Contents: 

Part I: School Systems, Curricula and Course Content

- Leo Rogers: The School Systems and School Mathematics in the

ELTMAPS Partner Countries; Inservice Course Description and Choice of Topics

Part II: Principles and Motivations

- Leo Rogers: Epistemology, Methodology and the Building of

Meaning in a Community of Practice in England 1960 – 1980 

- Despina A. Stylianou, Maria Meletiou-Mavrotheris: Building

Instructional Bridges from Elementary to Secondary School: A New Role for Technology

Part III: From the Classroom

- Leo Rogers: Questions for Teachers; Questions from Children 

- Marie Kubínová: Boxing 

- Marie Kubínová: Origami 

- Sue Pope: The Use of Origami in the Teaching of Geometry

- Jarmila Novotná, Leo Rogers: Word Problems: A Framework for Understanding, Analysis and Teaching 

- Giancarlo Navarra: Pop-ups 

- Leo Rogers: Some Explorations on a Square-dot Lattice: Areas, Dissections, Rational Numbers and More 

Part IV: Teaching Notes

- Leo Rogers: Dynamic Geometry Using Cabri géomčtre 

- Leo Rogers: Rational Numbers Posters 

- Leo Rogers: Polyshapes – Some Lessons 

- Jarmila Novotná, Marie - Kubínová: Some Experiences with Egyptian Fractions

- Sue Pope: The 1-100 Square and Other 2-Way Tables on a

Spreadsheet 183

- Marie Kubínová: Boxing. Some Notes on the Preparation of the

Lessons

Appendices

- Appendix 1: Booklists and other Published Resources 195

- Appendix 2: Internet Links 

Leo ROGERS, Jarmila NOVOTNÁ (Editors), Classroom contexts. Effective learning and teaching of Mathematics from primary to secondary school,  2003, pp. 230, € 19.00, ISBN 88-371-1396-X

Introduction: Changes in Classroom Practice

 

Radical changes in classroom practice were being developed in the 1960s and 70s by a group of English mathematics teachers whose didactical experiments in the classroom were discussed and critically analysed. Some of this experimental approach was written up in two books published in 1967 and 1977 (Rogers: Epistemology, Methodology and the Building of Meaning 1960 – 1980 in this book). At the same time, similar work was being carried out in France, Germany and Belgium and was partly influenced by the general awareness that the school mathematics curriculum and teaching methods had to be revised. Much of this work, while being influenced by theoretical ideas, came from the direct experience of teachers working in the classroom and was often based on intuition and sensitivity to children's problems of learning mathematics. At the same time, the work of Piaget was just becoming known to teachers, and it provoked many questions about standard classroom practice, and the widely held assumptions about children's’ learning. Today, we have moved on considerably. Our understanding of teaching and learning has developed new awareness of the fluidity and uncertainty of what constitutes the learning process, while at the same time, we are aware of certain approaches and contexts which, while they do not guarantee success, are more likely to produce favourable results for both pupils and teachers. There is also much less certainty about the nature of knowledge and of understanding. Reports of experimental work in the classroom which are sensitive to new knowledge in social and cognitive science is providing much more data which demands qualitative rather than quantitative analysis, and we are more understanding of the techniques in this field, and of the degree of certainty (or uncertainty) of the knowledge gained. In this book we have a variety of written means of communicating our ideas. Some as lesson plans, some as commentaries on a sequence of lessons, some examples of pupils’ work, and some more open descriptions of possible ways of working. Our basic working principles can be stated quite briefly: 

 • mathematics is not ‘given’ a priori, nor a fixed body of eternal truths 

 • mathematics is a human creation and consequently can be fallible and uncertain 

 • mathematics arises from the need to solve problems, and new mathematics can be created for specific purposes 

 • learning mathematics is a process of the individual creating new ideas or re-creating earlier knowledge for themselves

 • the creative activity of doing mathematics is similar in the child as in

the adult although they have different resources and experiences

 • learners are not ‘empty vessels’ to be filled with facts; we respect them for their independence and freedom to learn in different ways. 

The spirit of our communication is not new3; we share these beliefs and principles with a large number of mathematics educators and teachers. They are supported now by a considerable body of research into teaching and learning mathematics which has been developing new philosophy and methodology over the last 40 years. It has become clear that the surest way to improve our teaching is to listen carefully to what our pupils say, to reflect upon and evaluate their actions, to question our own prejudices and to recognise that understanding is often quite difficult to achieve, and this needs a sensitive approach by the teacher. We are not suggesting that there is one ‘best’ approach to the problems of teaching and learning mathematics, but we are offering our collective experience of ways which we hope can be adapted by the reader to suit the conditions in their own class, their school, and their educational context. We ask you then to engage with these activities yourself, to experiment with the situations, to think about questions to ask, to think about how you would enable your pupils to engage in similar activities, and to think about your own experiences and your responses to pupils

 

Leo Rogers and Jarmila Novotná