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The Language of Mathematics in Science The Language of A Guide for Mathematics in Teachers of Science 11–16 Science A note on navigating around within this PDF file Introduction: the language of mathematics in science Background About this publication Mathematics and science Thinking about purposes and using judgement Understanding the nature of data Assessment Process of development of this publication Further references on terminology and conventions Overview of chapters 1 Collecting data 1.1 Measuring and counting 1.2 Measurement, resolution and significant figures 1.3 Characteristics of different types of data 1.4 Naming different types of data 1.5 Where do data come from? 2 Doing calculations and representing values 2.1 Calculations and units THE LANGUAGE OF MATHEMATICS IN SCIENCE A Guide for Teachers of 11–16 Science The Association for Science Education (ASE) is the largest subject association in the UK. As the professional body for all those involved in The Association science education from pre-school to higher education, the ASE provides a national network supported by a dedicated staff team. Members include for Science Education teachers, technicians and advisers. The Association plays a significant role in promoting excellence in teaching and learning of science in schools and colleges. More information is available at www.ase.org.uk. The Nuffield Foundation is an endowed charitable trust that aims to improve social well-being in the widest sense. It funds research and innovation in education and social policy and also works to build capacity in education, science and social science research. The Nuffield Foundation has funded this project, but the views expressed are those of the authors and not necessarily those of the Foundation. More information is available at www.nuffieldfoundation.org. First published 2016 Association for Science Education College Lane, Hatfield, Herts AL10 9AA Tel: +44 (0)1707 28300 Email: [email protected] Website: www.ase.org.uk © 2016 Association for Science Education The materials in this publication may be reproduced for personal and educational use of a non-commercial nature without the permission of the publisher or author provided that the source is acknowledged. Permission is needed to copy or reproduce for any other purpose, and requests should be addressed to the ASE. ISBN 978 0 86357 455 9 Author: Richard Boohan ASE project team: Marianne Cutler, Richard Boohan, Richard Needham Mathematics advisers to project team: Andrew Noyes and Geoffrey Wake Steering group: Robin Millar (chair, University of York), Jeremy Hodgen (University of Nottingham), Andrew Hunt (formerly Nuffield Curriculum Centre), Jane Imrie (NCETM), Cheryl Lloyd (Nuffield Foundation), Rosalind Mist (Royal Society), Michael Reiss (UCL Institute of Education), Clare Thomson (Institute of Physics), Brian Cartwright (observer, HMI), Janet Holloway (observer, Ofqual). Awarding organisations: Matthew Bennett (AQA), Kathryn Booth (Edexcel), Natasha Chowdhury (OCR), Helen Francis (WJEC), Stella Paes (AQA), Michelle Spiller (OCR) Science and mathematics review panel: Peter Campbell, Brian Cartwright, Ian Galloway, Andrew Hunt, Jane Imrie, Philip Johnson, Scott Keir, Stephen Lyon, Roni Malek, Robin Millar, Robin Sutton, Mary Whitehouse Teacher review panel and others providing feedback: Dan Abbott, Christine Abdelmoutaleb, Damian Ainscough, Sarah Albenna, Nicola Arthur, Matthew Benyohai, Tim Bridle, Stephen Burrowes, Miriam Chaplin, Antony Checkett, Anthony Clowser, Steve Cooke, Ally Davies, Emma Dooley, Pat Dower, George Duoblys, John East, Stuart Farmer, Carolyne Gerrard, Alastair Gittner, Stephanie Gordon, Mark Harrison, Robin Hartley, Louise Herbert, Sarah Hinsley, George Hurst, Mike Jackson, Bob Kiddle, Mark Levesley, Calvin Lim, Claudia Patricia López, Nicola McGrath, Eliza McIntosh, Stewart McKane, Colin Oates, Muhsin Ogretme, Simon Richards, Emma Rivers, Dave Rockett, John Ryan, Alison Sefton, Annette Simpson, David Staniforth, Andreas Stockey, Alaric Thompson, Heather Thomson, Marc Tillotson, Ed Walsh, Gary Ward, Dorothy Warren, Colleen Wells, Nicola Wilberforce, Leonard Winning, Gordon Wright Copy-editing and typesetting: Andrew Welsh (www.andrew-welsh.com) Cover design: Colin Barker Cover image: Snowflake © Sergey Kichigin (www.dreamstime.com) Contents Introduction: the language of mathematics in science 1 Overview of chapters 6 1 Collecting data 9 2 Doing calculations and representing values 14 3 Choosing how to represent data 23 4 Drawing charts and graphs 35 5 Working with proportionality and ratio 41 6 Dealing with variability 50 7 Looking for relationships: line graphs 64 8 Looking for relationships: batches and scatter graphs 75 9 Scientific models and mathematical equations 87 10 Mathematics and the real world 107 Glossary for teachers 119 The Language of Mathematics in Science: A Guide for Teachers of 11–16 Science iii A note on navigating around within this PDF file To assist in navigation, this PDF file contains hyperlinks (in blue underlined text), and at the top left of every page there is a ‘Previous view’ button. It is recommended that this file be viewed using Adobe Acrobat or the free Adobe Acrobat Reader on a desktop or laptop computer in order to use this hyperlink functionality. In these Adobe applications, the standard shortcut key combination of Alt-left arrow (Cmd-left arrow on a Mac) is another way to go back to the previous view. The Language of Mathematics in Science: A Guide for Teachers of 11–16 Science iv Introduction: the language of mathematics in science The aim of this book is to enable teachers, publishers, awarding bodies and others to achieve a common understanding of important terms and techniques related to the use of mathematics in the science curriculum for pupils aged 11–16. Background This publication was produced as part of the ASE/Nuffield project The Language of Mathematics in Science in order to support teachers of 11–16 science in the use of mathematical ideas in the science curriculum. This is an area that has been a matter of interest and debate for many years. Some of the concerns have been about problems of consistency in terminology and approaches between the two subjects. The project built on the approach of a previous ASE/Nuffield publication, The Language of Measurement, and the aims are rather similar: to achieve greater clarity and agreement about the way the ideas and terminology are used in teaching and assessment. Two publications have been produced during the project. This publication, The Language of Mathematics in Science: A Guide for Teachers of 11–16 Science, provides an overview of relevant ideas in secondary school mathematics and where they are used in science. It aims to clarify terminology and to indicate where there may be problems in student understanding. The publication includes explanations of key ideas and terminology in mathematics, along with a glossary of terms. A second publication, The Language of Mathematics in Science: Teaching Approaches, uses teachers’ accounts to outline different ways that science and mathematics departments have worked together, and illustrates various teaching approaches with examples of how children respond to different learning activities. About this publication In developing this publication, the starting point was to identify relevant mathematical key words that should be included in the glossary. These were selected on the basis that the ideas form an important aspect of the current 11–16 science curriculum. Many familiar terms that pupils should know from elementary work in mathematics are not included (e.g. multiplication), although some terms are included that are currently not commonly used in 11–16 science but are potentially useful for science teachers to know about (e.g. box plot). The definitions of the selected key words are given in the Glossary for teachers at the end of this publication. Definitions are useful for clarity, but only go so far. The major part of the publication consists of ten chapters, each explaining ‘clusters’ of these key words so that their use can be seen in context. The chapters and the associated key words are based around ‘kinds of things we do in science’. For example, ‘Collecting data’ is concerned with terms such as ‘quantity’, ‘value’, ‘unit’ and ‘variable’; ‘Dealing with variability’ is concerned with terms such as ‘distribution’, ‘uncertainty’, ‘mean’ and ‘outlier’. The Language of Mathematics in Science: A Guide for Teachers of 11–16 Science 1 Introduction: the language of mathematics in science The clusters of key words are included in a panel at the start of each chapter, and a complete list of these can be seen in the Overview of chapters. Note that a number of key words appear in more than one chapter. Within the chapters, the key words are indicated in blue underlined text: each of these is hyperlinked to the relevant entry in the glossary. Each entry has hyperlinks back to the relevant sections in the chapters, so the glossary also acts as an index. The aims of the publication are to: • provide an overview of the mathematics relevant to science that may be studied by pupils at secondary school • indicate the relevance of the ideas to the activities undertaken in secondary school science • clarify the meaning of the terms used where there are common misunderstandings or where there are different meanings in different contexts • indicate as appropriate where there may be student misconceptions and problems in understanding • identify, where relevant, approaches taken in mathematics teaching
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