the mathematics teachers' development series

THE MATHEMATICS TEACHERS' DEVELOPMENT SERIES Pack 1: Investigative and Problem-Solving Approaches to Mathematics and their Assessment Alice Onion with Sue Burns, Jim Thorpe and Dylan Wiliam The Authors: Alice Onion has taught in secondary and further education. She worked for six years on Graded Assessment in Mathematics (GAIM) devising investigative and problem-solving activities and writing assessment material. She has worked as an Advisory Teacher and is now \ Mathematics Adviser for the London Borough of Lambeth. Sue Burns has taught mathematics in secondary schools. She has worked with a computer modelling project at the Institute of Education, London and is currently working with an 'A' level project at King's College, London. Jim Thorpe has taught mathematics in schools for twelve years, worked as an advisory teacher promoting investigative mathematics in Leicester shire schools, and has undertaken educational research at the National Foundation for Educational Research which included work for the APU. Dylan Wiliam is a mathematics education lecturer at King's College, London. He is currently seconded to the Consortium for Assessment and Testing in School (CATS) to co-ordinate the development of Standard Assessment Tasks for Key Stage 3 in English, mathematics, science and technology. Series Editors: Janet Day and Mary Ayres Acknowledgements: The authors would like to thank: —the LEAG for permission to use copies of assessment forms; —Chris Phillips, Teresa Smart and Peter Wilder for reading through parts of this pack and offering comments; —John Hunt, of Groundwork, for diagrams.

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THE MATHEMATICS TEACHERS'DEVELOPMENT SERIES

Pack 1: Investigative and Problem-Solving Approachesto Mathematics and their Assessment

Alice Onionwith Sue Burns, Jim Thorpe and Dylan Wiliam

The Authors:Alice Onion has taught in secondary and further education. She workedfor six years on Graded Assessment in Mathematics (GAIM) devisinginvestigative and problem-solving activities and writing assessmentmaterial. She has worked as an Advisory Teacher and is now

\ M a t h e m a t i c s A d v i s e r f o r t h e L o n d o n B o r o u g h o f L a m b e t h .Sue Burns has taught mathematics in secondary schools. She has workedwith a computer modelling project at the Institute of Education, Londonand is currently working with an 'A' level project at King's College,London.Jim Thorpe has taught mathematics in schools for twelve years, workedas an advisory teacher promoting investigative mathematics in Leicestershire schools, and has undertaken educational research at the NationalFoundation for Educational Research which included work for theAPU.

Dylan Wiliam is a mathematics education lecturer at King's College,London. He is currently seconded to the Consortium for Assessment andTesting in School (CATS) to co-ordinate the development of StandardAssessment Tasks for Key Stage 3 in English, mathematics, science andtechnology.

Series Editors:Janet Day and Mary Ayres

Acknowledgements:The authors would like to thank:—the LEAG for permission to use copies of assessment forms;—Chris Phillips, Teresa Smart and Peter Wilder for reading through

parts of this pack and offering comments;—John Hunt, of Groundwork, for diagrams.