ScienceMath-

Mathematical literacy and cross-curricular competencies

through interdisciplinary, mathematising and modelling

science

Wikipedia.org

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.

ScienceMath

Content

1 Science and Math1.1 Project Aims: Maths through Science1.2 The ScienceMath-Approach - Advantages1.3 Explanation through Examples

2 Mathematical Literacy2.1 Definition2.2 Contribution of Science

3 Interdisciplinary Teaching3.1 A Model 3.3 The Roof: An Evaluation Frame

1 Science and Math

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 the development 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.

1 Science and Math

The ScienceMath Approach

Interdisciplinary Approach with the Natural Sciences, especially Physics

- Learning Maths through scientific methods and contents

1 Science and Math

The ScienceMath Approach - Example

The Life-Guard Problem:

Q

u

w

50m 50m

50m

H

Find the quickest way to the drowning person.Regard: The shortest way is not the quickest.

Mathematics: Extremum problem

Physics: The Theorem of Fermat:Light moves like a perfect life-guard!

The ScienceMath Project: Teaching-Module: Fermat meets Pythagoars

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…

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

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

1 Science and Math

Learning mathematics meaningful and adequate

Example: Horizontal Launch and Parabola function

The physical experiment leads to a mathematical discussion….

Spring gunfixed on the white board

The ScienceMath Project: Teaching-Module: Horizontal launch

1 Science and Math

Learning mathematics meaningful and adequate

48 cm

… mathematical discussion:

Discussing the horizonal (constant) component and the vertical (quadratic) component.

The ScienceMath Project: Teaching-Module: Horizontal launch

1 Science and Math

Learning mathematics meaningful and adequate

Example: Modelling activities

The ScienceMath Project: Teaching-Module: Traffic Modelling

Imagine a crossing

Question:What is a safe durationof the yellow light?

1 Science and Math

Learning mathematics meaningful and adequate

Example: Modelling activities – What is a safe duration of the yellow light?

The ScienceMath Project: Teaching-Module: Traffic Modelling

Steps1. 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.

2 Mathematical Literacy

2 Mathematical literacy

The ScienceMath Approach –

supports mathematical literacy ……

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

2 Mathematical literacy

Aspects

1 Heuristic thinking which allows structured and plausible approachesthat 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

3 Familiarity with deductive reasoning

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 InterpretingAnd the sensible use of aids and tools

2 Mathematical literacy

Science - contribution to mathematical literacy?

Example: experiments

Aspect: Comprehensive understanding of mathematical concepts and processes

To a contribution to mathematical literacyTeaching should be in an integrative, functional and multifaced way.

Experiments fulfil this: see research results of ScienceMath

2 Mathematical literacy

Science - contribution to mathematical literacy?

Example: experiments

Aspect: Familiarity with 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.

Experiments have a great potential to improve deductive reasoning:

3 Interdisciplinary Teaching

3 Interdisciplinary Teaching

A Model*

* 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

First Definition:Cross-curricular/ interdisciplinary teaching is instruction within a field in which subject boundaries are crossedand other subjects are integrated into the teaching(how and for whatever purpose or objective)

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

3 Interdisciplinary Teaching

A Model

Interdisciplinary teaching is especially motivatedby the alien-ness of the cooperating subjects.The combination of the alien aspects enrich the learning!

The alien aspects can be - used- integrated- mixed.

3 Interdisciplinary Teaching

A Model

Cooperation Forms for Cross-Curricular Lessons

TM-FormTopic 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.

3 Interdisciplinary Teaching

A ModelCooperation Forms for Cross-Curricular Lessons

PT-FormParallel 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.

3 Interdisciplinary Teaching

A Model Cooperation Forms for Cross-Curricular Lessons

PP-FormParallel Planning Form

Charac-terisation:

Organisation: Initiative: one or more teachers,Permanent communication and common planningbefore and during teaching the module,Partly: common teaching according to the needs of the theme.

3 Interdisciplinary Teaching

A ModelCooperation Forms for Cross-Curricular Lessons

JP-FormJoint 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.

3 Interdisciplinary Teaching

A Model*

* 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

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.

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

3 Interdisciplinary Teaching

The Roof - Example

Mathematical aspects

Common aspects

contentheuristiccompetenc.

Organi-sation

extra mathematicalaspects

Explanation

Math teacher

Cooperation form

Cooperation partners

Thermic expansion and variable

3 Interdisciplinary Teaching

The Roof - Example

contentheuristicCompetenc.

Explanation

Organi-sationMathematical aspects

Common aspects

extra mathematicalaspects

Math teacher

Cooperation partnres

Cooperation form

GPS and fair Insurance Premia

More information

ScienceMath

The Partners

ScienceMath – The partner institutions

University of Southern Denmark,Syddansk Universitet,www.sdu.dk

Mulernes´ upper secondary school, Mulernes Legatskole,www.mulerne-gym.dk

ScienceMath – The partner institutions

University of Ljubljana, Univerza v Ljubljana,www.uni-lj.si

Diocesan Classical Gymnasium at St. Stanislav Institute, Slovenia, Zavod sv. Stanislava, Skofijska klasicna gimnazija,ww w.skg-stanislav.si

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

ScienceMath – The partner institutions

University of Schwäbisch Gmünd, Pädagogische Hochschule Schwäbisch Gmünd www.ph-gmuend.de,

Staufer-comprehensive secondary school, Staufer Gymnasium Waiblingen,www.stg.wn.schule-bw.de

Coordinator

ScienceMath – The Website

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.

All Modules:

ScienceMath

Now: Chose a module, a theme or a group for your professional development!

Thank You!