Easter Conference 2006 - Ormskirk

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The Theme

The theme for 2006 was ‘Maths without...’. More information below...

Photo Gallery

<< Easter Conference 2006 - Photo Gallery

The Keynote Speakers

Opening Address: Kath Cross & John Hibbs

Kath Cross and John Hibbs set the tone for the conference.

‘Mathematics lessons without...’

<< Listen to the 2006 Opening Address - (55 mins) Smaller file [3Mb]

<< Listen to the 2006 Opening Address - (55 mins) Higher quality [9Mb]

Kath and John retired in 2003 after many years as Her Majesty’s Inspectors for Schools (HMI). They will use this experience to discuss aspects of mathematics lessons which they think are important.

Sir Peter Williams

Sir Peter Williams is Chair of the Advisory Committee on Mathematics Education. He is also Chairman of the UK’s Engineering and Technology Board (ETB) and of the National Physical Laboratory. Sir Peter graduated from Cambridge University with an MA and PhD in Physics. He initially pursued an academic career, first at Selwyn College, Cambridge and subsequently at Imperial College, London. After a period with VG Instruments Ltd he joined Oxford Instruments plc in 1982. Sir Peter has previously held the posts of: Master of St. Catherine’s College, Oxford; Chairman of the Board of Trustees of the National Museum of Science and Industry; President of the Institute of Physics; President of the British Association for the Advancement of Science; and President of the Association for Science Education. He was also a member of the Post-14 Mathematics Inquiry Steering Group.

<< Listen to the 2006 Closing Address - (45 mins) Smaller file [3Mb]

<< Listen to the 2006 Closing Address - (45 mins) Higher quality [8Mb]

NCETM

Rob Smith from the NCETM National Centre for Excellence in Teaching Mathematics gave a talk about his work and the centre.

<< The slides from his presentation in PDF format [© NCETM]

Mathematical Indian Dance - Shantha Rao

Shantha Rao provided a fascinating session demonstrating Indian Classical dance and its mathematical connections.

The Sessions

As Session Leaders make material available, we will add it as downloadable items underneath the relevant session.

Puzzles and problems without the National Curriculum • A1

Enrichment materials for able pupils in years 5 and 6. These have been developed and used over a period of eight years with small groups of pupils in a local Primary school, following a request for ‘help’ some years ago. The materials will be available for participants to use. They are NOT intended to help with SATS or the National Curriculum, nor do they seek to accelerate progress - which is likely to lead to worse problems in later years. They may also provide some ideas for similar use with pupils in early secondary years. The children seem to have enjoyed them - but you must judge for yourself...

<< Joe Watson’s Session Notes

Mathematical Art • A2

Discussing a painting means looking at the painting and talking about what we see. This is what we shall do with a number of geometrical ‘pictures’. We shall work together as a group on ‘pictures’ suitable for KS3 and KS4 classrooms and create some new ones. The activities will provide a context for using and applying geometrical theorems, and will promote understanding of reasoning and proof. But above all they will encourage thinking creatively about how you explain what you can see and how – perhaps – the idea behind the picture might be generalised.

Maths without the confines of school • A3

A session to provide information on the advanced higher residential course run for able sixth formers in the scottish highlands each year. Previous residential courses for able KS3 pupils and involving up to 160 youngsters will also be described.

Mathematics without any idea where we are going but we will know when we get there! • A4,B4,C6,D8,E7,F5,G6,H1

We will open Points of Departure 1, 2, 3 or 4 and work on one of the activities. The point of departure will be very clear, the point of arrival will be entirely up to the participants.

Words and Pictures • A5

Exploring primary mathematics through the use of stories, objects and photographs. We will present a selection of stories, and with the group explore ideas for enriching mathematics for young children. We will also link objects to the stories to extend learning in a variety of context

Maths without understanding • A6 and B1

Did you know that by the time they are 14 over a third of children get the right answers for the wrong reasons? Many children who achieve correct answers do not have the depth of understanding needed for ongoing progress, and many harbour misconceptions that place their future learning at risk. This workshop explains why some children just don’t get it. Leave with the opportunity to browse the First Steps in Mathematics resources and take away some diagnostic tasks to see for yourself! We are a not-for profit organization owned by Edith Cowan University in Perth, Western Australia.

Maths without just sitting watching • A7

In Harrow we are exploring ‘Putting the active into interactive’ - planning lessons where practical activities for pupils are integrated with use of a single interactive whiteboard. I will lead a variety of activities which can be adapted across KS2 and KS3 (and maybe wider) to challenge and develop mathematical reasoning.

Maths without maths – How to breed an optimal tin of beans • A8

Mathematics is commonly used to optimise a design or a procedure. In its most basic form a function is constructed and a local or global minimum or maximum sought. Typical mathematical approaches vary from graphical solutions through to algebraic ones involving calculus. This session considers these approaches as a way to produce an optimal tin of beans. This is followed by a practical demonstration of optimisation using a genetic algorithm; repeating the optimisation but letting Darwinian selection and "sexual” reproduction solve the problem – audience participation is encouraged!

Exploring the TSM Resources CD • B2

The TSM Resources CD was distributed with the final Micromath and to all schools in September 05. This session will show how to get the most out of the CD - the web, Autograph, Excel, GSP, Cabri, etc

Mathematics without passengers • B3

Join the crew on this mathematical journey where everyone has a job to do. Activities with measures, shape and number will provide a context for problem solving with the whole group, and practical tasks for the KS2 and KS3 classroom.

Teaching maths without using People Maths ?? Time to come alive • B5

Alan and Bob have continued to look for kinaesthetic, collaborative and fun approaches to learning and doing mathematics. Come and share, help us trial some new activities; none from “People Maths, Hidden Depths&rdsquo;, but all with the same philosophy.

QCA Primary update • B6

These parallel sessions will provide information about latest developments in curriculum, assessment and qualifications. We will share: - latest insights into the current curriculum and pupil performance; - new developments aimed at strengthening teaching and learning; and - recent progress with projects relating to goverment initiatives. There will be opportunities for questions and discussion.

QCA Secondary and Post-16 update • B7

These parallel sessions will provide information about latest developments in curriculum, assessment and qualifications. We will share: latest insights into the current curriculum and pupil performance; new developments aimed at strengthening teaching and learning; and recent progress with projects relating to goverment initiatives. There will be opportunities for questions and discussion.

Mathematics without any questions • BC1 &D3

One interpretation of ‘investigations’ is that they involve presenting situations to pupils, and the pupils have to formulate their own questions. We shall work at several investigations ourselves, hear what some pupils have done, and consider the implications for the classroom. ‘Problems’ involve responding to specific questions, and pupils who are used to investigative work and asking their own questions can easily convert a problem into an investigation by asking questions like "What happens if..?"

Playing and Solving with Cabri • BC2

This session will take the form of a conversation with a 9-year old while constructing and solving problems using Cabri. The focus of the session will be on the pedagogy used to develop important concepts by using Cabri with younger learners. The files used in the session will be made available to delegates on the website.

Games on plane and sphere • BC3 and H6

Strategy games on the surface of the plane are useful and amusing tools for our students to play, and, at the same time, discover important properties of plane geometry. This same idea works just as well on the spherical surface. In the workshop, we make experiments on the physical plane and sphere, and, in addition, try the same on the computer screen.

Maths without enrichment? • BC4

Not worth contemplating once you have had a chance to familiarise yourselves with the NRICH website (www.nrich.maths.org) This will be a hands on session which will give you the opportunity to find out about all the latest developments at NRICH. Come prepared with topics that you will be teaching and see how NRICH can help.

Mathematics...without PS? • BC5

Surely not! It would be like g without tonic; Ap w/o cream; M w/o W; G w/o P…… To find out more, explore new environments, develop fresh situations then come join our workshop. While it was only for one year that ATM was w/o I and L!

Mathematics without...it seeming to be mathematics • BC6

The Sudoku craze involves numbers, but solving the puzzle isn’t mathematics; showing that, in a 3 x 3 magic square, the magic constant is three times the centre entry does not require any algebra, but arguably is mathematics. The session will allow participants to work on some problems/puzzles which, at face value, seem non-mathematical, but is it really so? At what stage does a fun activity, or even a seemingly pointless one, become a subversive means of teaching mathematics?

Maths with Outcome • BC7

Games are a relaxed and motivating way of practising number facts and coming to an understanding of mathematical ideas. But where’s the game you need? The first session will introduce a number of games both ‘home-made’ and commercial for particular occasions, for participants to look at and, preferably, play. The second session will be a discussion of different kinds of game that can be made. Come and devise and make games which are needed for particular purposes. Participants, please bring your games to share with others.

"ANZAN" Mental calculation based on images of Soroban beads • BC8

You will see visual images of the soroban and will learn about how it is used. In particular you will apprecaite the significance of zero and learn how the soroban is actually all about complimentary numbers. After this session you will be able to teach addition and subtraction in your classroom, without using an actual soroban, but by using visual images of numbers.

The Interactive Whiteboard: from classroom activity to professional development • C1

In this session we shall look at some uses of the Interactive Whiteboard in the mathematics classroom and consider how these might lead to changes in practice. The discussion will focus on some of the findings of recent research

MyMaths.co.uk: Inspiring e-learning without limits • C2 and E8

So you want digital resources written and trialled by real maths teachers? Got an IWB and want to play? Find out how to bring it alive with MyMaths.co.uk! Come and try out some exciting interactive lessons and activities for your IWB or pc, and see how you can develop mathematical thinking using this dynamic tool. MyMaths tackles the real understanding issues of difficult concepts and has lots of fun and games activities which really enthuse students. Types of activities at this session include dynamic graph sketching, geometrical visualisation and AT1 activities and puzzles. All delegates attending this session will be set up with a free 2 week trial.

Sorting tessellations and wallpaper • C3

What counts as a wallpaper pattern? Must a tessellation give a wallpaper pattern ? Or vice-versa? How may we sort wallpapers? Does colour make a difference? Please bring samples of your favourite wallpaper patterns. There will be talk of symmetry.

Maths without...scissors and glue • C4

Not that practical isn’t important. So much of the model making involving scissors and glue is possible by simply folding paper. You can accurately create shapes and models perfect for exploring mathematics.

Data handling using Autograph KS3 and 4 • C5

A chance to find, enter and analyse data using Autograph. A variety of diagrams will be created and, with tables of statistics be transferred to word.

Linking school mathematics to out-of-school mathematical activities • C7

A group of secondary teachers in the wider Leeds area have designed classroom projects which engage students in substantial ‘real life’ mathematical activities. I will describe the philosophy of this approach and some of the activities the group have carried out with their classes.

Straight lines without rulers • D1

In this talk we first look at some mechanical means of achieving straight line motion, or approximations to it, using a variety of linkages (visualised using Geometer’s Sketchpad) together with some of the maths behind their designs (Inversive geometry). We also consider some solutions to the classic surveying problem of the continuation of a straight path on both sides of a large, unmovable object in its way. For this we use both standard trigonometry and some results from projective geometry. If time permits, guidance will be given with relevant GSP techinques.

Still reading MT without having written for it yet? • D2

Reflecting upon and discussing what happens when people learn mathematics has always been central to ATM. Come and talk and write with others about your experiences teaching or learning mathematics. Everything written will be considered, if you wish, for publication in Mathematics Teaching. Wine will be provided!!!

Maths without...pencil and paper • D4

The Mathematics Test Development Team at Edexcel is investigating ways that mathematics assessments can be presented on a computer, rather than simply translating existing assessments from paper to screen. Our aim is to develop activities which fully utilise the benefits afforded by the computer. In this session you will be able to try out some ideas that we have developed for yourselves. There will also be time to discuss opportunities and issues related to on-screen assessment.

Mathematics without...the three part lesson? • D5

What do we gain? What do we lose? When it began, the National Numeracy Strategy introduced a particular structure to lesson planning and helped teachers to think about the use of the time available, but where are we now in primary and secondary schools? There are lots of different perceptions around what ‘the three part lesson’ does or does not mean, but we would like to focus on what makes an effective lesson or sequence of lessons that cover a particular topic, and how teachers decide what they do with the pupils' time. We will discuss these issues through engaging with some mathematical problems.

Autograph for AS, A2 • D6

Using Autograph for more advanced topics: calculus, trig, 2D and 3D vectors, probability and statistics. IWB use will also be demonstated

Maths without Harmony • D7

This practical session will explore links between maths and music especially rhythm. Bring a percussion instrument if you wish or be prepared to improvise. We hope that participants will join us to perform at the Musical Evening.

Folding a football and other new worlds with Cabri 3D • D9

Ever thought a football was useful and not very exciting? Think again. Cabri 3D enables us to easily construct a fold-up football and other polyhedra – and to keep on folding them. Extraordinarily beautiful shapes emerge, kaleidoscopes can be created and rich mathematical questions beg to be answered.

"ANZAN" Mental calculation based on images of Soroban beads • E1

You will see visual images of the soroban and will learn about how it is used. In particular you will apprecaite the significance of zero and learn how the soroban is actually all about complimentary numbers. By using visual images of numbers you will learn addition and subtraction.

Maths without...irregular polygons • E2

We will explore some of the more unusual aspects of convex polyhedra (with regular faces) including notions such as ‘valence’ and an analogy with prime numbers will be discussed. We might even do a bit of algebra! The session will be essentially ‘hands-on’, making, slicing and pondering which polyhedra can or cannot be made and why. The ideas come from Peter Cromwell’s book ‘Shapes in Space’.

<< Heather McLeay’s Session Notes

Mathematics without a calculator ? Pity! • E3

A workshop session exploring the use of a simple hand-held calculator (+ - x ÷ ?) in investigating patterns, limits, large and small numbers, estimation and 1 sign fig arithmetic, and leading to ideas of conjecture, exploration, justification and proof.

Excel without...fear • E4 and H5

Without previous experience? Without time? Without any further excuse come and explore the wonders of Excel. Enjoy data handling, filtering without fear and pivoting without pain, using Excel’s Filters and PivotTables. Find data sets on the web, without getting lost and, if there’s still time, find Excel skills you were once without, e.g. simulating dice throwing. Included without charge is a disk of DISCUS containing lots of ready to use interactive spreadsheets and worksheets, and datasets, plus a 2006 copy of CHIME (Census Handling Using Microsoft Excel) published by the RSS Centre for Statistical Education.

Maths without...enthusiasm • E5

GROUP DISCUSSION: Working with excluded pupils in a PRU a number of my pupils ‘hate’ maths. How do I/you engage them? How can we turn that switch back on? Bring your ideas and thoughts to this discussion group.

Tasks without...text • E6

Very often, a mathematical task is communicated by means of a piece of text. This session will explore the ways in which the software TurboDemo enables us to easily create "movies” about using software (using the examples of Autograph and Cabri) and hence to bypass words to a large extent. We will also discuss the pros and cons of this approach.

Teaching maths without a maths degree • E9

In January 2006 the 6 month Mathematics Enhancement Course (MEC) course will be rolled out across 12 regional centres. The MEC course is an opportunity for graduates with either a maths A-level, an element of the subject in their degree, or occupational experience to build on and deepen their knowledge prior to starting a Secondary Mathematics PGCE. During this session tutors from the MEC Pilot Course at Liverpool Hope/Edge Hill will share the elements of the course which have succesfully helped MEC students ‘deepen their understanding’ of ‘fundamental mathematics’. There will be a chance to explore and discuss different approaches to rich mathematical concepts which have rightly found a place on the MEC.

Would you sow mathematics without...ploughing first? • F1

More rich starting points for A level mathematics - open-ended ways to start an A level lesson that leave students receptive to new ideas and theory. Everything here can be used immediately in your classroom!

<< Jonny Griffiths' Session Notes

Statistics projects without...angst • F2

A highly-interactive computer program, Introduction to Statistics, will be demonstrated. It runs over a network or on a stand-alone computer, providing a comprehensive, friendly resource to support statistics projects. Students can browse its contents through menus or an index and tutors can construct study plans that collate sections of material needed by individual students, projects or groups. The material extends from data collection through numerical and graphical summaries (including correlation) to the logic of statistical inference and some statistical tests.

Feel the maths • F3

Kinaesthetic learners learn by ‘doing’. But is it enough just to ‘do’ something with a pile of Multilink or a set of cards or whatever? Perhaps kinaesthetic learning goes deeper than that. Perhaps it involves a whole experience of touch and movement that enables the learner to feel the maths, not just to do it. We will work with activities that are designed to help kinaesthetic learners to engage more effectively with key mathematical concepts. Bring you own thoughts and ideas for others to explore.

Hands On Maths in the Hall • F4

A largely practical session based on the Hands On Maths Roadshow from the Millennium Maths Project, using NRICH activities. Come along to discuss how the activities can be used to enhance lessons, open days, parents evenings, summer schools, primary liaison days, maths club - but mainly to get a taste of the activities yourselves.

What’s in the workshop that I could use to teach? • F6

A selection of activities and ideas that will engage pupils and motivate them. The session will be based around the resources in the workshop and will link the activities and ideas with the current frameworks and syllabi for mathematics.

Still teaching maths without using People Maths? • F7

Bob and Alan continue to look for new kinaesthetic, collaborative and fun approaches to learning and doing mathematics (See session C). However in this session working in small groups, you will get the chance to explore a few activities from “People maths, Hidden Depths&rdsquo; and possibly from earlier publications.

Maths on fire • F8

Learn how to turn matchstick puzzles into worthwhile mathematical activities. This highly practical hands-on session is a must if you want to ignite your children’s interest in creative maths.

Thinking through mathematics • FG1

The workshop is an opportunity to try out some mathematical activities designed to foster the generic thinking skills defined by the National Curriculum.

Interactive Mathematics Teaching • FG2

We shall work collaboratively on a range of activities suitable for KS3 and KS4 classrooms. Most activities will involve the use of one computer in the classroom and will be interactive and promote whole-class discussion. They will enable teachers to teach mathematics without being tied down to a particular approach, without having to decide on the abilities of pupils in advance. They will promote understanding and exploration of significant mathematical ideas; they will encourage a problem-solving approach that motivates the acquisition of knowledge and skills; they will challenge pupils to think and reason mathematically.

Claude’s playground • FG3

Claude is a creature, who, thanks to Cabri 3D, can do all sorts of things such as blow bubbles, jump on a trampoline and swing on a swing. This session will explore how to create Claude in action, using ordinary National Curriculum geometry in a 3D setting.

Developing a maths trail • FG4

This workshop is aimed at delegates who have never previously designed a maths trail ……In the first session we will walk around the campus looking at the built environment as a resource for the mathematics classroom. The second session will focus on using digital photographs taken as the basis for mathematical enquiry. The session leaders will endeavour to show ways in which the same photograph (or building) can be used with pupils at all Key Stages. It would be useful (although not obligatory) to bring your own digital camera

Maths without...enrichment? • FG5

KS3 geometry with one computer, a data projector and dynamic geometry software • FG6

In this double session we shall explore some of the beautiful geometrical theorems to which dynamic geometry software gives us access but which can be proved by recourse only to the content of the key stage three curriculum. We shall work with a single computer attached to a data projector and, in so doing, model a whole-class approach to working with learners in discursive, collaborative and challenging ways.

Maths without...algorithms • FG7

Maths without...Algorithms - or rather, the maths you do before applying them; in a word: heuristics. We shall take half a dozen problems: counting handshakes ("an old 'un but a good 'un"), map-colouring a football, arranging the court cards in a Graeco-Latin square, counting lines on a 3-D 0s and Xs board, analysing that game when there are more than 2 players, covering David Fielker’s 7x8 domino grid (see MT’s 188, 190), trying to break them down into parts, seeking symmetries and analogies, ..., and seeing how children have approached them in The Magic Mathworks Travelling Circus.

Highlights from the 2006 Edge Hill Year 9 Masterclass days • FG8

The Mathematics Department at Edge Hill has been delivering sponsored Royal Institution Masterclass activity days for gifted Year 9 mathematics pupils since 1997. In this session we present highlights of the activities that were planned and delivered by our BSc Secondary and PGCE trainees from these series. The practical tasks developing problem-solving skills, teamwork, lateral thinking, communication and perseverance of the 60+ pupils (and their teachers) who attended over 5 Saturdays from January to March will be shared. This session will be of interest to anyone wishing to generate ideas for extension activities Year 9 pupils.

Mathematics without...limits • FG9

The session will consider ideas on a common set of themes for mathematics from age 3 to 19. Delegates will be invited to engage with ideas on offer and their own as well

Concept cartoons in maths • G1

Learn how to use visual disagreements to probe children’s mathematical understanding. If you want to improve your formative assessment practice then this session is for you!

Area without...squares: proof without words • G2

There are many proofs of the pythagorean theorem based on dissection. If areas are measured in equilateral triangles rather than squares there are analogous dissection proofs for 60° and 120° triangles, matching those for 90° triangles. This session will explore some of them.

Secret codes and codebreaking - maths without...contrived context • G3

The Enigma project is an MMP schools outreach project that uses hands-on codebreaking to engage KS2 - A Level students with mathematics. This session (which includes the demonstration of a genuine WW2 Enigma Machine) aims to show how the science and history of cryptography can be used in the classroom as a context for the development of data handling problem solving and logical reasoning skills. Delegates will get the chance to put their code breaking skills to the test and will gain definitive verification that mathematicians can be heroes too!

From Archimedes to limits: history and pedagogy • G4

There are no limit processes as such in classical Greek mathematics, but by expressing some of Archimedes arguments algebraically, one can see how his methods led to the notion of limit in the 17th century. Then we can consider how this historical development may be suggestive for teaching.

<< Bob Burns’s Session Notes

Maths without...Misery • G5

Effective use of technology can make maths stimulating, fun and dare I say…easier! This session will be a springboard ofideas to inspire better use of handheld calculator technology. You will gain invaluable hints to help your students get an advantage in exams. This will lead to creative uses of digital media in maths classrooms.

This has worked for us! • H2

Ideas for the primary classroom to stimulate mathematical thinking. This session will look at a range of ATM and other resources and discuss how these can be used with effective questioning in the primary classroom. This session will include practical ideas and discussion

ICT Resources on the members only website • H3

This session offers an oppurtunity to play with the new ICT based resources developed by members, and to discuss possibilites for future resources.

A comparative study of mathematics teachers' objectives and didactic strategies • H4

Over the last three years, as part of a multinational team of researchers, I have been examining the teaching practices of both primary and secondary teachers of mathematics in Flanders, England, Finland, Hungary and Spain. We have collected systematically video taped recordings of lessons in all countries which, as part of the data analysis process, have been coded against a set of learning outcomes and pedagogic practices. In this session I will share, with the aid of some video clips, some of the outcomes of this work, highlighting both similarities and differences in the ways in which teachers work.

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