SA NC Doing Investigations

DOING INVESTIGATIONS: A RESOURCE BOOK FOR GET & FET MATHEMATICS & SCIENCE EDUCATORS

A project of the Shuttleworth Foundation.

EDITOR: Peter Glover,

B.Sc. (Hons), N.H.E.D. (Rhodes), M.Litt. (Cantab), Ph.D. (Oregon)

SHUTTLEWORTH FOUNDATION P O BOX 4163 DURBANVILLE 7551

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[Shutteworth Foundation Home page]

This resource book is licenced under the Gnu Free Documentation Licence [1] (FDL). This licence entitles anyone to print, copy or distribute the books without penalties from the copyright holders. The licence maintains the integrity of the authors while promoting free distribution.

[1][Gnu Free Documentation Licence]

MESSAGE FROM MARK SHUTTLEWORTH
It has been an honour to meet educators around South Africa who create, in their pupils, a sense of wonder about the worlds of science, technology and entrepreneurship. South Africa, sitting as it does at the intersection of cultures and economies, is an unexpectedly good place to think about technology and science. We have a track record of achieving remarkable results in science and engineering, much of that thanks to the educators who have inspired children to take an interest in the world in which they live. I hope this resource book helps to spread that sense of wonder while also recognising the work of a few out of the many who make such a difference.

PREFACE BY SIPHO DLAMINI
It is a little surprising that only now, after more than a decade of curriculum innovation in South Africa and with increasing emphasis on Curriculum 2005, we are starting to provide resource books for GET and FET mathematics and science teachers. The Shuttleworth Foundation is taking the initiative in producing a series of resource books that encourage teachers and curriculum developers to rethink and re-engineer how we should teach science and mathematics in schools. We cannot forget that teachers must also be curriculum developers for the process of curriculum innovation to prosper.

Mathematics and science curriculum development has three domains: the cognitive, the so-called conative and the affective. Cognitive development is concerned with knowledge and understanding. In mathematics and science this means key concepts and factual knowledge and these are identified and described in the Revise National Curriculum Statements as Learning Outcomes. Conative development is concerned with the practical and procedural knowledge found in science process skills and mathematical problem solving abilities, also described in the RNCS. Affective development is concerned with emotional, social, cultural and moral development. This is an important, although often forgotten, aspect of learning - and hence teaching. Its importance is recognized by the learning outcomes in various Department of Education policy documents and, importantly, the critical and developmental outcomes that underpin our whole education effort.

What, in the new curriculum, should be taught and learnt in school mathematics and science? Here are some answers to the question, in one possible direction. The kind of mathematics and science that needs to be taught in schools must give learners a confident grasp of content knowledge and understanding the procedural skills to know how mathematicians and scientists work  and appropriate attitudes to mathematics and science and their value and use in society and economy. This resource book illustrates the curricular relevance of independent investigation in achieving these teaching and learning goals.

Peter Glover has been active mainly in the science education world. He has taught, lectured and researched curriculum development. He has been director of an innovative curriculum organization, the Primary Science Programme, and has managed reform projects such as the Thlatloga Project, from which much material in this book emanates. He has developed and written science, technology and mathematics materials for Tlhatloga and elsewhere, including textbooks. Through his work he has always insisted on learner-directed, activity based approaches on the total immersion of teachers in their professional development activities  and in the creation of communities of professionals, especially through the formation of effective, mutual-support clusters of schools. In this resource book, he gives a sense of the best practice with which educators could enthuse learners to genuinely participate in mathematics and science, even in our many schools which still have the barest minimum of basic resources. It is therefore heart-warming to note that some of the materials in the book have been developed and used by the successful educators who were selected in the Maths and Science Teacher of the Year (MSTotY) competition. They share with us some very useful ideas on assessment practice and implementation.

I hope that this resource book and the series that will follow will help many educators to develop themselves into innovative mathematics and science educators in ways that are both satisfying to them and stimulating to their learners.

Sipho Dlamini MST Senior Project Manager Gauteng Institute for Educational Development

ACKNOWLEDGEMENT OF SOURCES OF MATERIALS
Some of the material in this book is the work of individual winners or runners up in the Maths and Science Teacher of the Year (MSTotY) 2003 competition e.g. materials they developed and presented as part of their portfolios for adjudication in Chapter 7. Individuals whose work is reproduced here are acknowledged in the book. The contents of Chapter 3, The wisdom of the winners: hints and ideas for science and mathematics educators  Chapter 4, Ideas for investigations and Chapter 8, Clusters, support networks and communities of practice is largely the product of a workshop held over three days when the MSTotY 2003 winners came together in Johannesburg in March 2004. The examples in Chapter 6 were written for the Tlhatloga Project, a development project for Intermediate Phase educators by the University of Montana Western from 2000 2003. Chapter 5 is based on material developed by Maryna de Lange, winner of the 2002 MSTotY award. Many of the ideas for investigation topics in Chapter 4 also came from Maryna whose classes at Saldanha Bay Primary are doing regular investigations. Finally, Chapters 1, 2, 9 and 10 were either written or compiled by the editor, sometimes with re-formatting. Other materials written or edited by the editor appear in Chapter 6. The investigation into numbers in Chapter 6 was developed by Professor Otis Thompson, formerly of the University of Montana Western. Three hundred teachers who took part in the Tlhatloga Project know the pleasure of his stimulating mathematical company.

There are many references in Chapter 10 to material from the web, a rich resource for educators with internet access. One hopes that in the not too distant future all educators will be able to use information from the web to the benefit of their teaching. The Shuttleworth Foundation s efforts should speed this process.

The names and contact details of the MSTotY 2003 winners and runners up are recorded here. Experienced colleagues are still an educator's best resource and the MSTotY finalists are, almost by definition, more committed to this than most. Every one, in his or her own way, is willing to help with the establishment of science and mathematics support networks and clusters. Most have already done so.