Vol. 29 No. 2 Summer 2024 1 Editorial Team: Kirsty Behan Alan Edmiston Peter Jarrett Alison Roulstone Les Staves Janet Goring Aroosa Parveen Letters and other material for the attention of the Editorial Team to be sent by email to: edmiston01@btinternet.com ©The Mathematical Association The copyright for all material printed in Equals is held by the Mathematical Association Advertising enquiries: Charlotte Dyason charlotted@media-shed.co.uk D: 020 3137 9119 M: 077 1349 5481 Media Shed, First Floor, West Wing, Beater House, Turkey Mill, Ashford Road, Maidstone, Kent ME14 5PP Published by the The Mathematical Association, Charnwood Building, Holywell Park, Loughborough University Science and Enterprise Park, Leicestershire, LE11 3AQ Tel: 0116 221 0013 Fax: 0116 212 2835 (All publishing and subscription enquiries to be addressed here.) The views expressed in this journal are not necessarily those of The Mathematical Association. The inclusion of any advertisements in this journal does not imply any endorsement by The Mathematical Association. Images copyright pexels.com Editors’ Page 2 Access for All – the 2024 Equals Conference 4 The Harry Hewitt Award 11 The 2024 award goes to Eddie Wang. You will be able to see photos of Eddie receiving his award in the next edition but here we include his nomination, written by one of his teachers Belasim Moosavi, to see why he is such a deserving recipient. If you have a pupil who you are impressed with then why don’t you nominate them for the 2025 award? How do you rate yourself? Nick Peacy 14 The archive piece this edition was written many years ago by Nick Peacy and friends. The is some lovely advice here for those who are seeking to audit and update their maths offer. A key aspect of this article is the idea of access for all - the very theme of the 2024 conference. I wonder is Nick’s words resonate with you and if they do please let us know your thoughts. RME – Realistic Maths Education by James Philips 24 I have heard James sing the praises of RME for several years now and here he takes the time to reflect upon the impact it has brought to his teaching and the pupils in his school. Managing my workload in the medium and long term - more thinking time to adapt my teaching 28 Hema Tasker reflects upon her workload and provides some timely advice in the process. Book review - This worked for me by Fiona Allen 29 Mark Pepper is very impressed with this publication from Fiona Allen and I had the pleasure of hearing her present her book at the 2024 Maths conference and I whole heartedly echo the thoughts of Mark. Fiona has taken the time to collect together so much classroom wisdom that is both valuable and insightful. This book deserves to be present in every maths department across the United Kingdom.
Vol. 29 No. 2 Summer 2024 2 Editors’ Page If you glance at the home page on the MA’s website you will see how busy we have become. The activity shown there reflects the diverse SEND offer that Equals is now able to provide. We have even launched a podcast called ‘Friends of Equals’ which actually reflects the key vision of Equals which is about peer networking and support. As I wrote in the last edition with Darra the help you need may be close at hand – please do get in touch if you need support or if there is something you feel passionate about regarding SEND. We are so pleased to be able to bring you the 2024 Equals Conference from Warwick and the full programme is included on the next page. Please do follow the link and book early to avoid disappointment as the last one sold out some 4 weeks before the start. The 28th September promises to be a significant SEND event and one not to be missed. The line-up of speakers is exceptional and the programme has been constructed to enable the day to meet so many SEND needs. The conference includes a wide range of inputs and it will serve to showcase the brilliant work currently taking place across the UK. The presenters have been carefully chosen to help the conference appeal to as wide as range as possible and also to address the theme of the conference which is access for all. The conference will be a key event for Equals as it will allow us to take stock of our development. We now have a growing editorial board and such a range of areas of influence that it is only sensible that we canvas opinion as to the direction of travel. Please use this link to book onto the conference: https://www.m-a.org.uk/equals-conference I want to bring your attention to a seminar we are offering with the OCR’s Maths Subject Advisor Steven Walker on the 27 June 2024 at 16:30. Steven’s presentation will look at the current special consideration regulations, from starting to teach through to sitting the examinations. This is an opportunity for teachers to share their experiences of teaching the content and preparing their students for the exams. We look at the range of qualifications from Entry Level Certificates through to A Level and also discuss what other assessment options may be needed in the future. Please use this link to book onto the seminar: https://www.m-a.org.uk/events/?id=307 Finally the Friends of Equals podcast can be found here: https://podcasters.spotify.com/pod/show/ al3372 The podcasts will provide an insight into the thinking of those colleagues working daily to support the needs of SEND learners. I would like to take the opportunity of welcoming Aroosa Parveen as the newest member of the Equals editorial board and you will get the chance to hear from her soon as she features in the third podcast. Aroosa is the maths lead at Kingsbury Academy, a special school in Coventry, and is someone who brings real insight and a passion for supporting the development of mathematics in all learners.
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Vol. 29 No. 2 Summer 2024 4 MA Equals Conference: Access for All Opening 9.00 – 10.00 Welcome and Refreshments Plenary 10.00 – 10.45 Les Staves - The roots of maths for children with very special needs Break 10.45 – 11.15 Refreshments A B C D Session 1 11.15 – 12.15 Pete Jarrett (Tutorum Learning & Assessment), Naina Singh (LKM School, Nharva, Maharashtra) Still struggling? Using data and observation to recognise challenges in learning Natasha Dolling How to use technology in the maths classroom to improve inclusion for children with SEND Louise Langford Representations of number- securing core mathematical structures and ideas Janet Goring A graduated approach to supporting pupils with maths difficulties? Lunch 12.15 – 13.00 L un c h Session 2 13.00 – 14.00 Alison Roulstone i-CAN Maths Workshop Tandi Clausen-May Multiplication Tables: survival strategies for dyscalculic learners Lara Lalemi Beyond the Western Canon: Enriching Secondary School Mathematics Education with Diverse Mathematical Knowledge Magdalene Lake The vicious cycle of poor reasoning: putting the horse back before the cart to address inequalities and improve maths attainment for everyone Break 14.00 – 14.30 Refreshments Session 3 14.30 – 15.30 Dominic Petronzi Understanding Maths Anxiety Steven Walker (OCR) Exam access for all Tracey Roberts No One Left Behind Rob Jennings The Dyscalculia Network Plenary 15.30 – 16.15 Kinga Morsanyi - Dyscalculia: What it is and what to do about it
Vol. 29 No. 2 Summer 2024 5 Opening Plenary Les Staves. The roots of maths for children with very special needs The presentation will discuss why it is important to have a curriculum that will encourage relevant math’s to grow for all children, including those who are at the earliest levels of learning. It will review the nature of relevant content and approaches to teaching and learning. Its starting points may relate to children who have not yet reached numeracy or are well behind age-related expectations. But I hope it will provoke consideration if its messages are relevant at later levels. Conference Session Outlines Closing Plenary Kinga Morsanyi. Dyscalculia: What it is and what to do about it Dyscalculia (specific learning difficulty in mathematics) is a condition that affects about 6% of the school-age population. Although dyscalculia is equally prevalent as dyslexia, and it can seriously affect people’s life chances, it is neglected by both educational professionals and policy-makers. Currently, in the UK (and in many other countries), a diagnosis of dyscalculia is almost non-existent, and educational support and official recognition is lacking. In this talk, I will present information about current conceptualisations of dyscalculia, how it can be identified, and how it can be discriminated from other conditions. I will also introduce a new screening tool to identify pupils with mathematics difficulties in the classroom and make some recommendations for best practice.
Vol. 29 No. 2 Summer 2024 6 Bio: Dr Kinga Morsanyi is a Senior Lecturer in Mathematical Cognition at Loughborough University. She has broad research interests, which lie at the intersection of research into mathematical cognition, reasoning and decision-making. Currently, one of her main research interests is in dyscalculia. Dr Morsanyi is researching the cognitive profile of individuals with dyscalculia, the demographic risk- and protective factors, typical symptoms (including problems in everyday settings), and co-morbidity with other developmental conditions. She is also leading the development of an app (Numeralis), which will comprise a standardized screening instrument for dyscalculia and tasks to assess the broader cognitive profile of learners. Dr Morsanyi is an associate editor or editorial board member of several academic journals, a member of the UK Young Academy, and an advisory board member of the Dyscalculia Network. Alison Roulstone. Practical strategies and interventions to support learners with difficulties in mathematics. i-CAN Maths Workshop Session i-CAN Maths is a maths magnetic counting frame that uses a Hungarian number frame (double five domino pattern). i-CAN Maths can help learners build good number sense using the maths mastery approach. Designed to be used one-to-one, in small groups and with the whole class i-CAN Maths is fully flexible and each session can be tailored to meet learners’ specific needs. i-CAN Maths encourages learners to visualize numbers, builds subitizing skills, and develops mathematical reasoning skills and mathematical fluency. Tracey Roberts. No One Left Behind Finding the right course for learners is often tricky, even trickier for pupils who are often disengaged or demotivated with education. The session will explore an alternative course for KS4 pupils to enable a positive and successful experience within maths. The qualification in particular will support learners with identified skill gaps in Maths and can be used to support progression or even run alongside GCSE. Come and see what we have learnt from delivering the course at both Levels 1 and 2 along with the changes in pupils’ perception to maths following their success, and how we make this work within our curriculum.
Vol. 29 No. 2 Summer 2024 7 Pete Jarrett (Tutorum Learning and Assessment), Naina Singh (LKM School, Nharva, Maharashtra). Still struggling? Using data and observation to recognise challenges in learning. This talk introduces an ongoing project that investigates the reasons for learners struggling when exposed to a Mathematics Mastery environment in an Indian rural school. Using data collection focused on observation of ‘why’ a learner is struggling, and analysis focused on multiple variables, teachers are empowered to recognise the most useful additional interventions at a class, small group, and individual level. Based on this understanding, a teacher development module has been devised that supports new teachers from the community to adjust to mastery teaching and support individual differences. This session will be delivered online from LKM School. Janet Goring. A graduated approach to supporting pupils with maths difficulties? Using current research and the findings of the SASC* working group on Dyscalculia and Maths difficulties, this presentation will explore the key barriers to learning maths and consider how students can be supported. As an introduction to a graduated approach, it will focus on classroom strategies and reasonable adjustments to prevent or reduce later difficulties as well as anxiety. It will be an opportunity for participants to evaluate their practice and consider how well they are meeting the needs of their SEND students through discussion with other teachers. Materials will be provided that have been tested and adapted by teachers and SENCos as part of a Maths Hub SEND project to audit and plan support. Natasha Dolling. How to use technology in the maths classroom to improve inclusion for children with SEND - the session info is the same. At LEO Academy Trust, we are excited to be at the forefront of using technology to improve inclusion. We believe that technology can be a powerful tool for ensuring that all children have the opportunity to succeed. Technology is being used to help children with SEND access learning, work independently, and overcome barriers to learning. I am excited to explore the future of technology in education. I believe that technology has the potential to revolutionise education and make it more inclusive for all children. I am excited to see how LEO Academy Trust and other schools continue to use technology to improve inclusion.
Vol. 29 No. 2 Summer 2024 8 Louise Langford. Representations of number - securing core mathematical structures and ideas This will be a practical session based on my articles in the Equals Magazine (Vol. 24 No. 3 and Vol. 28 No. 2) and experience of working with many pupils with Mathematical Learning Difficulties and Dyscalculia. It is appropriate to delegate teaching to all ages and stages, as well as those involved in professional development work. We will look at a variety of structures, that develop a secure representation of numbers within ten. This will include ‘cluster’ recognition, building on subitising and the idea of efficiently composing and decomposing number, linked to linear representations and understanding magnitude. We will explore how these representations expose different mathematical structures and ideas, to support retention and fluent application of number facts, enable learners to communicate their mathematical thinking, as well as secure a deep sense of number. Finally, we will consider the importance of core representations as vehicles to ‘transfer knowledge’ and enable future generalisations. Louise is a specialist teacher and assessor for Dyscalculia, Primary teacher, co-author of ‘A Deep sense of Number’ ATM publications (2021) and works as an LLME, as well as a Regional Community Co-Lead with the NCETM. Lara Lalemi, Creative Tuition Ltd. Beyond the Western Canon: Enriching Secondary School Mathematics Education with Diverse Mathematical Knowledge In recent years, there has been a growing recognition of the importance of incorporating diverse perspectives and knowledge into educational curricula, especially in mathematics. This talk highlights how traditional mathematics education often overlooks the rich and diverse contributions of global cultures and knowledges, leading to missed learning opportunities for school students to engage with the subject fully. The talk discusses the impact of colonialism on mathematics education and advocates for using an anti-colonial framework to critically examine and enrich the curriculum. By integrating captivating examples from ancient civilizations and indigenous cultures, teachers can encourage school students to gain a deeper appreciation for the universality and interconnectedness of mathematics across societies and with themselves in daily life. Through the incorporation of diverse mathematical examples, teachers can show students alternative ways problem-solving methods and different perspectives, fostering critical thinking and creativity. Moreover, exposure to the accomplishments of mathematicians from non-Western cultures can empower students from diverse backgrounds, allowing them to see themselves as active participants in the field of mathematics.
Vol. 29 No. 2 Summer 2024 9 Magdalene Lake. The vicious cycle of poor reasoning: Putting the horse back before the cart to address inequalities and improve maths attainment for everyone Reasoning is fundamental to good maths attainment for everyone, and yet, we often think that pupils must have certain mathematical skills before trying any reasoning, which leads to fewer opportunities for those with lower attainment to develop their thinking, and a vicious cycle ensues. In this session, we will look at who is at risk of this vicious cycle, why reasoning will improve number sense and calculation, and how to improve reasoning when number skills are low. Rob Jennings – The Dyscalculia Network The Dyscalculia Network has just signed a deal for a new maths assessment with Jessica Kingsley Publishing. It is due out next year and is entitled … ‘The Maths and Dyscalculia Assessment’ and is an assessment tool aimed at formulating a focused teaching intervention plan. Come along to this session and find out more! Dominic Petronzi. Understanding Maths Anxiety Math anxiety is associated with avoidance and reduced attainment and can define career decisions. But we’re still developing our understanding of how and why this develops. Research suggests that this can be grounded in initial experiences with math, and in some cases, children’s performance starts to decline from as early as 4 years of age. Research tells us that math anxiety is a complex construct, and this session will look at the distinctiveness of math anxiety, the range of factors that are implicated in its emergence and maintenance and understanding the role of emotions and the cognitive impact. We’ll also consider approaches to regulate attitudes and emotions about math, and also explore the movement towards understanding teacher math anxiety and the importance of this.
Vol. 29 No. 2 Summer 2024 10 Tandi Clausen-May. Multiplication Tables: survival strategies for dyscalculic learners Multiplication and multiplication bonds can present a terrifying challenge to learners who struggle to grasp numbers and numerals. For those who cannot interpret such ‘squiggle-based’ number sentences as ‘7 × 8 = 56’, the demand that they learn the multiplication tables can create an insurmountable barrier which blocks their path to any further development of their mathematical thinking. But by working entirely practically, with rectangular slabs of interlocking cubes, a Slavonic abacus, and our own fingers and hands, we can see all the bonds up to 10 × 10 and manipulate them physically as shapes and patterns rather than as ‘number facts’. This can make the multiplication bonds accessible, meaningful, and therefore more memorable. In this session we will explore ways to make, do, and above all understand, not just to ‘say’, multiplication and the multiplication tables. Steven Walker – OCR Subject Advisor (Maths). Exam access for all The presentation will look at the current special consideration regulations, from starting to teach through to sitting the examinations. This is an opportunity for teachers to share their experiences of teaching the content and preparing their students for the exams. We look at the range of qualifications from Entry Level Certificates through to A Level and discuss what other assessment options may be needed in the future. Steven originally studied engineering before completing a PGCE in secondary mathematics. He has taught secondary maths in England and overseas. Steven joined OCR in 2014 and worked on the redevelopment of OCR’s Entry Level, FSMQ and the A-Level Mathematics suite of qualifications. Away from the office he enjoys cooking and travel.
Vol. 29 No. 2 Summer 2024 11 The Harry Hewitt Memorial Award nomination By Belasim Moosavi Eddie is a 13-year-old student at Abingdon House School, London- a specialist independent school which supports pupils with special educational needs (SEN). Eddie, who has a diagnosis of autism spectrum disorder (ASD), joined Abingdon House School in 2021 after his family relocated from Hong Kong. As a result of some formative educational experiences, Eddie experienced considerable anxiety when undertaking activities and tasks at school, especially in maths lessons. It was clear he had cognitive and mathematical ability; however, his needs were a significant barrier to his academic progress. Eddie shared that maths would cause “frustration and fear of failing” which would often result in him experiencing distress in lessons, making him unable to engage with tasks and reluctant to work collaboratively. Eddie calculates missing angles in triangles publically in class with confidence
Vol. 29 No. 2 Summer 2024 12 With support from our multi-disciplinary team of SaLTs, OTs, SENCos, teachers and TAs who have been assessing, planning, and implementing a range of strategies over the last few years, Eddie has made significant progress and is now closing the gap between himself and his mainstream peers. While Eddie experiences this anxiety around maths acutely, fear of making mistakes is common to many students. This fear can be triggered by topics or experiences associated with past failure. To break this cycle, we identified triggers and then planned low-stakes collaborative activities to undertake as a first step, which helped Eddie to build confidence and create more positive associations. Fostering a supportive culture- where mistakes are seen as an inevitable, and ultimately useful part of learning- has also been a core aspect of Abingdon House School’s approach. As a model of learning, I share my own mistakes with students and open up dialogues about different strategies for solving problems, using elicitation techniques to guide the discussion while still allowing for variance. Combined with methodical approaches, these strategies have helped to emphasise the role of experimentation in maths education, with the effect of alleviating the pressure to get things right on the first attempt. When asked how this has affected him, Eddie said, “You get used to it because when you get something wrong, you are learning something. Working together with friends has also made me feel better and given me more confidence.” As his anxiety has reduced, Eddie has been able to enjoy maths much more. There was a particular lesson last December, which was part of a sequence on factors and primes, where this shift in Eddie’s attitude was most perceptible. While working through a problem, Eddie suddenly discovered for himself that primes have only two factors, and recognised the significance of this. He looked up at me with pure joy in his face, and I knew he was experiencing the particular thrill of mathematical pursuit and discovery. As a teacher, such moments, where you bond with students over a love for a subject, are among the most valuable and the ones you treasure the most. Eddie’s progress in overcoming these barriers has extended beyond the maths classroom with the support of his teachers and the wellbeing team at Abingdon House School. Jazmin Gahan, the Pastoral Lead, observes that, “Seeing Eddie’s confidence grow, not only in maths, but in the wider school has been wonderful to watch. He has even given tours to new students, demonstrating remarkable progress in making friends and facing new challenges.” Deputy Head James Gilbert-Farrell points to the progress Eddie has made with, “His ability to self-regulate, [which] has allowed him to access the curriculum more effectively, particularly in maths and music.” Maths teacher Jak Pennycook has witnessed Eddie, “Growing into a positive role model,” to his peers through the, “Commendable progress,” he has demonstrated. Meanwhile, form teacher Jonny Calabria highlights his emotional and social development, evident through the positive
Vol. 29 No. 2 Summer 2024 13 relationships Eddie has developed which, “Have served as encouraging and safe sources of his growth.” He describes how Eddie has, “Developed a stronger sense of agency over his emotions when confronted with challenging situations.” Ultimately, Eddie himself recognises that while he has made significant progress, there still needs to be an active commitment to continuing his positive journey. When asked how he feels about maths now, Eddie drew the below picture, illustrating his desire to continue on his positive learning journey by further developing strategies to regulate his emotions, revise weak spots, and experiment with new approaches to learning. As a school, we are unbelievably proud of Eddie and the progress he has made in maths and his other subjects. His holistic development over a relatively short period means that, at such a young age, his prospects are only widening. Eddie is still on his educational journey, but to see his happiness and pride in the efforts and progress he has made so far is fantastic- and that is, ultimately, the most important thing.
Vol. 29 No. 2 Summer 2024 14 Vol. 14 No. 1 Spring 2008 8 Background to Every Child Matters This section is an introduction to the ideas of Every Child Matters through the perspective of the mathematics curriculum. (taken from: www.everychildmatters.gov.uk) In 2003, the Government published a green paper called Every Child Matters. This was published alongside the formal response to the report into the death of Victoria Climbié, the young girl who was horrifically abused and tortured, and eventually killed by her great aunt and the man with whom they lived. The green paper built on existing plans to strengthen preventative services by focusing on four key themes: • Increasing the focus on supporting families and carers - the most critical influence on children's lives • Ensuring necessary intervention takes place before children reach crisis point and protecting children from falling through the net • Addressing the underlying problems identified in the report into the death of Victoria Climbié - weak accountability and poor integration • Ensuring that the people working with children are valued, rewarded and trained The green paper prompted an unprecedented debate about services for children, young people and families. There was a wide consultation with people working in children's services, and with parents, children and young people. Following the consultation, the Government published Every Child Matters: the Next Steps, and passed the Children Act 2004, providing the legislative spine for developing more effective and accessible services focused around the needs of children, young people and families. Draft Subject Booklet for trainees in Initial Teacher Training:Primary Mathematics Mathematics and Every Child Matters How do you rate yourself?
Vol. 29 No. 2 Summer 2024 15 Spring 2008 Vol. 14 No. 1 9 Every Child Matters: Change for Children was published in November 2004 and a website: www.everychildmatters.gov.uk was launched soon afterwards. The key outcomes for the Every Child Matters (ECM) agenda were drawn up after the consultation with children, young people and families. The five outcomes which mattered most to children and young people are set out below. Each of the five outcomes can be addressed through the Mathematics curriculum. Below each outcome is explored with suggestions for how this might be addressed for children with special educational needs. Not everything will be appropriate for all, but within each generic and specifically mathematical list, there should be something for all. This list is by no means exhaustive and should be regarded as a starting point rather than a prescription or restrictive in any way. ECM Key outcome Generic educational aspects Through the mathematics curriculum Be healthy • Work towards independent learning. • Actively enquire about differing environments. • Maximise physical, mental and emotional health. • Understand own needs and how to satisfy them – physical, mental and emotional. • Make positive relationships with others. • Learn to cook healthy meals – measuring quantities and time. • Learn to weigh and measure self – learn how to keep fit and avoid obesity. • Understand about the effects of alcohol and drugs. Stay safe • Keep safe in school and on school trips. • Work towards keeping safe when unsupervised. • Have stability and security. • Know about their place in the wider community. • Understand about appropriate and inappropriate behaviour of self and others. • Know where/who to go for help and support. • Understand risk and how to minimise it. • Understand 3D environment especially road use. • Understand effect of speed on effect of impact (road and rail traffic).
Vol. 29 No. 2 Summer 2024 16 Vol. 14 No. 1 Spring 2008 10 Enjoy and achieve • Achieve personal and social development. • Enjoy lessons. • Achieve to their potential. • Use alternatives to written recording where appropriate. • Develop ability to ask for support appropriately. • Enjoy mathematical challenge or puzzle. • Appreciate own success – positive self-assessment. • Learn to find place using street map e.g. Park, leisure facility. Make a positive contribution • Contribute to decision-making by making their voice heard (in school and the wider community). • Help and support others. • Be aware of and contribute to charity work – e.g. Red nose day, Children in need. • Analyse options. • Contribute to and listen to class discussion. • Show own work and thinking. • Comment positively on another’s work (peer assessment). Achieve economic well-being • Learn about ways to ensure their own economic well-being in the future. • Work towards independent living. • Understand and use money. • Learn about debt and how to avoid it. • Develop understanding about gambling in terms of chance of winning & losing. • Budgeting. • Value for money. Self audit for inclusion in mathematics lessons: How trainees and teachers plan their teaching, learning and support The self-audit has been written because of the demand for a straight-forward way for teachers and trainees to consider how inclusive their mathematics classroom is. We would be grateful to know: • if you feel the self-audit is generally useful. • whether there are ideas we should include or revisions we should make. The following self-audit list may help you reflect on aspects of the classroom environment which affect the learning of pupils with SEN and/or disabilities. The aim is a classroom ethos where all pupils feel confident, valued and able to contribute. This is conditioned as much by the physical environment and managing other adults effectively as by planning and modifying mathematics work for pupils with SEN and disabilities. All factors should be integrated in the conduct of a lesson responding to the diversity of pupils with their particular range of needs.
Vol. 29 No. 2 Summer 2024 17 Spring 2008 Vol. 14 No. 1 11 The physical environment Always Sometimes Seldom/Never 1. A welcoming classroom space with relevant mathematics displays in number, shapes, data handling and pupils’ own mathematics work, including that of pupils with SEN and/or disabilities. Visual timetables and prompts about what to do independently and how to ask for support. 2. The main board uncluttered with disparate writing, and frequently cleared to focus the class attention on the immediate work at any one time. Special spaces for special needs through consultation. 3. Background noise avoided, while allowing the class to respond and orally interact in natural ways, including chanting, without distracting other classes. Sound and light issues considered for all pupils with SEN. 4. Pupils’ seating and the main board position carefully planned for the shape of the room. Often a semi-circular arrangement of pairs of tables with whole class shared space in front of the board is appropriate. It should allow for the groupings for peer or adult support; sufficient room between chairs for pupils with mobility difficulties; clear view of board for all pupils; room for left-handers. 5. If a ‘carpet time’ or another way of whole-class sharing is planned, certain pupils need to be given their own space for access and participation. 6. Resources are accessible and clearly labelled. Equipment colour coded and labelled to encourage independent use.
Vol. 29 No. 2 Summer 2024 18 Vol. 14 No. 1 Spring 2008 12 Planning for the lesson Always Sometimes Seldom/Never Support planned for SEN individuals or groups in terms of resources. eg. large font handouts, simpler or extension worksheets. Visual aids, eg. measuring equipment, checked for clarity. Sound or tactile aids available as necessary. Pre-tutoring for certain pupils (eg. on mathematical vocabulary or context of learning). Questions prepared in different styles/levels for different pupils. A distraction-free area planned for pupils who may need it. Tasks linked back to earlier objectives or focused on investigating a topic, mathematising a situation, discussing or finding flexible ways to solve a problem, rather than the learning of a formal procedure. Scaffolding planned for some pupils. Other adult support targeted at individuals or groups. Teaching assistants clear about learning objectives/individual targets and deployed so that they encourage pupils to work independently when they can. TAs prepare resources (eg. task cards/simplified maps); to pre-tutor certain pupils (eg. with mathematics vocabulary, link with previous tasks) and to prepare themselves to simplify, scribe, and sign for pupils within a ʻscaffoldedʼ approach; to support pupils in assessment for learning. Where appropriate, ICT planned as an access strategy (speech or signsupported software/on-screen word bank / predictive word processing/ digital cameras).
Vol. 29 No. 2 Summer 2024 19 Spring 2008 Vol. 14 No. 1 13 Responsive lesson conduct Always Sometimes Seldom/Never All pupils clear about duration and overall structure of the day and the lesson (visual timetables referred to). An engaging lesson start, eg. a story or another ‘hook’ that allows various pupils in their ways to focus attention on something shared, often not directly mathematical at first. All pupils clear about the mathematical or logical task at the start of the lesson, eg. whether it is to practise some procedures, or generate ideas in any flexible ways for sharing. Key words, meanings and symbols negotiated and may be written up. Lesson runs in two or more cycles, as appropriate, of sharing time and independent work, individually, in pairs, or in groups. The sharing time periods are used to acknowledge all contributions and also to refine and focus the flow of work. The level of challenge should either be maintained or rising during the lesson, so that all pupils are working at their level or manageably ahead of themselves. Pupils accept that being challenged is good and that handling difficulties is a major aim of learning. During independent work period you give support and hints to different groups or individuals, keeping in mind their ideas and even priming some for a fruitful sharing period for the rest of the class. Responses to errors recognise the value of the thinking that led to it, since most errors are mixing of logical steps and or attention. Discussing common errors allows pupils to feel freer to handle mathematics, not frozen by fear of mistakes. Paired talk or buddy talk encouraged to maintain attention or to link concepts to pupils’ own varied experiences. Manageable mixed ability grouping or pairing is the norm except for extremes of the range. Transition from whole-class to independent/group work, and back, is clearly signalled. Praise for pupils keeping the rules and not excessively chastised for minor transgressions. Humour works wonder at times. Oral interactions and explanations of thinking out or through the mathematics is valued over and above neat recording except in the special cases for which it is needed. Alternatives to written recording offered where appropriate (eg. acting out and body language, scribing, mind maps, voice activated software and other use of ICT).
Vol. 29 No. 2 Summer 2024 20 Vol. 14 No. 1 Spring 2008 14 End of the lesson and after Always Sometimes Seldom/Never 1. Rounding off of the lesson involves a sharing period and some conclusions aimed for some parts of the lesson to be retained. 2. End of the lesson discussion can focus on one or more of the mathematics ideas explored and the progression to them during the lesson. This involves rehearsing early and unusual ideas and wordings, including those from the pupils with SEN and/or disabilities, thereby ensuring that all levels of attainment are included. 3. End of lesson discussion can also focus on the ways of working in class that have been found fruitful, eg. pair work, use of apparatus, and visual presentations. Praise for pupils making progress in collaborative working or sticking to task despite barriers. 4. Main points concluded or arising from lesson noted down and left on the board. Teaching assistants rehearse feedback with some pupils. 5. Pupils who remain puzzled and realise they have not fully understood or solved the task, encouraged to accept that is a fruitful state of mind valued by the teacher and advised on working further on their own or seeking help. 6. Pupils who are confident with the knowledge and insights they gained are encouraged to see where else in mathematics or other subjects this knowledge is relevant. 7. When appropriate the next stages of pupils’ learning are signposted and highlighted for individuals or groups to ensure they remain challenged. 8. Notes made on individual pupils about difficulties/successes in the lessons, based on their contributions rather than merely on written work, which needs only to be assessed in certain conditions and after chances of reworking.
Vol. 29 No. 2 Summer 2024 21 Spring 2008 Vol. 14 No. 1 15 Summary chart A summary chart is to give teachers ideas for the removal of particular barriers in the classroom. We would be glad to hear your ideas on adding to the chart concisely or any other suggestions for revision. Area Prepared support Activities Software (examples) Hardware (examples) SEN Language and communication Tasks pre-taped on audio or videotape. Symbols and other alternative communication systems: take time to find out the way of communicating that suits the child. Pupil grouping (eg. buddies) across attainment levels. Simulations and games for practising situations. Additional adult prepares pupil(s) for question and answer session. Word banks on computer files. Pictures and diagrams e.g. clipart. Good acoustics in class. Sound field systems to support poor acoustics. SLCN ASC Concepts, vocabulary Cards with words and pictures expressing the idea. Concrete and multi-sensory resources. Learning terms through a range of curriculum areas. Pre-teach key concepts. Wordscapes Story maps Care with metaphor ‘Mouth of river’etc. SLCN ASC MLD Writing Pre-devised writing 'frames': computer files to scaffold pupil’s writing. Changes to key press functions/ font size/colour settings. Word processor for drafting and redrafting. Spelling and grammar checker. Planning software e.g. Inspiration. Talking word processor with word predictor Texthelp Co-writer Write: Outloud. Touch typing training. Good colour printer for quality & valued result. Portable tape recorder for note taking. Voice activated word processor. Dyspraxia/ Developmental Coordination Disorder Dyslexia
Vol. 29 No. 2 Summer 2024 22 Vol. 14 No. 1 Spring 2008 16 Reading Use of story and narrative. Texts which are rich in rhyme and repetition. Some large text books. Font size: at least 12. Font: Arial, Comic Sans. Symbols and text together in prepared material. Writing with Symbols Clicker. Additional adult prepares reading with group before lesson. Shared text work. Talking word processor Texthelp. Read & Write Making books that are meaningful to the reader. Communicate in Print. Enlarging photocopier. Large display calculator/ talking calculator. Dyslexia/SPLD MLD VI Reading from the internet. Changing the look of the screen: typeface, colours etc. Use of ‘simplifying’ browser such as Widgit Software Webwide. Dyslexia/SPLD MLD Analysing and interpreting/ problem solving. Step-by-step descriptions of the procedures to be followed. Databases and spreadsheets of various degrees of sophistication. Excel Data logging hardware Digital camera. Improving own learning and performance. Taped details of project in hand. Survey of equipment available to pupils for independent study. Access to internet. Symbol or other visual schedules and timetables. Schedules for fair use of equipment. Kidspiration Microsoft Office calendar ‘Handheld’ devices, such as personal digital assistants allow extended practice of mental mathematics.
Vol. 29 No. 2 Summer 2024 23 Spring 2008 Vol. 14 No. 1 17 Motivation (Most ideas on this table contribute) Teaching to build confidence through targeted praise. Avoidance of ‘culture of right answers’. Reduction of anxiety by carefully chosen tasks, building on pupils’ preferred methods and encouraging collaborative working. Ability to take risks safely e.g. through simulation or design packages. Structured software with high rewards. Excel Problem-solving games. The Sims Successmaker (suits some pupils better than others) Digital cameras allow instant records of eg. patterns in the environment. Photocopier/ scanner for rapid back-up of work. BESD Presentation Word processing etc programmes for quality handouts. Powerpoint Can be used to create pupil interactive resources. Word including charts. Interactive whiteboard. Accessible technology. www.rnib.org Dyspraxia or Developmental Coordination Disorder Visual impairment Mobility Risk assessment to allow challenge cf Wiegand & Beveridge (1999). Sensory trails, multi-sensory environments, such as simulated rain forests. Theatre, role play, reconstructions. Carefully designed firsthand experience of site visits and fieldwork. Google Maps Videoconferencing PD Sensory impairment
Vol. 29 No. 2 Summer 2024 24 My experience of teaching Realistic Maths Education in a special school setting by James Philips Fosse Way is a 3-19 special school in Radstock, near Bath. We have students with a wide range of abilities, many of whom are autistic, and a small cohort of pupils each year will sit the foundation GCSE. From 2018-2021, the school took part in an Education Endowment Foundation-funded trial of Realistic Maths Education (RME) run by Manchester Metropolitan University. RME was developed by the Freudenthal Institute in the 1970s and is widely taught throughout the Netherlands. While the RME trial was aimed at mainstream pupils in years 7-8, I have found it to be an essential approach for pupils in SEND settings, who may have had repeated experience of being taught the same content in the same way. As a result, RME has fundamentally changed the way that I approach my lessons. The following is a brief outline of how RME does things differently and how it has impacted my teaching. Teaching through context RME lessons are taught through extended use of context. A single context, such as working in a fish and chip shop, will be used for an entire lesson, or often a series of lessons. For our pupils who may find generalisation difficult, it really helps to remain within the context for longer to ensure the maths is secure before moving on. The context does not need to necessarily be a ‘real life’ scenario, it could be from a story for example, but it must make sense within the experience of the learner. I devised a series of lessons for younger students using ‘The Doorbell Rang’ by Pat Hutchins, where students physically acted out the story, including leaving the room and ringing a bell. An excellent resource for teaching maths through story is: www.mathsthroughstories.org. In the first instance, formal mathematical language is not used, and the contexts provide useful ‘hooks’ for remembering the maths later as we move into more abstract maths. When teaching the unit on algebra from the RME website (www. rme.org.uk), I was able to remind students that they already had experience of expanding brackets and factorising when we looked at the fish and chips unit.
Vol. 29 No. 2 Summer 2024 25 A unit on pi begins with an image of a circular pool. The discussion is around a competition, where one swimmer goes across the pool and back, while the other swims a lap of the edge. At this stage there is no mention of diameter or circumference unless a student brings it up, and many students will initially think that the first swimmer travels a longer distance. The image provides a useful reference point once formal mathematical language is introduced. RME has taught me to evaluate my resources critically and whenever I use resources from popular maths schemes of work, I try to ask myself the question “Is this realistic?” If a question is not realistic then this can be a useful discussion point with the students. Where can you see the two swimmers? Source: www.rme.org.uk A different approach to representation and structure RME is very much compatible with teaching for mastery as taught in UK classrooms, with a strong emphasis on use of ratio tables and bar models (often taught in a similar way to a double number line). However, it considers how models are used in a careful way that is sometimes missing in popular maths resources. For example, there is often a presupposition that students have a strong understanding of bar models and can apply this understanding straight away to novel mathematical content. RME makes a distinction between ‘models of’ the context being taught and ‘models for’ solving a mathematical problem. For me this is a crucial distinction that possibly exposes a limitation of the concrete-pictoral-abstract approach. A bar model representing a money sharing problem may be useful in exposing the structure of the maths but it does not represent the actual ‘thing’ that we are talking about (it is a ‘model for’ solving the problem). This introduces a layer of abstraction that might challenge some of our learners. When the students are asked simply to ‘draw something’ to represent a sharing problem involving three sandwiches and four people, a bar model naturally emerges but it is also an image of the context itself (a ‘model of’). RME carefully moves from informal ‘models of’ through to more formal ‘models for’, finally moving on to abstract notation only when students are ready and it repeats this cycle for each new topic. Even when I am not working with the RME resources, I am always conscious of using ‘models of’ whenever possible when I introduce new content, for instance a battery bar on a phone is a more powerful image than an empty number line. Real-life situations at home such as making porridge, cutting up a lasagne or measuring my shoe laces with a tiny ruler have all made their way onto Smart Notebook the next day in my lessons!
Vol. 29 No. 2 Summer 2024 26 Two students’ different approaches to sharing three sandwiches between four people using a ‘draw something’ approach. Classroom Culture RME classrooms have a strong focus on oracy and students are expected to take ownership of the lesson, starting with a student reading out the text on the board. Students are encouraged to come to the board and explain their ideas, often using gestures and open prompts such as ‘what can you see?’ or (importantly) ‘where can you see?’. The teacher acts as a facilitator of the discussion, asking students to clarify or expand upon the contributions of their peers. All contributions are valid, and misconceptions are not immediately shut down but are explored with the learners, who hopefully will develop their ideas and discover an appropriate solution or solutions for themselves. The RME resources often begin with a question that has no mathematical content but is intended to introduce the context. A question such as ‘what is your favourite fruit’ is a great way to get a conversation started. This creates a kind of behavioural momentum that naturally segues into a mathematical context about fruit juice. Within reason, the teacher does not always keep the discussion focussed purely on the maths. In the sandwich example above, a student may decide that it is not fair for someone to get the end piece of the sandwich, which shows that they are ‘in the context’ and their peers can help them to decide whether another solution is possible. I believe this goes some way to reducing maths anxiety in some learners as they are not immediately confronted with anything overtly mathematical. To contrast, I taught a lesson on reverse percentages involving the use of skirting board as a ‘model of’ the context. Even though some students were not familiar with the word, we could see skirting board in the room so it was within their realm of experience. I then moved on to a question involving interest on a bank account where we were using the bar model as a ‘model of’ the same kind of problem. All of the students
Vol. 29 No. 2 Summer 2024 27 struggled with this even though the maths was the same. We spent the rest of the lesson discussing saving and bank accounts and the students were able to access the problem in the following lesson. In SEND settings these discussions may take place within a group rather than the whole class, depending on the needs of the students. Many teachers in special education will be familiar with students whose ability in fluency greatly exceeds their reasoning and problem solving, however through teaching RME I have also found that some students have excellent problem-solving skills even where they struggle with retrieval of fluency facts. Perhaps these students had previously not been given the chance to show, and develop, what they know? More generally I have seen a richer quality of discussion take place in my own lessons and that of some of my fellow teachers. Hopefully some of the benefits of RME discussed here will be of interest to teachers in specialist settings. More information about RME, including a video of an RME lesson in practice, research articles and ready-to-teach resources from the trial, are available at www.rme.org.uk. Question and Answers with OCR Maths Subject Advisor Steven Walker Catch up with out latest webinar; -Watch the webinar recording -Read the recommended blog posts -Get your own questions answered! or visit www.m-a.org.uk/equals-online
Vol. 29 No. 2 Summer 2024 28 Managing my workload in the medium and long term - more thinking time to adapt my teaching by Hema Tasker If this headline is true: ‘All full-time staff in primary and secondary schools continue to work more than a fifth of their total average hours before school/after 6pm/on weekends’ then this equates to around 10 hours per week. There has been a slight decrease in the proportion of hours worked outside ‘normal’ hours since 2009’ in a DfE report on Teachers’ workload diary survey. I can hear your shock, don’t worry. I have not had a decrease in my workload. Unpacking this report I was really shocked to see that 2.3% of the time for Primary teachers and 5.7% for secondary teachers was spent contacting parents. I try to send positive emails home and now I know why I rarely get to that part of my ‘to do list’. The largest amount of time was spent in planning lessons [1]. This got me thinking, I am very good at short term planning from week to week [4] but where can I improve my organisation in the medium and long term? I started with the key points from Sanchez et al (1999) [3] as this helped me list all the things considered during my PPA when planning the teaching for a unit. This helped me to break down the key information I needed for a medium term plan. What do I need to teach, how do I teach and assess this, then I factored in the weeks in the term...this is where my method of pen and post-it notes came in handy, I can now fit these notes onto the actual weeks of teaching I have (using the school calendar I removed any collapsed days, christmas meals, planned trips etc). Now I have a medium term plan for my learning objectives which fit around the assessment dates etc! I also know when I have to write reports so I can manage my workload a bit better making sure I have the data I need to write reports and can plan my home life to manage this increase in workload. For year groups that have exams I approached this in a slightly different way, I removed the dates for study leave, revision, mocks etc and then planned my teaching around key points. It takes time to plan but I was able to plan homework for the holidays that students could complete independently and use the lesson to focus on tricky concepts and exam technique. What does this mean for me? I know when my workload peaks in the year and I can plan the other things I need to do around this. If I gain a lesson I have ‘bonus revision time’ which could be a fun activity or past paper practice for KS 2, 4 and 5 where I can direct students to specific areas or question types. Most importantly I feel less stressed!
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