Explain this
ATM Conference 2011 • The sessions
The richest professional development for maths teaching and learning
ATM has been involved in the business of the professional development of mathematics educators for over fifty years. The Easter Conference is the annual highlight of ATM’s programme of professional development events.
Conference 2011 • Celebrating Gattegno
Mon 18 – Thu 21 Apr 2011
It is 50 years since the first ATM conference. Over the years many people have been inspired and challenged by all that conference has to offer. For me, conference is an opportunity to enjoy doing maths with others, to share ideas and improve my teaching. I always leave filled with excitement, looking forward to trying out everything I’ve learned with my students.
Full details of the ATM Conference 2011
The Gattegno Strand
The people running sessions within the Gattegno Strand have identified that a part or the whole of their session will have some relation to the work of Caleb Gattegno. Given the theme of the conference we felt that it may be helpful this year for conference members to be able to identify this link more explicitly within the session programme. It is important to note that this does not mean that other sessions within the programme will not be influenced by Gattegno as over the years many sessions at ATM conferences have had this influence.
The Sessions
- AB Double Sessions • Mon 16:00-17:30 & Tue 09:00-10:30
- A Sessions • Mon 16:00-17:30
- B Sessions • Tue 09:00-10:30
- CD Double Sessions • Tue 11:00-12:30 & Tue 16:00-17:30
- C Sessions • Tue 11:00-12:30
- D Sessions • Tue 16:00-17:30
- EF Double Sessions • Wed 09:00-10:30 & Wed 11:00-12:30
- E Sessions • Wed 09:00-10:30
- F Sessions • Wed 11:00-12:30
- G Sessions • Wed 16:00-17:30
- H Sessions • Thu 09:00-10:30
AB Double Sessions • Mon 16:00-17:30 & Tue 09:00-10:30
AB1 • The Subordination of Teaching to Learning • Aidan Harrington and Geoff Faux
In Gattegno's book "What we owe children", he explores how a teacher's role changes if they put their attention onto learning rather than teaching. These two sessions will draw on this work , together with exercises and discussion, to explore how our own practice might develop and change.
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AB2 • Learning the students and metacommenting • Laurinda Brown, Tracy Helliwell and Jan Winter
Gattegno said: “The students learn the mathematics, the teacher learns the students.” What does this look like in practice? What does the teacher do? We will explore these ideas practically through observation and discussion of lessons using ‘metacommenting’.
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AB3 • Numicon: A multi sensory approach to the teaching and learning of early number skills • Helen Farmery
A workshop where participants gain an overview of the theory that underpins Numicon whilst taking part in practical activities that address mathematical problem solving in the KS1/2 inclusive classroom. The session addresses the difficulties that early numeracy presents to many young children and highlights how, by providing structured imagery in an environment where children construct their own understanding, these difficulties are overcome.
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AB4 • Get to Know GeoGebra and Logo (for KS1 to KS3) • Alison Parish
This hands-on session will look at how a dynamic geometry program (GeoGebra) and Logo (both are free) can be used with primary and lower secondary pupils to encourage mathematical thinking whilst addressing skills often taught through textbooks. The session will look at where the two programs are relevant to the mathematics curriculum and, after an introductory tour to the programs, delegates will be encouraged to develop some ideas for use with their own classes. Starter files will be available for adapting. No knowledge of the programs is required!
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AB5 • History of Mathematics in the Curriculum: Opportunities and Choices • Leo Rogers
This session will offer materials on the History of Mathematics for the classroom for experiment and discussion. Most have been used with different pupils from KS2 (Years 6/7) to KS5 and with PGCE students. Some of this material has already appeared on the ‘History Corner’ on MTi and been published in the May 2010 issue of Mathematics in School.
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AB6 • ATM Inspirations - 40 years on • Kathleen Cross and Anne Haworth
In the year of ATM’s 50th conference, we reflect on how ATM inspired us as new teachers and continues to inspire us 43 conferences later. Every Easter we come home enthused with new ideas that help us to work with others to see the beauty of mathematics and to make mathematical connections. In these seminars we will share some of our favourite mathematics (such as spirals and tessellations) and invite you to work on it with us. What is its continued relevance for today’s classroom? How can it help you to assess what your students know, understand and can do? How can such ways of working help your students to become better mathematicians?
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A Sessions • Mon 16:00-17:30
A1 • An interface between mathematics and art: the work of Max Bill • Hilary Povey and Max Caley
This workshop explores the mathematics of some of Max Bill's artworks. Bill said art should be 'the expression of the human spirit, intended for the human spirit, and it should have the sharpness, the clarity and the perfection that must be expected from the human spirit'. The concrete art movement of which he was a part used ordered systems and gave life to these through colours, space, light and movement. Bill thought art should find a mathematical mode of thought to guarantee control of the creative principles. We will experiment with our artistic impulses working within some simple mathematical constraints.
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A2 • Learning the number system • Wendy Brady
Having become one of the army of one-to-one tutors I have discovered that regardless of age and the learning targets set, what underpins lack of progress is weak understanding of the number system. I will discuss how this affects progress, how and when we need to extend developments and some simple tasks to verify, understand or develop understanding.
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A3 • Working Mathematically with very little • Doug Williams
Sometimes we think that we must have heaps of equipment and fancy computers to help students learn to work like a mathematician. As valuable as these resources are, the most important component is a teacher who 'lives by' the Working Mathematically process in the preparation, presentation and evaluation of their lessons. Distilled from a Maths on the Move one day session of the same name, this workshop offers an outline of the sort of investigations you can begin with simple materials such as pencil and paper, packs of cards, dice and counters.
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A4 • Rich Task Maths for Y5 to Y8 • Barbara Ball
We shall work on one or two tasks from this new ATM publication. They are based on some of those in Task Maths, a series of books written by Barbara and Derek Ball some 20 years ago. These tasks are designed to help learners develop and extend their mathematical knowledge and understanding while working on engaging activities. The tasks are intended to develop confident and creative mathematicians, who are willing to engage with others and take responsibility for their own learning.
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A5 • Big Ideas: A modular approach to KS3 • Christopher Martin
Throughout my first few years teaching I noticed more and more that I was teaching the same things again and again and that the learners were having the same difficulties. With the introduction of the new National Curriculum I decided to put together a new modular Scheme of Work encouraging Relational Understanding within the topics, I hope that we will work on these during the session.
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A6 • Using software to gain statistical insight • Stella Dudzic
Statisticians use specialist software to process data; the main skills they need are understanding which techniques are appropriate to use and what the results mean. School students sometimes get bogged down in the calculations and drawings and lose sight of what the data are telling them. This session will look at using software commonly available in schools to help students gain statistical insight. One computer at the front using Excel Autograph and TI Nspire software will be used.
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B Sessions • Tue 09:00-10:30
B1 • Mental mathematics with dice and playing cards • Liz Gibbs
This is a hands-on workshop, where you will be able to use a wide selection of dice and playing card games to enhance and develop children’s mental calculation methods. You will be encouraged to play all the games in pairs or small groups. During the workshop, there will be some discussion time to adapt the games to suit the needs of your own class.
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B2 • Linking mathematics and music • Chris Messenger and Lucy Sayce
Consciously or unconsciously musicians and composers function mathematically. According to a myth, Pythagoras was prompted by blacksmiths’ hammers on anvils to examine the link between their masses and the harmonies they produced. Researchers in Los Angeles found that pupils who learned to play the piano and read music improved their numeracy. In these sessions we will explore some of these links both for rhythm and harmony. Be prepared for some practical experience along the way. Your experience of the sessions will vary according to your own musical background but we will try to cater for a wide range. We hope that discussion will arise about how ideas could be further developed in the classroom.
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B3 • Investigating uses for soap bubbles and balloons • Caroline Ainslie – Bubblz
A session with primary school teachers (including foundation level) and teacher trainers to investigate the many ways that balloons and soap bubbles can be used to enhance mathematical learning and help convert children and teachers who have been switched off by maths in the past. Alternative resources to balloons will also be discussed allowing greater accessibility to the activities.
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B4 • Flexagons • Leanne Williams and Jayne Stansfield
An exploration into the wonderful world of flexagons! Whether you have never heard of these bizarre paper-folding mysteries or consider yourself to be a bit of a fl-expert, all are welcome on this voyage of discovery to understand how a strip of paper can be so much more. The session will include a brief history of flexagons, demonstrations, hands-on construction of some of the forms that flexagons can take and plenty of mathematical group discussion and analysis as to how and why these paper tricks work.
Website referred to in Leanne’s Conference session
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B5 • Number, Algebra and Geometry in Dynamic Geometry Software • Kate Mackrell
Dynamic geometry software has moved far beyond its roots in geometry. In this session, we will compare the ways in which different dynamic geometry programs (Cabri, Cinderella, GeoGebra and Geometer’s Sketchpad) enable the integration of number, algebra, geometry (and a bit of handling data) through looking at some approaches to exploring the area of a circle.
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B6 • Stats with Attitude! • Sidney Tyrrell
Thoughts, ideas and resources for teaching statistics at all levels, with an emphasis on delivering concepts, rather than proofs and detail, to those who are not mathematicians. Real data, real stories and hopefully some real surprises! Resources to take away.
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CD Double Sessions • Tue 11:00-12:30 & Tue 16:00-17:30
CD1 • Awareness - but of what? • Lyndon Baker and Leif Kragh
When we share mathematical problems with children and colleagues what awarenesses are we hoping to seed and fertilise? How can we be sure of the level and nature of awareness that has been raised in others? How can we safely build further on these differing states of awareness in the classroom? Come and join us, look at a few problems, share some insights and possible solutions but also examine more closely just what newer horizons are now visible.
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CD2 • Constraints • MacMaths - John Hibbs
Using ideas pinched from the classroom active research, the group will explore the constraints placed on teachers of mathematics ('What stops me teaching the way I wish to teach?') and seek strategies to get around these.
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CD3 • Active learning and progression using the same tasks across KS1 to KS4 • Helen Williams and Mike Ollerton
This session will explore how the same ideas can be used across the KS1 to KS4 age range. An important issue will be to consider progression and ways of achieving this both conceptually and cognitively.
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CD4 • Using origami to nurture mathematical thinking • Sue Pope and Tung Ken Lam
This practical workshop will be an opportunity to explore how folding paper can provide a motivating context for the development of mathematical understanding. We will share models that can be used with a range of learners and discuss teaching strategies. We will show how origami can be used in many aspects of mathematics.
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CD5 • The Cube • Paul Stephenson and colleagues from The Magic Mathworks Travelling Circus
A popular target age-range for Royal Institution masterclasses is years 8-9. Two years ago in Swansea we tried out on some of your good selves such a workshop on the topic of figurate numbers. This year our subject is symmetry. Through a large number of experiments, involving vast quantities of Multilink, rather less Polydron, and perspex cubes partially filled with water, we aim to prepare your 13-year-old role-playing selves for formal work on the group concept when you enter the sixth form in 2015. The typical masterclass consists of two sessions of an hour and a quarter. By taking a double session at this conference we aim to allow half an hour for criticism.
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C Sessions • Tue 11:00-12:30
C1 • Gattegno - Taking us beyond routine practice • Judy Sayers
A workshop looking at ways in which we can go beyond practising mathematics. We will look at a selection of activities for primary children and discuss how we might take children beyond the practising of what they already know. We will look to see how Cuisenaire rods and Multilink can support this approach. We will also take a critical look at the use of the Nintendo DSi maths training program in this regard. In so doing we will think about what children can achieve if we go beyond practising procedures.
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C2 • Gattegno’s mathematizing • Els De Geest
Gattegno states that only awareness is educable. In his book “The awareness of mathematization” he describes awareness of mathematics as the dynamics of (mathematical) relationships and uses mental activities to work on this. He argues that equivalence allows thinking in terms of what one is allowed to do to transform a problem. In this session we will play with the notions of equivalence, imagery and substitution in the context of mathematical tasks to explore Gattegno’s concept of mathematization: becoming aware of dynamics of mathematical relationships.
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C3 • Using Autograph at A level • Alan Catley
This session will focus on a wide variety of applications of Autograph to teaching and learning Pure Maths, Mechanics, Statistics and Decision Maths. The flexibility of the software makes it the ideal classroom tool and there will be many demonstrations of how it can be used to keep the learners totally focused on the mathematics being studied. Delegates attending will be provided with access to a wealth of lesson plans and student ‘activity’ sheets that will be of immediate use in the classroom.
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C4 • Developing mathematical thinking through "low threshold - high ceiling" tasks • Liz Woodham and Lynne McClure
The NRICH website initially published problems for high-attaining pupils. Recently we have catered for a wider range of children by creating “low threshold - high ceiling” tasks. In this session we will work on an activity and discuss how such tasks allow all learners to engage with key mathematical processes, regardless of prior achievement levels.
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C5 • Resources created with Cabri 2 Plus and Cabri 3D to teach “perimeter and area” at a middle school level • Jean-Jacques Dahan
As a French middle school teacher wanted to teach perimeter and area by using dynamic geometry, she asked me to prepare some files with Cabri 2 plus and Cabri 3D to help her to do it. I achieved several files and she put them in her courses after designing them. I will present these files and how they were used by the middle school teacher with her students. Some files model the unfolding of triangles, polygons and arcs; other ones allow the user to discover experimentally number Pi.
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C6 • WOW! • Joe Watson
An enrichment session aimed at stimulating interest in mathematics through some surprising results. Though some of the topics should be comprehensible to students at KS4 (able) and above, a detailed discussion would require a greater background. Come along and see: Why -1 = ?, How to write down some very big numbers, A very irrational curve, Why all the rational numbers between 0 and 1 don’t amount to much, How some sums can be rearranged to give any answer you wish, Why there are many different infinities, Some geometrical coincidences...
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C7 • Real World Maths- Teaching Primary Maths Through Relevant and Engaging Contexts • Karen Wilding
Do you use contexts such as sports events, parties and young enterprise projects to teach maths? Come and be excited and inspired by simple, yet effective, ways to engage both learners and teachers of mathematics in the Primary classroom. This practical workshop will demonstrate how by beginning with maths in ‘Real World’ contexts we can show children the relevance and application of this fascinating subject in every part of our lives. The session will also look at how ‘Real World’ maths is embedded within the ‘Learning and Teaching Cycle’ to ensure high quality practice at all levels.
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D Sessions • Tue 16:00-17:30
D1 • An Introduction to Cuisenaire - Theory and Practice • Andrew Jeffrey
In the spirit of Gattegno, this hands-on session will consider the origins of (and Gattegno’s thinking behind) the use of Cuisenaire in the classroom. It is not merely a sit-and-listen session; delegates will also try around a dozen activities to take away and use in the primary classroom. It is designed for teachers with little or no previous experience of using Cuisenaire rods, who wish to explore the potential of these multi-sensory resources for themselves. Other interested parties are always welcome of course!
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D2 • Using Autograph at KS3 and GCSE • Alan Catley
This session will focus on a wide variety of applications of Autograph to teaching and learning algebra, geometry, graphing, data handling etc. The flexibility of the software makes it the ideal classroom tool and there will be many demonstrations of how it can be used to keep the learners totally focused on the mathematics being studied. Delegates attending will be provided with access to a wealth of lesson plans and student ‘activity’ sheets that will be of immediate use in the classroom.
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D3 • Celebrating Number Sense through Rich Tasks and Rich Discussions in the Primary Classroom • William Lacefield
Research in mathematics education supports a rationale for engaging young learners in rich tasks characterized by meaningful problem solving opportunities and thought-provoking discussions. During this session, participants will engage in selected rich tasks rooted in number and operations. Follow-up discussions will focus on common characteristics of rich tasks as well as resources to assist teachers as they plan for innovative instruction.
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D4 • Working Mathematically with Infants • Doug Williams
Derived from Calculating Changes, enriched by the Task Centre and Maths300 and integrated with Maths With Attitude this new resource supports K-2 teachers to build their curriculum around the concept that all students can learn to work like a mathematician in best practice classrooms. The workshop will introduce you to the kit through activity, expose its simple and flexible framework, which includes a week by week planner, and highlight teaching craft features such as threading and investigations which captivate students. As one teacher wrote: "Kids love the Poly Plugs and are enjoying the other activities from the WMI program."
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D5 • Escher’s Horses and Escher’s Sea Horses • Bob Burn
We will look at Escher’s Horse tessellation and perhaps some others, and search for other tiles which might be used to make the same tessellation. What shapes might they be? Might they be long and thin? Might the area vary from tile to tile? Then we will look at Escher’s Sea Horses which have a bit more symmetry, and search for tiles which may make the same tessellation with or without half turns. The sea horse pattern has links with conventional school work. The first half of the workshop will be a repeat of a workshop at ATM 2009, with some supplementary worksheets for those who came then. Please bring a pencil, a ruler and a rubber
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D6 • Developing mathematical thinking through "low threshold - high ceiling" tasks • Alison Kiddle
The NRICH website initially published problems targeted at highly achieving maths students. Now we try to cater for a much wider range of students by creating “low threshold - high ceiling” tasks. This session will offer delegates the opportunity to work on one of these tasks, and to see how such activities allow all students to engage with key mathematical processes, regardless of their prior level of achievement.
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EF Double Sessions • Wed 09:00-10:30 & Wed 11:00-12:30
EF1 • The Science of Education: teaching and learning mathematics • Dave Hewitt
The phrase ‘Science of Education’ comes from Caleb Gattegno who proposed that there are ways to consider the ‘cost’ of learning something. I would like to explore this idea further to see whether such this notion might inform the way in which we go about our task of teaching mathematics. The session will involve a number of activities as well as reflection and discussion from those activities. It will be suitable for those teaching any age of student.
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EF2 • Small people - are we aware of their awarenesses • David Cain
Inside the heads of very small children are powers which we ignore at our peril – and even worse, at their peril. Let us throw the theories of Piaget and his ilk out of the window and look at the levels of mathematics that we should be offering to these young people so that they can exercise their powers to the full. We will do lots of mathematics and spend time questioning what kinds of awarenesses we can expect from six and seven year-olds or ten and eleven year-olds. Perhaps more importantly, we will examine what awarenesses they already possess. Even more importantly, we will discuss what levels of awareness their teachers should possess!
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EF3 • Engaging young minds - developing number awareness • Ian Sugarman
Practical sessions exploring how equipment and virtual equipment can help 4-7 year olds develop number awareness through exploiting their natural inclination to subitise small numbers.
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EF4 • Mobile Maths • Jayne Stansfield
This workshop is based around the final project of a Maths Enhancement student which was inspired by the art of Alexander Calder and explores the mathematics of balance. In this workshop we will use these ideas to make a Calder style mobile and show how the maths can be adapted for use in classrooms at a range of levels throughout primary and secondary. This is a double session. The first part will explore the mathematics involved. We will build our mobiles in the second part which will take place in the workshop. You may attend either part separately if you wish.
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EF5 • Isosceles triangles and other shapes • Derek Ball
This two-session workshop focuses mainly on cutting up polygons, but you will not require scissors. We may also do some fitting of shapes into other shapes. As usual, the cutting up will be done more by the participants working in groups than by the session leader. Some of the cutting will be done in our heads. The ideas will be mainly relevant to key stages 3 and 4, although, as with all geometry, they might just as well be appropriate for students at key stage 2 or key stage 5...
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EF6 • Dynamic Geometry, Dynamic Art • Kate Mackrell
The connections between art and static geometry are rich, diverse, and well known. Dynamic geometry software enables us to explore some of the additional possibilities that arise when representations of geometric objects are set in motion; beautiful objects emerge, evolve, and transform, sometimes in quite unexpected situations. In this session we will create a variety of simple, beautiful objects using Cabri II Plus, Cabri 3D, Cinderella, and Geometer’s Sketchpad 5, and discuss some of the mathematics behind these objects. Please bring your own laptop. Demo versions of each software will be provided.
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EF7 • Geomegami: Connecting Girls with Mathematics Through Origami • Charlene Morrow
Participants in this workshop will both experience and hear the theory behind a two-week origami workshop that connects girls with geometry through a set of carefully designed projects. The beauty of the paper and the objects that are constructed provide motivation to work through challenging projects. The focus will be on principles for encouraging girls to become confident and find interesting connections with mathematics. These ideas have been developed over 25 years of experience directing a month-long summer mathematics program for academically motivated girls. A booklet detailing the origami workshop and associated learning principles will be shared.
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E Sessions • Wed 09:00-10:30
E1 • Confidence and Creativity in Excel • Sidney Tyrrell
Starting from scratch this session introduces Excel 2007, including conditional formatting, PivotTables, Filters and IF statements. These are powerful tools, none are particularly tricky and each can help you and your students get more out of maths and stats. Gain confidence in the know how, and get creative.
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E2 • Introduction to the National Stem Centre • Lydia Showan
The National STEM Centre is home to the UK’s largest resource collections for STEM subjects ages 5-19. Come along to investigate: a treasure chest of inspirational resources, including hands-on kit; how our online community can support your school/college and networks; where to look for wider STEM support.
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E3 • Practical Geometry: level 1 to 3 • Joe Murray
A very practical session addressing shape and space objectives for less-able pupils in secondary or as first exploration in KS2. The approach will use images of triangles and quadrilaterals which children will sort, classify, match, explain, talk about, reason with, etc. There will be opportunity to look at extensions of this work and share ideas which participants have developed with less-able. All of the ideas have been extensively used in school and in regional SEN mathematics conferences in the North.
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E4 • Using NRICH to support exceptionally able students and their teachers at • Steve Hewson
Key Stages 4 and 5
In this interactive session we will explore recent innovations and developments on the NRICH website designed to help the development of exceptionally able students. We will discuss the special needs of exceptionally able students, the difficulties facing their teachers and, of course, have a go at some problems for ourselves. The session will be aimed at the Y11/12 content level but may be of wider interest given that exceptionally able students often work well beyond their age. Mathematically less confident teachers very welcome!
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E5 • cre8ate maths workshop • Colin Jackson
This workshop will introduce participants to cre8ate maths. cre8ate maths’ origins were as a continuing professional development project which sought to engage teachers through involvement with the development of high quality mathematics curriculum materials. The workshop will very briefly introduce participants to the background to the project but in the main they will have the opportunity to try some of the materials developed by the project.
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E6 • Mathematical Balloon Modelling • Caroline Ainslie- Bubblz
A balloon modelling workshop with a difference. Participants will learn the basics of balloon modelling, then be challenged to create a 3D shape. It is surprising how much visualisation is required to create even the simplest of shapes. Bring a challenge of your own!
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F Sessions • Wed 11:00-12:30
F1 • It’s a Kind of Magic • David Crawford
In this session I will present some mathematical tricks suitable for pupils of widely differing ages. These will range from simple number tricks which could be used for encouraging practice of calculation skills or as vehicles for introducing different algebraic skills to mathematically based card tricks useful for investigation or entertainment. There will be plenty of opportunity for delegates to engage with the tricks so please bring pen, paper (and calculator) and prepare for some mathematical amusement.
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F2 • Rich Task Maths for Y9 to Y11 • Barbara Ball
We shall work on one or two tasks from this new ATM publication. They are based on some of those in Task Maths, a series of books written by Barbara and Derek Ball some 20 years ago. These tasks are designed to help learners develop and extend their mathematical knowledge and understanding while working on engaging activities. The tasks are intended to develop confident and creative mathematicians, who are willing to engage with others and take responsibility for their own learning.
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F3 • From Challenge Cards to Mathematics • Jenny Murray
Come and do some mathematical problems in this workshop session. We have been collecting challenging and intriguing problem-solving material for classroom use, specially suitable for Key Stages 2 & 3. The resources are designed to encourage learners to think and talk mathematically to each other as they work on a problem together. Most of the activities are in the form of ‘Challenge Cards’ with accompanying equipment to manipulate but some material is taken from the NRICH website and elsewhere. We hope to stimulate discussion between participants by working on the resources together.
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F4 • Ringing the Changes - the Mathematics of Bell Ringing • Joyce Brown
This session takes a look at the mathematics of change ringing, with an opportunity to have a go with a set of hand bells. With 4 different bells, there are 24 different "changes" that can be rung, but there are particular rules about the order of ringing these, which lead to symmetry, Fibonacci numbers, Pascal's triangle and networks. Group Theory is involved, but this talk will not be at that level; the mathematics is accessible to all, and has been given to both primary and secondary masterclasses.
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F5 • Convince Me! • Joe Watson
When does a hunch/conjecture become a theorem? Why do we find some explanations convincing? Are proofs necessary? What do pupils feel about proof and explanations? Some ('neat') proofs lead to the reaction…'of course!' To help us, we will use lots of pictures, beads, football crowds, examples of children's work, some false conjectures, and some 'neat' proofs.
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G Sessions • Wed 16:00-17:30
G1 • Encountering algebra with rod props • Don Steward
Why bother to get bricks out and spend time picking them up off the floor? This is aimed at Cuisenaire rod novices, providing resources and ideas (based on Gattegno's) for those who are partial to utilising student prowess, talk and a focus on relationships. Using manipulatives and rod thinking smoothly enables many students to travel towards a formal knowledge of what algebra is and what it does for you. By alluding to resources, some tasks and classroom experiences, participants will be offering a range of suggestions and perspectives about helping to move students on from just playing with them - to more serious playing. Don Steward has worked as MEDIAN which has collected and disseminated ideas for teaching secondary topics.
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G2 • Using geoboards in KS 2 • Liz Gibbs
This is a hands-on workshop, where you will be able to use and explore geoboards (also known as pin-boards). You will be encouraged to build, investigate, solve problems and record a variety of shapes. Geoboards, coupled with square dotty paper supports activities in measurement and number. During the workshop there will be time to look at how working in this way can enhance the children’s learning experiences and transfer these fundamental experiences to paper based activities.
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G3 • Educating awareness of the ‘big ideas’ in mathematics • Jenni Back
This will be an interactive workshop based on ideas that we have been using and developing with teachers and children in various schools around the country. We will try out some tasks that we have developed to use with young children to help them access the big ideas in mathematics.
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G4 • Getting to know GeoGebra through Celtic Art • CANCELLED
Unfortunately this session has been cancelled due to circumstances beyond our control.
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G5 • Exploring the M in STEM • Sue Pope and Rebecca Edwards
This discussion group will explore the potential of STEM to provide curriculum coherence for the learner and enhance learning in the constituent disciplines of science, design and technology, engineering and mathematics. We will share examples of the use of exciting and motivating STEM experiences as the launchpad for developing rigorous conceptual understanding and positive attitudes.
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G6 • Stan’s Café in the classroom • Vivien Townsend
Two years after the memorable and moving Stan’s Café exhibition at Swansea, where each grain of rice represented a person, find out how schools in Warwickshire were inspired to use rice, beads, tea bags, potatoes and other cheap resources to make data come to life in the classroom. We will create our own exhibition during the workshop, will consider the opportunities to make meaningful links with other subjects and will discuss the possibilities for involving parents and the wider school community in our data handling.
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G7 • Supporting Struggling Pupils • Rosalind Martin
This session aims to equip teachers with practical, hands on activities which strengthen pupils’ basic understanding of number, especially using the Kinesthetic learning style. The ideas largely originated from recent Dyscalculia research, and the resulting resources have been refined as different pupils have responded to them. - Identifying problems without testing - Building confidence with place value - Increasing speed and accuracy with mental arithmetic - What if they CANNOT remember their tables? - Long multiplication that makes sense - Long division - helping weaker students to make it work. Participants will leave the workshop with a selection of photocopiable and interactive-whiteboard-friendly resources.
2 • 3 • 4 * See key
G8 • 1 Computer, 1 Data Projector, 1 Piece of Software • Doug Williams
Maths300 supports teachers to model what it means to work like a mathematician in best practice classrooms. It highlights learning features that fascinate, captivate and absorb kids. For some investigations one of those features is software and Maths300 has developed one piece with over 60 sub-programs to support and extend problem solving. It is used most fully when students can design and carry out their own experiments, in pairs, on their own computer, but given only one computer and a data projector, such as in an interactive whiteboard classroom, exciting things can still happen. The session will explore a smorgasbord of problems and link each to its software extension.
1 • 2 • 3 • 4 • A * See key
G9 • Elliptic Curves - a light-hearted introduction • Jonny Griffiths
Elliptic curves are sexy currently; Andrew Wiles used them to prove Fermat’s Last Theorem, and they are at the heart of much cryptography. But what are they, and why are they so interesting? This session will introduce the beginnings of the subject; it will be active, and there will be lots of pictures! The good news is that elliptic curves are more than useful, they are beautiful too. Nothing beyond A Level Maths will be assumed.
5 • T • A * See key
G10 • Soroban, the Japanese Abacus and Mental-arthimetic • Kimie Markarian
When performing mental arithmetic using soroban images, the brain requires much less effort. Its calculation proceeds from left to right, using number facts only up to ten. Its positive effects have already received international recognition. In this session to create images of numbers, we draw the images on paper instead of using an actual soroban. In this way the images are clearly created onto the brain. The aural exercises using number bonds 5 and 10, bridging, and times tables, leads to real understanding of mathematical processes.
1 • 2 • 3 • T • A * See key
G11 • More pupil power - learners as teaching aids • John Suffolk
The workshop will continue the work at conferences in the last three years in which learners at all levels become teaching aids, becoming shapes, perimeters of shapes, graphs and other objects of their own learning. The activities in which all can participate and develop their maths with understanding and laughter cover much of the curriculum.
2 • 3 • 4 * See key
G12 • Vitamin D Maths • Jocelyn D'Arcy
Starting points and ideas for curriculum focused secondary lessons that take place outside.
3 • 4 * See key
H Sessions • Thu 09:00-10:30
H1 • Possibilities For The Classroom • Colin Foster
We will look at examples of ‘possibility tables’, which are grids of cells with values of two variables running horizontally and vertically. Learners are invited to think of examples of mathematical objects that can go in each cell, or express generalities regarding what is possible or impossible. Participants will be encouraged to try some possibility tables for themselves, consider their use in the classroom and devise others. It will be ‘possible’ to work on different areas of mathematics and to have different age learners in mind.
2 • 3 • 4 • 5 • A * See key
H2 • Gattegno vs Freudenthal: Battles of the Early Years • Tony Wing
The workshop will explore the contrasting approaches of Gattegno and Freudenthal to early years’ number teaching. We will refer to selected observations of both Gattegno and Freudenthal concerning the merits (and demerits) of structural apparatus (particularly Cuisenaire rods) and number lines, for supporting the early development of number ideas and calculating, and review activities for children that they recommended. In the light of more recent work (e.g. Sfard 2008) we can review whether their differences remain relevant today.
1 • T • A * See key
H3 • The Staffroom in the Ether • Rebecca Hanson
Would you like there to be a friendly maths staffroom that you can drop into at 24 hours a day? Somewhere where you can get advice, explore you own ideas, help others, sound off or just eavesdrop on interesting conversations? In this session Rebecca Hanson will take you on a tour of the available chat sites and discuss the practicalities and benefits of using them. She might tell a few stories of the things which have happened on them too.
1 • 2 • 3 • 4 • 5 • T • A * See key
H4 • √66 and all that • David Acheson
Square roots can help bring mathematics to life in many different ways, ranging from the number system itself to chasing the exact value of pi, exotic methods of proof, playing with the infinite, flying an aeroplane and even cooking a hot dinner.
G * See key
H5 • Mathematical Mazes • Vivien Townsend
Inspired by the Working Outside the Classroom area of the NCETM website and drawing on the session leader’s recent work with KS2 pupils and KS3 teachers, this active workshop explores the possibilities of using mathematical mazes in the classroom. We will experience three styles of giant maze, at different levels of challenge, and consider the mathematics that we’re doing. We’ll also have a chance to create our own mazes and discuss the possibilities of using mazes back at school. In addition, you will leave with a couple of irresistible starter activities that you can use in school tomorrow.
1 • 2 • 3 * See key
H6 • Celebrating problems • James Robinson
I intend here to work on some problems from past conferences, various resources I have found over the years and who knows? Maybe even something new! All of them are problems that I have used with students. Ideas will be suitable for years 7-77 as any good problem begins simply, but can be extended to the complex.
3 • 4 * See key
H7 • Making algebra more accessible with use of computer interactivity • Karen Finch and Dave Hewitt
This session will involve working on some of the issues which have arisen from an NCETM funded project on the use of Grid Algebra in two schools in the West Midlands. The session will involve some activity with Grid Algebra, a limited amount of reporting back on issues raised from the project with the purpose of us working on those issues in small groups and as a whole group. Possible issues are: when does working with numbers become working algebraically? What might motivate students in algebraic activity? Do difficulties students have with algebra change due to the teaching approach? Etc….
2 • 3 • 4 • A * See key
H8 • Linking mathematics and music • Chris Messenger and Lucy Sayce
Consciously or unconsciously musicians and composers function mathematically. According to a myth, Pythagoras was prompted by blacksmiths’ hammers on anvils to examine the link between their masses and the harmonies they produced. Researchers in Los Angeles found that pupils who learned to play the piano and read music improved their numeracy. In these sessions we will explore some of these links both for rhythm and harmony. Be prepared for some practical experience along the way. Your experience of the sessions will vary according to your own musical background but we will try to cater for a wide range. We hope that discussion will arise about how ideas could be further developed in the classroom.
3 • 4 • 5 * See key
H9 • I Can – Working with Learners of all ages with Learning Difficulties • Alison Parish
Given the opportunity and encouragement, learners can often achieve more than many people expect. This session will demonstrate how a group of adults with learning difficulties became keen to learn more about mathematical skills and the additional benefits to them as individuals. The session will be appropriate for anyone with an interest in learners with learning difficulties. The session will include opportunities to hear about activities that were used with them as well as a chance to share ideas and to create some resources that can be used with any age group.
2 • 3 • 4 • 5 • T • A * See key
H10 • Exploring pattern blocks in Key Stages 1 & 2 • Liz Gibbs
This is a hands-on workshop, where you will be able to experience the versatility of using pattern blocks though Key Stages 1 and 2. Pattern blocks are an essential classroom resource. They can be used to support and enhance children’s mathematical experiences. This workshop will provide teachers with a wealth of ideas to support children’s thinking in number, handling data, fractions, problem solving and shape and space.
1 • 2 * See key
H11 • Argumentation and reasoning with students with low prior attainment in KS4 • Nichola Clarke
I will present for discussion some of my research findings on the reasoning and argumentation of KS4 students with low prior attainment in mathematics. Then we will work together on a variety of ways of reasoning in school mathematics, and on classroom tasks and teaching strategies for developing reasoning.
2 • 3 • 4 * See key
H12 • Using Constructions Constructively • John Smith
In this practical session we will use constructions to develop and reinforce properties of shapes. The activities will involve the use of a straight edge and a pair of compasses (so practise using them beforehand !) All the activities have been used successfully with pupils working in late primary and secondary.
2 • 3 • 4 * See key
Key
The letters and numbers indicate the age ranges for which each session may be most appropriate.
F • Foundation
1 • Key Stage 1
2 • Key Stage 2
3 • Key Stage 3
4 • Key Stage 4
5 • Key Stage 5
T • Tertiary
A • Advisory
G • General
