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

M athematics in A ction A Grundtvig-1 Project ( ) Denmark (project Manager) Hungary Lithuania Netherlands Norway Slovenia Spain

M athematics in A ction 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

M athematics in A ction 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

M athematics in A ction Process and Results Examples of good practice Some relevant background theory A common way of working in practice Setup of MiA Teacher Workshops (Professional Development) Handbook

M athematics in A ction Research questions Concerning learning 1. 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 M athematics in A ction 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?

M athematics in A ction 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?

EMMA, Florence, 6 Sept 2007 M athematics in A ction Examples of good practice Denmark- Learning math on the work floor Spain - Dialogical Learning Netherlands- Learning in practice based on Problem Solving

EMMA, Florence, 6 Sept 2007 M athematics in A ction Rationale underlying math courses at the work place 1.learners feel at home 2.work place situations and materials are available 3.employers are motivated to support 4.math courses at the work place is included in the national programme ‘preparatory adult education – mathematics

EMMA, Florence, 6 Sept 2007 M athematics in A ction Principles for math courses at the work place 1.cooperation between teacher and learners 2.use of materials from work place and learners’ life 3.use of concrete materials 4.investigations of topical mathematical problems 5.development of usable algorithms 6.learners’ needs, interests and experiences are fundamental 7.becoming aware of math in everyday life is one of the goals

EMMA, Florence, 6 Sept 2007 M athematics in A ction Adult Learning Starting points 1.Adults are free to learn 2.Learning often happens in a functional situation 3.Learning in practice is characterized by learning through authentic materials 4.Every learning situation is a socio-cultural determined situation 5.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

EMMA, Florence, 6 Sept 2007 M athematics in A ction Paulo Freire – Dialogical Learning (Spain) Egalitarian dialogue Cultural intelligence Transformation Instrumental dimension Meaning creation Solidarity Equality of differences

EMMA, Florence, 6 Sept 2007 M athematics in A ction Paulo Freire – Learning through experiences (NL) The learner decides on the actual program Learning from and through experiences Mutual learning and teaching Education and schooling in mutual relation

EMMA, Florence, 6 Sept 2007 M athematics in A ction Problem Solving – six steps (NL) 1.Bring the learner in a potential mathematical situation 2.Identify problems in the situation 3.Plan the problem solving procedure 4.Solve the problem 5.Check the result 6.Review the process. What did the learner learn? (MvG – 2002)

EMMA, Florence, 6 Sept 2007 M athematics in A ction Relevant Literature Paul Ernest (…) Transfer of Information Freire: Dialogical Learning Greeno et al (1999) “Learning in and for Participation in Work and Society” Learning in practice (MvG, 2002)

EMMA, Florence, 6 Sept 2007 M athematics in A ction 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

EMMA, Florence, 6 Sept 2007 M athematics in A ction Problem solving Perspective -self-management -learning skills -communication skills -teamwork skills -problem- solving -data-handling skills

EMMA, Florence, 6 Sept 2007 M athematics in A ction 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 become 4.Learning in practice is based on shared knowledge - Learning in school often focuses on individual knowledge 5.Learning is often situation-based and situation-bound Greeno at al (1998)

EMMA, Florence, 6 Sept 2007 M athematics in A ction Problem Solving – six steps (NL) 1.Bring the learner in a potential mathematical situation 2.Identify problems in the situation 3.Plan the problem solving procedure 4.Solve the problem 5.Check the result 6.Review the process. What did the learner learn? (MvG – 2002)

EMMA, Florence, 6 Sept 2007 M athematics in A ction Six steps in practice - some experiences Denmark Hungary Netherlands Spain

EMMA, Florence, 6 Sept 2007 M athematics in A ction 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

EMMA, Florence, 6 Sept 2007 M athematics in A ction MiA Teacher Workshop (MTW) - Materials Invitation Pre-Questionnaire (background information) Guidelines for the six steps in practice Relevant literature Suggestions for ways of organizing the workshop Post-Questionnaire (evaluation) Questionnaire for the workshop leader (evaluation)

EMMA, Florence, 6 Sept 2007 M athematics in A ction MiA Teacher Workshop (MTW) – Experiments Lithuania Norway Slovenia

M athematics in A ction Research questions - evaluation Concerning learning 1. 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 M athematics in A ction Research questions - evaluation 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?

M athematics in A ction Research questions - evaluation 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?

EMMA, Florence, 6 Sept 2007 M athematics in A ction Result – MiA Teacher Handbook