M athematics in A ction Communalities across differences Mieke van Groenestijn Florence, 6 September 2007.

Mathematics in Action

Communalities across differences

Mieke van Groenestijn

Florence, 6 September 2007


A Grundtvig-1 Project (2004-2007)

Denmark (project Manager)Hungary

LithuaniaNetherlands

NorwaySlovenia

Spain


Aims

1. Improvement of learning of adults, in particular concerning mathematics /numeracy

2. Professional development of teachers in adult education

3. Awareness of the importance of numeracy


Focus in MiA

1. Learning and doing mathematics in such a way that adults really can experience the usefulness of mathematics in actual real life situations

2. Differences between learning in school and learning in real life situations

3. Teacher training in teacher education and in settings for professional development or in service training


Process and Results

Examples of good practiceSome relevant background theoryA common way of working in practiceSetup of MiA Teacher Workshops (Professional Development)Handbook


Research questions

Concerning learning1. Why do adults come back to school?2. What do they want to learn?3. How do they learn best?

EMMA, Florence, 6 Sept 2007


Research questions

Concerning teaching:1. Why do we teach adults in adult learning centers?2. What do we teach?3. What can be the meaning of an adult learning center for learning in practice, in out-of-school situations?4. How can we arrange a situation in which the adult learning center can be a center for transfer of learning in a school situation to learning in an out-of-school situation?


Research questions

In general:1. How can we challenge adults to learn more about mathematics in an out-of-school situation? 2. What role can an adult learning center play in supporting and coaching learning mathematics in out-of-school situations?



Examples of good practice

Denmark - Learning math on the work floorSpain - Dialogical LearningNetherlands - Learning in practice based on Problem Solving



Rationale underlying math courses at the work place

1. learners feel at home2. work place situations and materials are available3. employers are motivated to support4. math courses at the work place is included in the national

programme ‘preparatory adult education – mathematics



Principles for math courses at the work place

1. cooperation between teacher and learners2. use of materials from work place and learners’ life3. use of concrete materials4. investigations of topical mathematical problems5. development of usable algorithms6. learners’ needs, interests and experiences are fundamental7. becoming aware of math in everyday life is one of the goals



Adult Learning Starting points

1. Adults are free to learn2. Learning often happens in a functional situation3. Learning in practice is characterized by learning through

authentic materials4. Every learning situation is a socio-cultural determined

situation5. Learning focuses on ‘shared cognition’ rather than

‘individual cognition’6. Learning often happens via showing - imitating –

participating and applying earning often happens in a functional situation



Paulo Freire – Dialogical Learning (Spain)

Egalitarian dialogueCultural intelligenceTransformationInstrumental dimensionMeaning creationSolidarityEquality of differences



Paulo Freire – Learning through experiences (NL)

The learner decides on the actual programLearning from and through experiencesMutual learning and teachingEducation and schooling in mutual relation



Problem Solving – six steps (NL)

1. Bring the learner in a potential mathematical situation2. Identify problems in the situation3. Plan the problem solving procedure4. Solve the problem5. Check the result6. Review the process. What did the learner learn?

(MvG – 2002)



Relevant Literature

Paul Ernest (…) Transfer of InformationFreire: Dialogical Learning Greeno et al (1999) “Learning in and for Participation in Work and

Society”Learning in practice (MvG, 2002)



Paul Ernest - Transfer of knowledge

1. Applications Perspective:Transfer of learning is application: applying general knowledge in specific concrete situations through modeling

2. Cognitivist Perspective:Transfer of learning from one set or type of tasks to another – the transfer is disembedded knowledge

3. Problem Solving Perspective (constructivist):Transfer of learning from one situation to another through transport of personal transferable skills (with a person)

4. Situated Cognition Perspective (social theorists)Transfer of learning from one social context to another through the development of new capacities and facets of self



Problem solving Perspective

- self-management- learning skills- communication skills- teamwork skills- problem- solving- data-handling skills



James Greeno – points for discussion

1. Learning is fundamental to and a natural part of human activity- Learning in a classroom setting is artificial. It is a not-natural situation. Adults learn best in actual real-life situations.

2. Learning, motivation and activity are not separable- If adults don’t see the need for learning (e.g. a particular subject) then they may not be motivated to learn

3. Adults don’t learn just to do but to become4. Learning in practice is based on shared knowledge

- Learning in school often focuses on individual knowledge5. Learning is often situation-based and situation-bound

Greeno at al (1998)



Problem Solving – six steps (NL)

1. Bring the learner in a potential mathematical situation2. Identify problems in the situation3. Plan the problem solving procedure4. Solve the problem5. Check the result6. Review the process. What did the learner learn?

(MvG – 2002)



Six steps in practice - some experiences

DenmarkHungaryNetherlandsSpain



MiA Teacher Workshop (MTW) - Goals

• Enhance the expertise of mathematics/numeracy teachers in adult education in general

• Create a common basis for communication between mathematics/numeracy teachers in adult education in European countries

• Improve the quality of adult mathematics/numeracy education in Europe by developing common starting points in different European countries

• Improve the success rate of mathematics/numeracy courses in Europe in general



MiA Teacher Workshop (MTW) - Materials

InvitationPre-Questionnaire (background information)Guidelines for the six steps in practiceRelevant literatureSuggestions for ways of organizing the workshopPost-Questionnaire (evaluation)Questionnaire for the workshop leader (evaluation)



MiA Teacher Workshop (MTW) – Experiments

LithuaniaNorwaySlovenia


Research questions - evaluation

Concerning learning1. Why do adults come back to school?2. What do they want to learn?3. How do they learn best?




Concerning teaching:1. Why do we teach adults in adult learning centers?2. What do we teach?3. What can be the meaning of an adult learning center for learning in practice, in out-of-school situations?4. How can we arrange a situation in which the adult learning center can be a center for transfer of learning in a school situation to learning in an out-of-school situation?



In general:1. How can we challenge adults to learn more about mathematics in an out-of-school situation? 2. What role can an adult learning center play in supporting and coaching learning mathematics in out-of-school situations?



Result – MiA Teacher Handbook

M athematics in A ction Communalities across differences Mieke van Groenestijn Florence, 6 September 2007.

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