presentation of contents within different contexts. The learners’ autonomy is supported by the software’s non- linear structure and its flexible ways of application. Promotion of learners’ mathematical competence The content of ActiveMath provides the learners with different non-standard exercises and especially focuses on modelling and problem solving abilities.

4. Theoretical foundations Marianne Moormann, 29.01.20073 Theoretical foundations Learners’ autonomy ⇨ Mathematical literacy Active and situated learning ⇨ moderate constructivist learning approach Promotion of learners’ mathematical competence ⇨ standards-based learning

5. Theoretical foundations Marianne Moormann, 29.01.20074 Mathematical literacy "Mathematical literacy is an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgements and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen.“ (Pisa Consortium 2000) focus on “lifelong learning” Implications of the quotation: preference for methods and procedures instead of declarative facts

6. Theoretical foundations Marianne Moormann, 29.01.20075 Moderate constructivist learning approach (Mandl) Learning processes are considered to consist to a noteworthy extent of active and individual constructions of knowledge structures. This affects the roles of learners and teachers in class. The active part shifts to the learners’ side. Teachers provide learning opportunities and offer assistance. The idea of situated learning is closely related to learning from a constructivist perspective. LeActiveMath focuses at learning by doing in a real problem solving environment.

7. Theoretical foundations Marianne Moormann, 29.01.20076 Standards-based learning Educational standards draw on general educational goals. They specify the competencies that schools must impart to their students in order to achieve certain key educational goals, and the competencies that children or teenagers are expected to have acquired by a particular grade. These competencies are described in such specific terms that they can be translated into particular tasks and, in principle, assessed by tests. Educational standards thereby constitute a key mechanism in the effort to secure and improve the quality of the work done in schools. The standards can serve as a guide for schools and classroom instruction and give educators a frame of reference for their work. (Klieme expertise, 2004)

8. Theoretical foundations Marianne Moormann, 29.01.20077 Competency models Competency models translate the content and levels of general education into specific terms. They thus constitute a pragmatic response to the issues of construction and legitimisation raised in traditional debates on education and curricula (Klieme expertise, 2004)

9. Examples of ActiveMath content Marianne Moormann, 29.01.20078 A piece of content

10. Examples of ActiveMath content Marianne Moormann, 29.01.20079 One of the applets

11. Examples of ActiveMath content Marianne Moormann, 29.01.200710 Different options

12. Examples of ActiveMath content Marianne Moormann, 29.01.200711 Mastery colours

13. Thank you Marianne Moormann, 29.01.200712 Thank you for your attention! Marianne MoormannProf. Kristina Reiss moormann@math.lmu.de reiss@math.lmu.de phone: 049(0)89-2180-4563phone: 049(0)89-2180-4451 Department of Mathematics Chair of mathematics education Theresienstrasse 39 30888 Muenchen Germany http://www.mathematik.uni-muenchen.de/~didaktik/