ATM Conference 2013 • 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 2013 • Maths for Real
Tue 02 – Fri 05 Apr 2013
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.
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. 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.
On line booking for sessions is now closed but you can book on to sessions on arrival at the Conference provided the sessions you require are not already full.
- AB Double Sessions • Tue 16:00-17:30 & Wed 09:00-10:30
- A Sessions • Tue 16:00-17:30
- B Sessions • Wed 09:00-10:30
- CD Double Sessions • Wed 11:00-12:30 & Wed 16:00-17:30
- C Sessions • Wed 11:00-12:30
- D Sessions • Wed 16:00-17:30
- EF Double Sessions • Thu 09:00-10:30 & Thu 11:00-12:30
- E Sessions • Thu 09:00-10:30
- F Sessions • Thu 11:00-12:30
- G Sessions • Thu 16:00-17:30
- H Sessions • Fri 09:00-10:30
AB Double Sessions • Tue 16:00-17:30 & Wed 09:00-10:30
One Size Fits All explores the benefits of delivering rich tasks that can be accessed by all Mathematical abilities. A strong element of these tasks emphasises the communication of methods and strategies that the learners use to solve the problems.
Due to popular demand. 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.
The Science of Education Working Group focuses on the use of Gattegno’s ideas and is currently working on the power of imagery. We will run this session as our day meetings when members of the group offer an activity and the rest of us engage in the mathematics together followed by reflection. As convenors, we will begin by offering some activities and by the second session members of the group at conference can share their own favourites. We aim to produce an ATM publication and you are invited to contribute writing during and after conference.
A Sessions • Tue 16:00-17:30
How long can we survive without numbers? This session is based around a haunting story of a person who dislikes mathematics intensely mainly because he doesn’t understand how numbers work. An alien drops our number system down the loo and poses a problem of redesigning a system from 4 very odd shaped numerals. As the session unravels, the logic behind our number system becomes clearer and teachers/practitioners start to question the way they have traditionally taught place value. This is an emotive session that presents challenge and initial confusion but teachers have reported the power of its key messages and how it raises empathy for kids who just don’t get it and don’t see the huge role that number plays in our daily lives.
A great school project - cross curricular, with LOADS of mathematics, we will build a 4 stage 3D Sierpinski Gasket over the course of the conference. Starting with 8 cm tetrahedra (edge length), building up to a fractal with 1.28 m edges, consisting of 256 paper tetrahedra.
When real life intrudes unexpectedly into the mathematics classroom, what can the teacher do? Situations could range from learners spotting something ‘interesting’ out of the window (‘Miss, there’s someone on the roof!’) to a sudden power cut plunging the classroom into darkness (‘We can’t see so we can’t do any work!’). In this session we will consider ways in which mathematics teachers might prepare for the unexpected so as to be able to respond with a relevant mathematical task when something unanticipated takes place. I will offer some classroom scenarios (‘real’ and imagined) and the group will be invited to work on bringing mathematics into, or finding mathematics in, the particular situations. Please feel free to bring along your own examples of unexpected happenings in the classroom, with or without mathematical responses!
In this session I will look at some mathematical tricks that can be used to encourage students to engage in arithmetical pratice and to provide a justification for algebraic manipulation. It will be a "hands-on" session so please bring pen, paper calculator (if you think it will help you) and your enthusiasm.
Calculating changes across the school when you stop thinking of something like 8 + 7 as an instruction to calculate and start thinking of it as an opportunity to investigate. Then the answer isn’t 15; it’s the variety of ways we can convince someone the answer is 15. This workshop offers an opportunity to experience such activities, consider the teaching craft involved and learn about web support from Calculating Changes, a network of teachers committed to enhancing children’s number sense. The network assumes access to Poly Plug and simple calculators and includes a detailed core curriculum for Years K - 2.
Matrix logic puzzles provide opportunities for critical thinking, meaningful cognitive struggle, and clever problem solving. When matrix logic puzzles are incorporated into the mathematics teaching/learning environment, pupils must reason deeply and eliminate possibilities in order to find solutions. In this session, participants will work collaboratively to explore and solve a variety of matrix logic puzzles. Follow-up discussion will include a focus on strategies for creating these types of puzzles.
This session will explore some free resources related to the mathematics ideas in A Level science. The resources can be used by teachers of A Level Mathematics to introduce ideas in mathematics and to show where they are used or they can be used by teachers of A Level science to improve student understanding of the underlying mathematics. The resources do not require participants to have knowledge of mathematics beyond GCSE.,,"
B Sessions • Wed 09:00-10:30
This workshop will focus on doing several of the mathematical activities developed by The Mathematics Education Centre (MEC) at Sheffield Hallam University.,,"
A group of qualified MaST teachers describe the ongoing impact of the programme on their practice and their schools. ,,"
In this interactive session participants will engage in practical activities, will work collaboratively, share ideas and engage in mathematical conversation to explore how we can support children’s mathematical learning using the ‘real’. Participants will experience the power of the Numicon approach, using concrete and visual apparatus that are so successful in helping children to really understand mathematical ideas, concepts and operations thereby promoting flexible mathematical thinkers not only at school but at home and in everyday life.
Ri Mathematics Masterclasses aim to open the eyes of young people to the excitement, beauty and value of mathematics through hands-on and interactive sessions which go far beyond the school curriculum. Come along to find out more about the programme and masterclass network, have a go at some activities and get some ideas to take away. It’s then your turn to share your favourite mathematical idea and look at ways of developing it into a masterclass style activity. You will work with your peers to explore different directions in which to take your ideas and bring them to life.
In this hands-on workshop, you will have the opportunity to engage with a range of tasks that have been developed by 10 school/university partnerships from 7 countries during the EU Comenius funded project ‘EdUmatics’ (2009-2012). The EdUmatics project has produced five professional development modules for teachers that focus on different aspects of technology integration in secondary mathematics. These modules include a range of classroom video resources that provide an insight into differing practices from the participating countries. You are advised to bring a laptop installed with a computer software packages that supports the linking of multiple representations in mathematics such as Geogebra or TI-Nspire.
The session will look at learning maths in a project base, exciting, tactile and functional manner. Planned for the KS3 Condensed curriculum, the curriculum each year is taught over 5 units. Session will look at ways to deliver the units and make it applicable for different classrooms. There is a series of scheme of learning, tactile activities, quality written communication activities and project components to be completed. The session looks at ways to deliver maths in a creative and motivational approach.
No details available.
CD Double Sessions • Tue 11:00-12:30 & Tue 16:00-17:30
In this session we will offer mathematics tasks for everyone to work on that lend themselves to working enactively with physical resources
The multiplication tables are still with us. There must be better ways of getting to know them than chanting them, and better methods for recovery of single items than reciting them. We shall explore other ways of organising multiplication facts, and possibilities for treating them as a source of problems, and as an area for mathematical exploration and investigation rather than merely something to be remembered. In other words, can we treat the tables as an area of mathematics, rather than just a prerequisite for calculation?
Discover properties of platonic solids by solving puzzles. Balloons will be used in the workshop as well as other easily obtainable resources such as plastic straws, old magazines and pipe cleaners.
C Sessions • Wed 11:00-12:30
A two year project funded by the Royal Academy of Engineering and in conjunction with MEI has resulted in the production of 43 resources designed to show maths in an engineering context at level 3. These free resources will be described and additionally one, or more, will be presented in detail as an interactive workshop activity.
Gattegno maintained that we can exhaustively identify the awarenesses needed in any domain and redefine teaching as the activity which leads students to cover this ground for themselves without missing any essential steps and without wasting time. To this end he developed the Cui curriculum and related textbooks. Like the proposed primary curriculum, Gattegno covers all four arithmetic operations, fractions and product tables at KS1. He did this by introducing algebra as a formal language first, before number. What does algebra look like to infants? We will cover Cuisenaire code, trains, staircases, patterns, decimal fractions and percentages in practical exercises.
In this workshop session we will explore some approaches to learning how to graph functions that encourage understanding of some of the underlying concepts. We will also discuss how to implement these to secure this understanding and so be able to apply it in real life situations. Some of these real life situations will be considered and evaluated for their classroom impact!
Ensuring maths is applicable, relevant and embedded in real-life experiences has become a priority for many teachers in recent years. The impact upon motivation, progress and standards can be extremely significant when children learn through such approaches. However, excited children are often mistaken for children who are learning effectively and phrases like 'It was great! They didn’t even know they were doing maths!' are frequently overheard. This session will explore how teachers can create the right journey between ‘real-world’ -‘maths world’ -‘real-world’; resulting in a ‘maths sandwich’ if you like...
Every Child Counts offers schools two powerful approaches to improving mathematical understanding and breaking cycles of underachievement. Numbers Count - an intensive specialist teacher led intervention for the children who have the greatest difficulties in mathematics. 1stClass@Number - a lighter touch intervention delivered by a trained teaching assistant to small groups of children. In this session Every Child Counts National Advisers will share some of the findings from their successful work over the past four years which is about making mathematics accessible and real to all children.
Since we first gave a Royal Institution Y8 masterclass on this topic, we have developed the subtopics as more extended maths club activities. The subtopics are surfaces with particular properties: minimal surfaces, ruled surfaces, developable surfaces. We investigate minimal surfaces with Cyril Isenberg’s kit; ruled surfaces with craft wool and shirring elastic (and, on the ‘people’ scale, rope); developable surfaces with paper (most interestingly John Sharp’s D-forms), Polydron, and drinks cans variously deformed.
This session will explore some free resources related to the mathematics ideas in A Level social science. The resources can be used by teachers of A Level Mathematics to introduce ideas in mathematics and to show where they are used or they can be used by teachers of A Level social science to improve student understanding of the underlying mathematics. The resources do not require participants to have knowledge of mathematics beyond GCSE; they are mainly statistical.
D Sessions • Wed 16:00-17:30
Mathematics is used everywhere. In this session, Chris will describe experiences and uses gained over 24 years of industrial and academic application. Topics will cover iPhone applications, library indexes, sausages, digital music processing, salmon lice, water power and pregnancy.
As part of the 4-year ICCAMS project (based at King’s College London and funded by the ESRC) we worked with some Year 8 classes and their teachers to develop lesson materials on multiplicative reasoning. We will report on our experiences and explore some of the activities that we produced, and we will discuss how the materials might be used in the classroom.
A mathematician’s work begins with an interesting problem. Therefore in a curriculum built around learning to work like a mathematician, students will often be invited to begin their work in this way. Hands-on problem solving tasks from Mathematics Task Centre are the world’s largest source of such interesting starting points and offer much more than the tip of the puzzle described on the card. In this workshop you will explore a sample of these tasks and find out about their depth, their multiple lives, stories of success from experienced colleagues and the web support provided by Mathematics Centre.
Few primary teachers are familiar with mathematics as a language. What do teachers look for when they observe students working with rods and algebraic writing? What does Gattegno mean by equivalence and how does he harness the idea to create rich opportunities for students to learn? Reasoning with equivalence: colour, length, difference, parity, fractions as magnitudes, products. Reasoning about equivalence: sets, functions, domains, objects, arrows, permutations and combinations. Exercises with Complete Patterns. Formative assessment of student work in Years 1-6. Sessions based on eight years experience of re-introducing Cui in the Tizard network of primary schools.
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; how list functionality provides packages of resources to support teaching; how our online community can support your school/college and networks; where to look for wider STEM support.
In primary masterclasses, children enjoy lively sessions which, through games, activities and investigations, develop their mathematical reasoning, problem solving and communication skills. In this session delegates will hear about the programme and masterclass network, and will get ideas to take back to young mathematicians. It’s then the turn of the delegates to share their favourite mathematical idea and look at ways of developing it into a masterclass style activity. You will work with your peers to explore different directions in which to take your ideas and bring them to life.
A dynamic and practical demonstration of how we have successfully included the innovative and exciting ‘Maths 300’ activities into our Year 7 and 8 lessons and programmes. Come along and also experience ‘Polyplugs’ (an innovative and engaging resource we use in the teaching of Fractions) and a novel approach to the teaching of Problem Solving techniques.
EF Double Sessions • Thu 09:00-10:30 & Thu 11:00-12:30
Pupils appreciate the power of algebra when they generalise for themselves, rather than having generalisations presented to them, and when they use algebra to justify and solve problems. Exploring different ways of forming and transforming expressions and equations gives them insight into the algebraic relationships that underpin number and enables them to make appropriate decisions, rather than relying on (and misapplying) given rules. At Improve Maths, we are working on materials to develop a clear teaching progression that applies these principles consistently across the secondary phase. We will share findings from early trials and seek your thoughts on further developments.
Come and do some real maths in the form of challenging problems. Some of what is on offer will be whole group activities but most is material for pairs working together. Much of this is in the form of ‘Challenge Activities’ which are designed to encourage learners to think, and talk mathematically to each other, as they work on a problem together. We also hope to stimulate discussion between participants by working on the games and other resources.
What often prevents learners from seeing mathematics as real, for them, is that they do not readily make connections between the different topics they meet in the mathematics curriculum. So, in this seminar, we will work together on how, as teachers, we can help learners to see these connections. We will do this by exploring some of the big ideas/themes that run through the curriculum and see how these can be made explicit. We shall probably explore some ideas such as sets, finite and infinite number systems, justification and proof, discrete and continuous variation and isomorphisms and we will seek to identify how, in the teaching of conventional topics, an exploration of these ideas can help develop understanding and create an awareness of the richness and interconnectedness of mathematics.
A double session which involves working collaboratively. The mathematical tasks are introduced in such a way as to ensure quality of discussion, interaction and creative thinking. Children have to use their common sense and resourcefulness. We will consider the value of such tasks from both a cognitive and social point of view. You will have the opportunity of creating some of your own tasks.
E Sessions • Thu 09:00-10:30
Exploration of the meaning of division, and clever things to do with long division, suitable for all those who suspect that long division is not the end of the story.
The class are ‘hooked’ into the story! As you reach the cliffhanger, the children freeze in anticipation. Do you know that feeling? This problem-solving workshop will enable you to replicate that moment with your pupils by triggering their natural curiosity. The session will aim to bring conventional word problems to life using digital media and concrete resources. The question: ‘but then what happens?’ is a natural one that children need to ask regularly in order to be confident problem solvers! Come and explore how to stimulate this natural curiosity.
Sensible suggestions about the behaviour of graphs may fail, and constructing examples to show fallibility is one way of facing them. Another possibility when things are hard to prove, is to show that really good ideas can collapse when we shift from the real numbers to the rationals. That clears up why proving may be difficult and what the difficulty may consist of.
However swift they appear to be, mental events happen over time. In this session, we will test the idea of a moment of learning being a two stage process. Using terminology that Gattegno developed, we might characterise these stages as those of ‘presence’ and ‘awareness’. During the first, we are present to some part of our world, during which time potential awarenesses gestate. This is followed by an ‘awareness’, which may (or may not) come to consciousness. The cycle then continues, as the new awareness leads to a reconfiguration of our presence.
Join Rob Eastaway and Andrew Jeffrey for an assortment of some of their favourite maths ideas to engage you and your class. You’ll discover the power of Zequals, an engaging game of Cops and Robbers, and as many other nuggets as we can squeeze into a workshop. Why ‘Maths Marmalade’? Because it’s a bit like Maths Jam (look it up!), but with slightly chunkier segments.
Mathematics contains all sort of sequences formed by applying a rule successively to elements of a set; the results of one outcome being used for the next; or with the steps needing to be found between a chosen start and finish. Such exploration leads to some interesting links, challenges and results. We will explore a number of such chains, mentally, by pencil and paper, algebra, origami, calculator, and People Maths methods.
F Sessions • Thu 11:00-12:30
As part of the 4-year ICCAMS project (based at King’s College London and funded by the ESRC) we worked with some Year 8 classes and their teachers to develop lesson materials on algebra. We will report on our experiences and explore some of the activities that we produced, and we will discuss how the materials might be used in the classroom.
National Numeracy is a new independent charity that focuses on adults and children with low levels of numeracy. We launched, with strong coverage in the media in March 2012 and aim to challenge prevailing attitudes, influence public policy and research, identify and promote effective approaches to improving numeracy. Where possible, we will work in partnership with others - such as ATM - to achieve these aims. In this session we hope to provide a brief overview of the organisation and what we have done so far before a discussion with all who attend for their views on future approaches and activity.
The session will review current practice for introducing the decimal number system to children emphasising how flawed this is. These flaws pose condiderable difficulties for less able children. The Helical Number Line offers an alternative in the form of an intermediate step. Children welcome this idea, because it makes sense and is fun to use.
Jenni will share some of the experiences of teachers and children involved in the NCETM’s Host Schools Project. We will look at some resources we have used with children and teachers and consider the important mathematics ideas that are key to supporting children to move on from counting strategies to using known facts, from addition and substraction to multiplication and division, from informal methods to using algorithms with understanding. The workshop will involve doing some mathematics, discussing the key issues and hearing from some of the teachers involved in the project.
A session for anyone, especially the less confident, who would like to know what a PivotTable is, and can do for you, as well as learn about filters, formatting (conditionally), spinners and sliders, dynamic charts, simulations and macros, plus the tips no-one has told you. Take away DIY spreadsheets to practice on.
A tangram is a geometric puzzle consisting of a square cut into seven specific polygons that can be arranged to form countless other shapes. Tangrams have the power to influence mathematics teaching and learning in meaningful ways, inspiring lessons in critical thinking, number sense, geometry, and measurement. In this session, participants will be encouraged to think deeply as they create tangrams, explore a variety of puzzles, and brainstorm creative ways to use tangrams to engage learners. This session is suitable for students in teacher training programmes, Newly Qualified Teachers, and anyone who wishes to learn more about tangrams.
G Sessions • Thu 16:00-17:30
cre8ate maths was an innovative CPD project run by the Mathematics Education Centre (MEC) at Sheffield Hallam University in Yorkshire and the Humber. The CPD involved teachers in the development of real world mathematics materials targeted at KS3. The materials are freely available on the web. During the workshop we will do several of the activities from the less obvious industrial sectors.
An aim of this session is to share the solutions that readers of MT have found for the ‘Maths Medicine’ geometry tasks published over the last year. We will reflect on the heuristics that might have been used and consider how seemingly different solutions may demonstrate the interconnectedness of geometric ideas. If there is time, we might try to devise and/or solve similar tasks. I might also report how GeoGebra was used to devise animations for the tasks and how these can be exported as QuickTime movies and Java applets.
The latest version of Autograph can run in a web-based environment, so that investigations can be undertaken remotely. This session will cover a number of lesson plans up to KS4 and 5 • and will show how to save files ‘to web’. Douglas will also demonstrate Autograph being controlled through an iPad and a graphics tableT • And will explore the growing collection of web-based tutorials and blogs that concern Autograph. All attendees will receive a copy of the current version of Autograph.
Explore the structure and patterns of 3 by 3 magic squares, unpick the complexities of 4 by 4 squares, including a few ideas with algebra...then on to the ‘Order 8’ square made famous by Dan Brown in ‘The Lost Symbol’, Finish up with some REAL ‘square activities’ with a cross-curricular relevance. ATM Sheffield Branch
The session will review current practice for introducing the decimal number system to children emphasizing how flawed this is. These flaws pose considerable difficulties for less able children. The Helical Number Line offers an alternative in the form of an intermediate step. Children welcome this idea, because it makes sense and is fun to use.
This session will be about how the Mathletics program can be used to enhance and support teaching in the classroom.
Recent studies show there were many different ways of proving mathematical theorems before Euclid’s methods became accepted. Participants will be offered some insights into ideas from different cultures that can be adopted for the secondary classroom. Problems, explanations, and suggestions for the classroom will be available as pdf downloads.
In this session, I will share some resources from pupil challenge days with young children from across the primary age range. You can audition to be in Captain Townsend’s mathematical pirate crew, find out whether you have what it takes to be a super hero and see if you can solve the mystery of who killed Lady Lenton. We’ll look at what makes mathematics real for pupils and consider the power of pretending. Be prepared to join in!
This workshop is a multiplication journey that begins with children first arranging objects in equal rows - an array model - and takes us through to the visualisation of abstract algebraic formulas. It explores activities which use concrete objects, semi-concrete representation such as graph paper and virtual representation through software, to simultaneously develop meaning in multiplication and facility with times tables. Although there will be activities for you to ‘use tomorrow’, the session will also stimulate thought about planning the multiplication journey through the school so that more students are more successful at multiplication matters.
From counting through bartering to substitution and Turing machines, exchanging some things for others seems to lie at the heart of almost every topic in school mathematics. Participants will be invited to engage in a choice of a range of tasks from early years to sixth form (or beyond) based on the notion of exchange, and to offer examples of topics unrelated to exchange!
H Sessions • Fri 09:00-10:30
IMaST stands for Integrated Maths Science and Technology. Research has shown that the Imast programme can increase attainment for participating students. This session is a hands on and interactive workshop demonstrating the power of STEM for KS2 and 3. Attendees will go away with many ideas on how closer links between the subjects can benefit students and teachers alike.
Changes to the National Curriculum inevitable mean that teachers have to consider changes to their teaching and classroom practice. This session will consider working with the new NC which includes mathematical thinking and problem solving rather than a purely concentrating on skill and kill.
We will look at Coxeter’s film "Dihedral Kaleidoscopes" for 15 minutes and then try to find what sort of prisms made of mirrors generate wallpaper patterns. Can a prism of mirrors that "works" be used to make different kinds of wallpaper?
Café Conundrum offers curious questions, tantalising tasks, remarkable riddles, perplexing puzzles and enticing enigmas, but most of all it offers choice. An opportunity for students to choose - and own - their mathematics learning. It is one model teachers have developed to build classrooms in which students are learning to work like a mathematician. Explore this model through Menu Maths Packs from Mathematics Centre and be introduced to other models such as Pass On Problem Solving and Replacement Units. All models have web support for later follow up.
In this session we will give you some ideas for science experiments in your maths classroom and will try a few of them out!
Using the principles of guided reading, guided Maths can have a significant impact on developing communication and reasoning across the primary phase using a range of pedagogical activities to deliver high quality talk for Maths opportunities.
Douglas makes a point of keeping tabs on what’s ‘up there’ and what’s valuable for the busy teacher. Lesson ideas will abound in this session from web-based apps, including Google Earth, GapMinder, blogs, tutorial videos and dynamic software. We will also consider what’s ‘down here’ to view it all on - new gadgets coming out almost daily, so who know what will be new come next April.
Probability plays an integral part in shaping our understanding of the world. Throughout education we can encapsulate children’s imagination and enhance their understanding through exploring ideasof probability that relate to real life. This session will explore how the concept of probability is formulated theoretically and experimentally. We will allow for the intuitive development of the concept of probability through interactive engagement. A range of activities will be presented suitable for a variety of levels of knowledge and capability. Participants will be provided with ideas and open activities to cater for a range of levels of engagement.
Stars have fascinated the human race throughout history. In this session we will look at some mathematical ideas related to stars, and make 2D and 3D stars ourselves. It is based on an idea that caugt my imaginiation in MT200.
Join us on as tour of some old, some new and a few borrowed problems and situations. These will offer access to several strands of maths, different strategies for solving and will allow you to buy one get one [or several] free. Activities are ideally suited to Y7 to Y9 and will challenge more-able Y5 and Y6 so ideally suited to transition work. MA APSE students, Sheffield University.
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
16+ • 16+
T • Tertiary
A • Advisory