ScienceMath - Mathematical literacy and cross-curricular competencies

1. ScienceMath - Mathematical literacy and cross-curricular competencies through interdisciplinary, mathematising and modelling science Wikipedia.org

2. ScienceMath is an European Cooperation-Project between universities and schools of Denmark, Finland, Slovenia and Germany to support Mathematical literacy and cross curricular competencies through interdisciplinarity, mathematising and modelling science It is supported by the European Commission.

3. Content 1 Science and Math 1.1 Project Aims: Maths through Science 1.2 The ScienceMath-Approach - Advantages 1.3 Explanation through Examples 2 Mathematical Literacy 2.1 Definition 2.2 Contribution of Science 3 Interdisciplinary Teaching 3.1 A Model 3.3 The Roof: An Evaluation Frame

4. 1 Science and Math

5. 1 Science and Math Project Aims: Math through Science Idea is to encourage mathematic learning in contexts of natural sciences and pupils´activities. Aim is thedevelopment of proven teaching sequences and –modules that lead to a comprehensive and multidimensional learning of mathematic contents and concepts. Results:The project offers concrete teaching and learning material to integrate the formal aspects of the European mathematical lessons into interdisciplinary and applicable contents.

6. 1 Science and Math The ScienceMath Approach Interdisciplinary Approach with the Natural Sciences, especially Physics - Learning Maths through scientific methods and contents

7. 1 Science and Math The ScienceMath Approach - Example Mathematics: Extremum problem The Life-Guard Problem: Physics: The Theorem of Fermat: Light moves like a perfect life-guard! Find the quickest way to the drowning person. Regard: The shortest way is not the quickest. The ScienceMath Project: Teaching-Module: Fermat meets Pythagoars

8. 1 Science and Math The ScienceMath Approach - Advantages • linked learning • learning mathematical concepts in their various aspects • learning mathematics meaningful and adequate • learning mathematics through authentic experiences and intuitive • supporting mathematical literacy Will be explained through examples of the project…

9. 1 Science and Math Authentic Experiences and intuitive mathematical understanding Example: Physical experiments and concept of function Think of sitting on a sea-saw The relation between power and power-arm is inverse proportional. You can experience it by changing your place on the sea-saw or by changing the position of the force measure at the lever. The ScienceMath Project: Teaching-Module: Functional relations 1, 2, 3

10. 1 Science and Math Learning mathematical concepts in their varous aspects Example: Concept of function and variables Heat the water. Measure the temperature every 5 minutes  Correspondence aspect Investigate the changing behavoiur  Covariance aspect The ScienceMath Project: Teaching-Module: Temperature, Thermal Expansion, also Functional relations

11. 1 Science and Math Learning mathematics meaningful and adequate Example: Horizontal Launch and Parabola function Spring gun fixed on the white board The physical experiment leads to a mathematical discussion…. The ScienceMath Project: Teaching-Module: Horizontal launch

12. 48 cm 1 Science and Math Learning mathematics meaningful and adequate … mathematical discussion: Discussing the horizonal (constant) component and the vertical (quadratic) component. The ScienceMath Project: Teaching-Module: Horizontal launch

13. 1 Science and Math Learning mathematics meaningful and adequate Example: Modelling activities Imagine a crossing Question: What is a safe duration of the yellow light? The ScienceMath Project: Teaching-Module: Traffic Modelling

14. 1 Science and Math Learning mathematics meaningful and adequate Example:Modelling activities – What is a safe duration of the yellow light? Steps • Reality: Verbal model: Describe the determining factors: • e.g. stopping distance of the car. • 2. Real model: Physical investigation: • How do the following factors influence the stopping distance? • 3. Mathematisation and mathematical model: • Simplifie the model: Regard only a few factors; • Calculation in a mathematical model; • 4. Proofing the model: Physical activities: • Measure the duration of the yellow light • and compare with the mathematical model. The ScienceMath Project: Teaching-Module: Traffic Modelling

15. 2 Mathematical Literacy

16. 2 Mathematical literacy The ScienceMath Approach – supports mathematical literacy ……

17. 2 Mathematical literacy Definition „Mathematical literacy is an individual’s capacity to identify and understand the role mathematics plays in the world, to make well-founded judgements and to use and engage with mathematics in ways, that meet the need of that individuals life as a constructive, concerned and reflective citizen.”(OECD, 2006) This includes: …* *according to Zell, S. (2009): Mathematical literacy and how scientific experiments can promote that conception. Proceedings to MACAS 3, University of Moncton, Canada

18. 2 Mathematical literacy Aspects 1Heuristic thinking which allows structured and plausible approaches that can be applied to inner and outer mathematical problems • Comprehensive understanding • of mathematical concepts and procedures • within the conceptual groups of • numbers and operations in context • functional relationships • space, shape and measurement • data handling 3Familiarity with deductive reasoning

19. 2 Mathematical literacy Science - contribution to mathematical literacy? Example: experiments Aspect: Heuristic Thinking Quantitaives Experiments contain mathematical concepts  Heuristic strategies are applied: • Inductive reasoning • Analogies • Specialisation • Decomposition and combination • Sketches • Identifying essential components It includes: Changing within inner mathematical representations, Communicating, Reflecting and Interpreting And the sensible use of aids and tools

20. 2 Mathematical literacy Science - contribution to mathematical literacy? Example: experiments Aspect: Comprehensive understanding of mathematical concepts and processes To a contribution to mathematical literacy Teaching should be in an integrative, functional and multifaced way.  Experiments fulfil this: see research results of ScienceMath

21. 2 Mathematical literacy Science - contribution to mathematical literacy? Example: experiments Aspect: Familiarity with deductive reasoning Experiments have a great potential to improve deductive reasoning: If experiments are done to confirm a hypothesis, these hypothesis were inferred deductively. If generalisations are made after the experiment, these will also involve deductive reasoning.

22. 3 Interdisciplinary Teaching

23. 3 Interdisciplinary Teaching A Model* First Definition: Cross-curricular/ interdisciplinary teaching is instruction within a field in which subject boundaries are crossed and other subjects are integrated into the teaching (how and for whatever purpose or objective) * According to Beckmann, A. (2003/2009): A Conceptual Framework for Cross-Curricular Teaching, The Montana Mathematics Enthuisiast, ISSN 1551-3440, Vol. 6, Supplement 1, pp. 1-58

24. 3 Interdisciplinary Teaching A Model There are many forms fo interdisciplinary teaching: • It could take place • only for to show a short example, • during a teaching sequence or a teaching module, • in a project • It could concern to • a subject´s theme which is enriched • by methods and contents of another subject • a common theme of different subjects • a theme which does not relate to a special subject

25. 3 Interdisciplinary Teaching A Model Interdisciplinary teaching is especially motivated by the alien-ness of the cooperating subjects. The combination of the alien aspects enrich the learning! The alien aspects can be - used - integrated - mixed.

26. 3 Interdisciplinary Teaching A Model Cooperation Forms for Cross-Curricular Lessons TM-Form Topic and Major Subject-related Form Characterisation: Aspects (contents, methods…) from scientific subjects (physics, chemistry, biology…) used in mthematics lessons. Organisation: Initiative: mathematics teacher, Communication with colleagues teaching scientific subjects, Colleagues support mathematcs teacher.

27. 3 Interdisciplinary Teaching A Model Cooperation Forms for Cross-Curricular Lessons PT-Form Parallel Topic - related Form Characterisation: Organisation: Initiative: one or more teachers, Communication and common planning of the school year or parts of it, Parallel teaching of the same theme and permanent exchange between the teachers during this period.

28. 3 Interdisciplinary Teaching A Model Cooperation Forms for Cross-Curricular Lessons PP-Form Parallel Planning Form Charac- terisation: Organisation: Initiative: one or more teachers, Permanent communication and common planning before and during teaching the module, Partly: common teaching according to the needs of the theme.

29. 3 Interdisciplinary Teaching A Model Cooperation Forms for Cross-Curricular Lessons JP-Form Joint Planning Form Characterisation and Organisation: Initiative: one or more teachers, Team teaching: All subjects melt together to one subject! Possible: project-oriented teaching with subject-oriented project parts.

30. 3 Interdisciplinary Teaching A Model* Second (detailed and summarising) Definition: Cross-curricular teaching (TM, PT) and subject-integrative instruction (PP, JP) means dealing with a (subject-related or non related) topic, In which the subject borders are exceeded and other subjects are integrated. The instruction is done in co-operation. (cross-curricular or subject-integrated) Exceeding subject borders results in contact (use, integrate, mix) with other subjects. The interest lies in an enrichment of learning in each of the subjects. * According to Beckmann, A. (2003/2009): A Conceptual Framework for Cross-Curricular Teaching, The Montana Mathematics Enthuisiast, ISSN 1551-3440, Vol. 6, Supplement 1, pp. 1-58

31. 3 Interdisciplinary Teaching The Roof – An Evaluation and Planning Frame for modules • For a quick overview teaching modules can be characterised by the roof-frame* • There are ready frames to the teaching modules (see ScienceMath-website/ volume) • While planning a module the concerning roof can be created • the roof can be basis for discussion a module (e.g. in the theme group) *Idea: Simon Zell, University of Education, Schwäbisch Gmünd

32. 3 Interdisciplinary Teaching The Roof- Example Thermic expansion and variable Organi- sation heuristic competenc. content Mathematical aspects Explanation Common aspects extra mathematical aspects Math teacher Cooperation partners Cooperation form

33. 3 Interdisciplinary Teaching The Roof- Example GPS and fair Insurance Premia heuristic Competenc. Organi- sation content Mathematical aspects Explanation Common aspects extra mathematical aspects Cooperation form Math teacher Cooperation partnres

34. More information

35. ScienceMath The Partners

36. ScienceMath – The partner institutions Mulernes´ upper secondary school, Mulernes Legatskole, www.mulerne-gym.dk University of Southern Denmark, Syddansk Universitet, www.sdu.dk

37. ScienceMath – The partner institutions Diocesan Classical Gymnasium at St. Stanislav Institute, Slovenia, Zavod sv. Stanislava, Skofijska klasicna gimnazija, ww w.skg-stanislav.si University of Ljubljana, Univerza v Ljubljana, www.uni-lj.si

38. ScienceMath – The partner institutions Turku University, Turun Yliopisto, www.utu.fi Turku teacher-training school, primary and secondary school, Turun Normaalikoulu, www.tnk.utu.fi

39. ScienceMath – The partner institutions Staufer-comprehensive secondary school, Staufer Gymnasium Waiblingen,www.stg.wn.schule-bw.de University of Schwäbisch Gmünd, Pädagogische Hochschule Schwäbisch Gmünd www.ph-gmuend.de, Coordinator

40. ScienceMath – The Website All Modules: www.sciencemath.ph-gmuend.de This project has been funded with support from the European Commission. This publication reflects the views only of the author(s), and the Commission cannot be held responsible for any use which may be made of the information contained therein.

41. ScienceMath Now: Chose a module, a theme or a group for your professional development! Thank You!