Vol. 29 No. 4 Spring 2025 1 Editorial Team: Kirsty Behan Alan Edmiston Peter Jarrett Alison Roulstone Les Staves Janet Goring Aroosa Parveen Mark Pepper 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, unsplash.com Editorial 2 Equals Awards 3 Equals News 4 What’s in a name? by Mundher Adhami 6 This piece was written, almost 20 years ago by a dear friend of mine. I was fortunate to get to know Mundher at the start of the CAME project and his support and encouragement inspired me to finally complete my own PhD this year in tribute to his impact upon my life. It was Mundher who really opened my eyes the benefits of understanding how children think and view the world mathematically when trying to teach. This piece has been picked to highlight the fact that our Summer edition will be an inclusion special. If you have any thoughts or ideas then please get in touch as we would love to hear your views. If you had the pleasure of knowing Mundher and would like to share any memories please get in touch. Changing the curriculum by Mark Pepper 10 In his regular piece Mark looks forward to two changes that are due to come later this year: the new Ofsted framework and the maths curriculum. Foetal Alcohol Spectrum Disorder Part 2 by Steve Butterworth 13 In this second piece Steve outlines how his research is progressing and appeals for help to find out just how much is known about Foetal Alcohol Syndrome Disorder. Interview with Robert Lewis 16 I recently had the pleasure of meeting Robert Lewis Assistant Headteacher at Shenstone Lodge School. Shenstone Lodge is a primary SEMH school taking care of children with complex social, emotional and mental health needs with a large proportion of trauma related behaviours. During our time together I listened with great interest as he described one of the intervention they are involved with as part of the wider support for their pupils. Some of their pupils are taking part in brain scans as part of their commitment to understand the pupils they are seeking to support. Robert describes how this fits within the supportive ethos promoted by the school. This piece is simply an introduction, and the project is still in its very early stages, more information will be shared when it becomes available. Robert has kindly offered to talk about this during SEND November. New guidance on the assessment of a Specific Learning Difficulty in Mathematics by Janet Goring 18 For the past year Janet has chaired a working party looking at specific maths difficulties. The report is out very soon and in the first of two articles Janet takes the time to share the outcomes and the implications for teachers. A personal account of what it means to be autistic by Alison Flack 24 After listening to one of our podcasts Alison got in touch to encourage teachers to reconsider their views on autism.
Vol. 29 No. 4 Spring 2025 2 Editors’ Page As editor of Equals there is nothing I like more than to receive an email containing an offer of an article for publication. Equals is built upon professional collaboration and the challenge that comes when people share, or seek help with, their thoughts or something they have done or would like to do. A clear example of this is the piece by Alison Flack in this edition of Equals. Alison put pen to paper to get her side of the story over after listening to one of our podcasts. Please do respond to this article or any of the other pieces in this edition – we really do want to know your views, what you think and would love to help your voice be heard. Why not submit an article about something you have been doing or to tell the SEND story of your school? I ask this for it is something that is currently on my mind for at the moment I am visiting many special schools as part of my work for the Math’s Hubs. Time and time again I find myself listening to colleagues who are making the correct professional decisions for the pupils in their care. Most days I just sit there in amazement at the quality of the work taking place. A lovely example of this was a visit to meet Jade at Newark Orchard School near Lincoln. The quality of the continuous maths provision in the early years class I saw was just wonderful. The outcome of this is for me, when visiting a neighbouring schools is to simply say; ‘Go and see what xxx is doing down the road’. Please do take this opportunity to share what you are doing to support your SEND learners in mathematics. The Summer edition of Equals will be in the form of an inclusion special. This was prompted by the archive piece in this edition What’s in a name? written by my dear, and very much missed, friend Mundher Adhami. Mundher clearly articulates how the CAME approach has inclusion at its heart and has stood the test of time. I teach as much as I can and currently this is mainly in special schools and it is lovely to be able to turn to the CAME lessons to provide the pupils with a joyful and memorable mathematical experience. Finally, I will end this editorial with an appeal for information for it has come to our attention that the number of SEND units within mainstream schools is increasing. This is due to the fact that places in specialist provision are limited and that more and more pupils are being taught in this way. Please let us know your experience of this as the implications for both the pupils and their teachers are very serious indeed.
Vol. 29 No. 4 Spring 2025 3 The Equals Awards The Harry Hewitt Memorial Award This prize is awarded to any pupil who has overcome barriers with mathematics and is now making real progress. Do you have a pupil, like this, who has struggled but is growing in confidence as they engage with mathematics? Why don’t you celebrate their success in Equals? We are offering a prize of a £25 book token to the best entry we receive and the opportunity to have the work published in Equals. Choose a piece of work that both you and your pupil consider successful and send it to Equals. Please include: • the original piece of work, photograph or photocopy. • an explanation from the teacher of the piece of work and its context and a description of the barriers which the pupil has overcome or is in the process of overcoming. • the pupil’s age, school and the context of the class in which they learn and, if possible, some comments from the pupil about what they are pleased with about this piece of work and/or the learning it shows. The Ray Gibbons Memorial Prize To honour the memory of Ray Gibbons, who founded Equals, we are pleased to open submissions for the 2025 the Ray Gibbons Memorial Prize. This prize will be given to anyone you feel deserves recognition for their work within the field of SEND and mathematics. If you know someone who deserves to receive public praise for their work then please let us know. A short biography and a few words on why you are recommending them are all that is required. We are offering a prize of a £25 book token to the best entry we receive and the opportunity to have their work published in Equals.
Vol. 29 No. 4 Spring 2025 4 News section Watch this space for details of a new network for special schools Equals has begun to develop a Maths Network for Special and AP schools. We look to become your go-to HUB for all things SEND maths. As we continue to work on how this will look, we would love you to indicate your interest so we can keep you updated and involved throughout the process. Sign up here using the link below, or scan the QR code to register your interest today! The Friends of Equals Podcasts These can be found here: https://www.m-a.org.uk/podcasts The podcasts will provide an insight into the thinking of those colleagues working daily to support the needs of SEND learners. Developing Financial Literacy We have received a research invitation from our friend Dominic Petronzi at the University of Derby. He is seeking to determine whether a financial literacy-based storybook approach for children aged 6–7 years can have a positive influence in terms of increasing children’s understanding of foundational concepts such as saving, earning, budgeting, and distinguishing between needs and wants. The research adopts a pre/post intervention approach that would require teachers to support in the delivery of storybook readings and related activities over 1 week. If you would like to get involved please complete and return the gatekeeper form which can be found here: https://www.dropbox.com/scl/fi/7gmk2w9uvqxemvk62x3ej/Appendix-A-GatekeeperPermission.docx?rlkey=p7b96p2rffew01jyendsiz2yo&st=ar7cdwwh&dl=0 Announcing the Summer SEND seminars – https://www.m-a.org.uk/send We are offering the following one-off seminars on the following topics: Metacognition, Anxiety and Oracy. • Metacognition with Kat Adams on the 5th June @ 3.45 • Zones of regulation with Sue Johnston-Wilder on the 10th June @ 3.45 • Oracy with Alan Edmiston on the 23rd June @ 3.45 Metacognition – Kat is the Deputy Head at Rocklands School a special school in Litchfield. They have been exploring the role of metacognition to support the learning of their pupils. Kat has kindly offered to reflect upon this work and to offer some advice for others who are interested.
Vol. 29 No. 4 Spring 2025 5 Zone of Regulation – a long standing friend of Equals Sue Johnston-Wilder has recently published a book on this topic and will use the session to share both her wisdom and her current areas of interest. Oracy – this topic is very popular at the moment and Alan will use this session to explore some of the theoretical roots of oracy and to share the findings of his recent research. SEND November We are pleased to announce November as the month of SEND CPD. This year we will not be running a conference but we will be offering a whole series of sessions covering all aspects of SEND provision. There will be several sessions each week for the whole of November and these will be shared in the Summer edition of Equals.
Vol. 29 No. 4 Spring 2025 6 Schools can still claim to be inclusive while streaming, setting, or otherwise formally labelling pupils. They are differentiating and catering for pupils’ different abilities or, more truly, levels of achievement, and allocating equitable resources. This is a formal institutional method of fulfilling the principle of equal worth. But there is a more genuine sense of inclusiveness that involves pupils across the achievement range working together in the classroom and benefiting from being different, and even recognising that they are complementary to each other. Arguments about achievement labelling First let’s rehearse some arguments about achievement setting. These are to do with differentiation by attainment in a subject like mathematics or by achievement in general. Let’s not concern ourselves with motivation or behaviour although these aspects inevitably enter into setting or streaming decisions. Many teachers agree that setting or streaming may be valid, or even necessary at the extreme ends of the achievement range. Children, and learners in general, would not benefit from classroom talk or interactions that are either trivial for them or way above their levels of understanding. In current curriculum terms and NC levels, many teachers think a group of pupils can communicate fruitfully amongst themselves, and benefit from each others’ ideas and sorting out of errors, if the range of achievement in the group is 3 national curriculum levels or less, e.g. between NC 2 - 4 or NC 5-8. That is equivalent to a range of 6 years in ‘mental age’ in the subject, measured by hypothetical average progress of 1 level in 2 years. There is little use in grouping pupils who are working at level 2 with those working at level 8, unless the latter act as teachers, which requires rare pedagogic skills. Therefore the working groups must be near-ability. Hence the formula: ‘near-ability’ groups in mixed-ability setting. However, there is also the issue that unless there is a range of levels in any group, pupils at the same level and with the same background may reinforce their misconceptions by missing out on sorting them out! So the formula may better be phrased as ‘maximum manageable achievement range groups in mixed achievement/ability setting’. That implies that the full mixed achievement setting is not manageable. I myself have sympathy with this view in terms of teaching mathematics, if the full range includes 4 or 5 national curriculum levels. This is rare in a mainstream school in this country today although this may change as more children with SEN are admitted to mainstream secondary schools. The top and bottom 10 percentiles of ability by national standards across the cognitive capabilities are rare in mainstream schools, especially at secondary level. That is because of the many mechanisms which cater for the geniuses/very ‘gifted’ children and for those judged to have extreme special needs. That makes any narrow ability ranking of pupils in the mainstream school largely artificial since at most it would include the middle 80% of the population where the abilities are diffuse and less susceptible to measurement. The most you can say is that this pupil is ‘about average or higher’ for his age, or that he is ‘about average or lower’ and then allow for a possibility of occasional mislabelling. Vol. 13 No. 3 Autumn 2007 4 Working above or below their achievement levels is the main cause of many mathematical misconceptions What does inclusive teaching really mean? Teachers compare two well-tried mixed-achievement approaches in the classroom, SMILE and CAME. Mundher Adhami summarises their views and offers some of his own.1
Vol. 29 No. 4 Spring 2025 7 Autumn 2007 Vol. 13 No. 3 5 In my experience with schools since the mid 1970s, including through assessments in the SMILE, GAIM, and CAME projects, a school would most likely have a profile from the 10th to the 70th percentile, or the 30th to the 90th percentile with few, if any, outside this range. Narrow setting by attainment or ability, and labelling by levels, therefore, hides much of the commonality amongst these pupils. That is the case even in cognitive terms alone, quite apart from the equally valid social and emotional terms, with their all-important motivational charge. For example a ‘level 4 pupil’ may well have reached level 5 in spatial abilities and level 3 in number ability or in algebra, or vice versa, and therefore will work differently in different mathematical topics. Unless classroom work clearly allows a range of level 3 to 5 work and beyond in each topic at the same time, most pupils will either be working below or above their achievement level. That is the main cause of many mathematical misconceptions, temporarily covered up by memorised procedures. It is also the reason for boredom, switching off and even hatred of mathematics, something that does not occur so strongly in any other subject. These arguments lead to a preference for much of mathematics teaching to be in manageable mixedachievement groups, at least to age 14 or thereabouts. That is not happening at present. The reasons are partly to do with the focus on teaching for tests and exams, and therefore on procedural and rote learning, which is necessarily level-focused. But the other, and lesstalked-about reason, is that teaching generally is a difficult task, and especially where it involves engaging with mixed achievement groups. However, my generation of mathematics teachers did experiment successfully with such methods. And even now there are some who teach in such ways, although, according to HMI reports, rather few. Teachers’ views on approaches to mixed-ability teaching Rachel Gibbons and I explored the issue with small groups of colleagues at the Easter conference of the Mathematical Association this year, 2007. First a personalised approach was offered when colleagues were asked to choose one mathematical task from three open tasks from SMILE2 to work on, individually or in pairs, for about 20 minutes, with the teacher observing the work closely, ready to intervene where it seemed necessary. They then discussed together what they had found useful or problematic. Then the whole group worked briskly on a CAME3 lesson for another 20 minutes. (Some details of the tasks are given elsewhere). Then followed the main reflection session. The reflection was based on a simple frame to highlight the advantages and disadvantages of the individualised open-ended work and the wholeclass thinking lessons. The two approaches were exemplified in the brief shared experiences the colleagues had earlier in the session, which served to prompt more general observations and ideas. First colleagues individually jotted words and phrases in each of the four cells for a couple of minutes, then worked in pairs to produce some better phrasing and priorities, then we collected all the ideas on a flipchart, briefly discussing their meanings and connections. Here is a full list of the ideas as transcribed from the flip chart, with largely verbatim wording agreed by individual colleagues even if not agreed as a group. Each bullet point originated from one or a pair of colleagues. pupils at the same level and with the same background may reinforce their misconceptions by missing out on sorting them out shared experiences of mathematics
Vol. 29 No. 4 Spring 2025 8 Vol. 13 No. 3 Autumn 2007 6 Do we need to go further than recognising the pros and cons of teaching and learning situations? Isn’t it sufficient to accept that almost everything we do has good and bad in it, and the main decision is on the least harmful or most fruitful in the particular case? Can we be sure of anything in teaching and learning? Aren’t we operating always on assumptions and hunches that ‘something is happening’ in the minds and souls of the pupils, but we cannot be sure? My own answer is yes to all these. But there are qualifications, and the awarding of these has to do with acceptance of differences’ amongst pupils and teachers, and how catering for these differences has to be part of the entitlement of pupils for their education and the development of their individual potential. Potential for synthesis The Cockcroft report recommendations of a quarter century ago (see elsewhere) remain valid. In current terms these recommendations can be formulated as the need for a balanced diet of mathematical experiences by all pupils to include: 1. Direct teaching of new material building on prior knowledge that is assumed to have been understood, with exposition and demonstration as in lectures, preferably with opportunities for interactions. 2. Individual or group open investigation and problem solving activities, worked on at pupils’ own levels, with the teacher circulating, prodding and offering hints. Individualised or paired work on open tasks in a class, e.g. SMILE/GAIM/ATM4 Whole class in the CAME style Advantages • Everyone is involved in their own way. • Less competitive with others in the class. • More open than in normal lessons. • Children who normally sit back will have a go. • Broader range of choice. Children select their own tasks. They target themselves. • More competitive in a good way. • Takes away fear. • Could be done in groups rather than by individuals if they chose. • Personal satisfaction. Sense of achievement. • Better differentiation by ability and pace of work. • Easy to link with prior knowledge. • Can be linked to real life contexts. • Access by different learning styles • The teacher values all contributions from different pupils. • Links to the rest of the curriculum are possible where needed. • Use of language and symbols explained. • Sharing and discussion of ideas offered in the class. • Shared experiences of mathematics. Disadvantages • Doubt and loss of confidence when they cannot do it. • As a teacher you cannot give them help as much as needed. • No sharing of ideas. You are on your own. • Difficult for the teacher to manage. • As a pupil you are stuck at your own level. • Misses out on mathematical vocabulary. • Needs time. Needs patience. The children need to be confident to do it. • One can get lost. Less conversation between students, less exchanges of ideas and practice in articulating thought. • Some pupils may sit back and not engage. • The lesson goes at the teacher’s pace. • The work could be faster or slower than what some people want. • Less satisfaction than when you work on your own. • Differentiation between pupils is difficult. • There is the illusion of covering the topics. • Some children may dominate class discussion.
Vol. 29 No. 4 Spring 2025 9 Autumn 2007 Vol. 13 No. 3 7 3. Whole class thinking maths activities. Activities designed to allow collective exploration and discussion of concepts from scratch up to the most challenging logical and mathematical thinking possible in the class. These may start with a motivational ‘story’ or a ‘hook’5 but then proceed in steps at a responsive pace. The pace should be appropriate to the majority of the pupils in the given class at the start but increasingly moving to challenging even the most able pupils by the end of the lesson, relying on various levels of partial understanding by the rest, and on keeping them thinking after the lesson. 4. Drill & practice lessons where the pupils hone techniques and familiarise themselves with efficient methods of solving routine or novel mathematical questions. In each of the four types of mathematics lesson above a few features could be present in various proportions: a. Use of real-life familiar contexts where possible. b. Use of natural language and how that is linked to mathematical language; encouragement of oral interactions using mathematics in the classroom. c. Use of practical apparatus, audio visuals and technology, without allowing these to create obstacles or diversions. Professional development as key It is clear to many of us that the main reason for repeated failure of education reforms, especially with investigations and problem solving in mind, is that the teachers themselves have had little or no experience of this type of learning, and so find it extremely difficult to pursue. We do what has been done to us! And the problem is plainly not the teachers’ subject knowledge, narrowly defined as understanding of mathematics as a coherent system with connections. Rather, it is the knowledge of how pupils construct their own mathematical knowledge, and the progression in the subject with its diverse routes. For that kind of subject knowledge to develop in teachers, whether they have honours degrees in mathematics, or are good teachers who have been forced into teaching a subject they dislike, there is no substitute for themselves first engaging in open ended investigation and thinking maths lessons, and reflecting on these experiences with colleagues. The successes of SMILE and GAIM and many similar experiments in the 70s and 80s were based on teachers coming together and collaboratively creating lessons, trialling them in the classroom and coming back to discuss them. The ILEA of the time, the government, and charitable bodies like Nuffield greatly aided those experiments. But the spirit of experimentation seems to have declined with time in favour of officially promoted, narrow, direct teaching. Educational researchers do not seem to go for large scale experiments. The CAME approach still adheres to the original principles of the SMILE and GAIM experiments, linking them to the cognitive development theories as a background, but now the schools themselves have to pay for the courses. That slows down the dissemination of good practice until the pendulum swings further, and we enter a new era of experimentation and creativity in teaching and learning. Back to Cockcroft, I say! Cognitive Acceleration Associates 1. Based on the proceedings of workshops at the Mathematical Association annual conference at Keele University 11-14 April 2007, run by Rachel Gibbons and Mundher Adhami. 2. SMILE- ‘Secondary Mathematics Independent Learning Experience’, an ILEA-funded project that started in the 1970s in London. Rachel Gibbons was one of the original teachers and then an inspector involved with the project. 3. Cognitive Acceleration in Mathematics Education, a project developed at Kings College London, based on exemplar Thinking Maths lessons for Secondary and primary classes. 4. GAIM- Graded Assessment in Mathematics, a 1980s project based at Kings College London directed by Margaret Brown, which paved the way to descriptions of the GCSE grades and NC levels. Its GCSE syllabus, serviced by the author, was based on teacher assessment of open-ended work and flexible ways of fulfilment of topic criteria. ATM- Association of Teachers of Mathematics was prominent in promoting open-ended investigations, and Anne Watson serviced a GCSE syllabus based on such activities. 5. Alan Edmiston, a CAME tutor from Sunderland , promoted the idea in the ongoing development of the approach that most or all classes need a starting story on which the thinking lesson ‘hangs’. Another CAME tutor, Mark Dawes, from Cambridge, developed the idea further as a need for a ‘hook’ that can be a story or a puzzle or a dramatic event that galvanises the whole class at the start of the lesson. The notion emphases the motivational factor, as distinct from logical or mathematical terms, and therefore can be seen as a necessity rather than a luxury. In the example given the hook is examining fresh twigs of parsley and mint, offering the idea of mathematising nature.
Vol. 29 No. 4 Spring 2025 10 Probable changes in the inspection of schools A significant change in the manner in which school inspections will be carried out can be anticipated as a consequence of the recently updated version of the School Inspection Handbook which came into force on 16 September 2024. The evidence for this becomes apparent when a comparison is made between the Handbook and the Ofsted Report (July 2023) Co-ordinating mathematical success, the mathematics subject report. Co-ordinating mathematical success, the mathematics subject report This Report superficially gives fulsome praise to the teaching of maths in primary schools. Nevertheless, this approval is confined to a specific method of teaching which is strongly aligned to the 2013 iteration of the maths NC which was then in force and is characterised by a marked increase in the use of rote learning. It also consists of a significant reduction in the provision of opportunities for the development of qualities associated with autonomy, creativity and problem-solving. The most stark example of this consists of the unprecedented absence of any reference to Using and Applying. This close adherence to the 2013 NC is confirmed by the assertion (P5): Curriculum is now at the heart of leaders’ decisions and actions. The use of differentiation is also condemned with the assertion (P5): Generic approaches, such as the expectation that all teaching should be differentiated, have dissipated. The School Inspection Handbook (updated 16 September 2024). This revised version of the Handbook is currently in force and is characterised by a significant shift away from the prescriptive undertones of its predecessor. This whole approach is far more accommodating with its support for greater autonomy for schools and for individual teachers which is evident in para 291: How the changes to the maths National Curriculum can influence the whole tenor of maths education in schools At the time of writing the revised maths NC has not yet been published. Whilst the key elements would have consisted of the content and the statutory assessment of it, the focus of this article will be on probable changes to the whole ambience of maths education in schools. This will include consideration of the inspectorate, the provision of maths education for learners with SEND (special educational needs and disabilities), mental wellbeing and inclusion policies.
Vol. 29 No. 4 Spring 2025 11 …the choice of teaching methods is a decision for providers. Furthermore, there is an expectation that schools make provision for learners with SEND. Para 283 states that Ofsted will evaluate: How well the school identifies, assesses and meets the needs of pupils with SEND. In a GOV.UK press release dated 3 February 2025 this requirement is emphasised further: Increasing focus on support for disadvantaged and vulnerable children and learners, including those with SEND, making sure these children are always at the centre of inspection. Whilst the general approach is non-prescriptive, there is one significant exception to this. This consists of vigorous opposition to a form of teaching that involves the excessive use of memorising facts. Para 283 states that teachers should not: …prompt pupils to learn glossaries or long lists of disconnected facts. An important change in maths GCSE exams A welcome policy that reduces the requirement for the memorisation of facts has already been introduced as candidates taking the maths GCSE exam will no longer be required to memorise formulae as these will be provided on the exam paper. Endorsement of the policies contained in the Handbook by Bridget Phillipson Bridget Phillipson, secretary of state for education, addressed the Education Select Committee on 15 January 2025 and she confirmed that her comments were …in accordance with the directions of the Ofsted Handbook. She highlighted the importance of mental wellbeing and the need for mainstream schools to provide educational programmes to cater for the specific needs of learners with SEND. She stated that mainstream schools would be required to include children with SEND and that the possibility of this being made a statutory requirement was being considered. She acknowledged that despite this strong commitment to inclusive policies it would continue to be necessary to retain some special schools to meet specific needs as such institutions would have specialist staff as well as the physical resources to meet the educational needs of the learners. Options for inclusive policies It is difficult to envisage how the policy on inclusion will be implemented, but it could be helpful to consider this in the context of a specific disability. With this in mind I will consider the options regarding learners with a visual impairment (VI). This is appropriate as I have had a considerable amount of experience, as a retired teacher and lecturer, of teaching within this sector. I have taught learners with a VI in all three settings of a mainstream school, a special school for pupils with a VI and a unit for the education of learners with a VI within a large secondary school. The mainstream school The learner with a VI, who I will call Jane, was involved in all aspects of school life and formed good relationships with her classmates. Whist she came equipped with essential resources associated with her VI, which included a laptop and a braillette
Vol. 29 No. 4 Spring 2025 12 (a portable device that converts written text into braille), all her needs could not be fully met. The LEA VI advisory teacher had a high case load and so was only able to make occasional visits which were extremely helpful. Her support included the provision of a mobility route to enable Jane to access the classroom and other parts of the school with confidence when she first joined the school. Unfortunately, Jane was not provided with a classroom teaching assistant to support her. The special school for children who are blind or have a visual impairment The facilities were ideal to meet the needs of the learners. There was an abundance of physical resources and the teaching staff held the VI teaching qualification. The school also had residential settings and a high proportion of the learners boarded at the school as they did not live in close proximity to the school. This effectively made the school a closed community in which all of the learners had the same disability. This meant that for many of the learners they had virtually no social interaction other than with their peers at the school. The VI unit within a secondary school This was an appropriate setting in which specialist equipment to meet the specific needs of the learners was available. Furthermore, all of the teaching staff held the VI teaching qualification. Whilst most of the teaching and learning took place in the unit, interaction with the rest of the learners took place at playtimes and at events such as assemblies and at various sports events. Hence friendships naturally developed between the learners. The probable effect of these policies on the retention of teachers It can only be hoped that the effect of the implementation of these proposed policies will be that teachers will get greater job satisfaction and feel reduced levels of stress which should have a beneficial effect on the retention of teachers.
Vol. 29 No. 4 Spring 2025 13 Foetal Alcohol Spectrum Disorder Part 2 by Steve Butterworth In my previous article, December 2024, I outlined the need for research to determine the level of maths curriculum access that pupils with Foetal Alcohol Spectrum Disorder have at KS3 and KS4. This piece will focus upon the next steps for my research, beginning with what is currently known about Foetal Alcohol Spectrum Disorder and my desire to understand where the difficulties lie for both the learners and the adults who are seeking to support them. To help, I have devised some questions which will gauge the level of knowledge that busy maths teachers have of Foetal Alcohol Spectrum Disorder and a) whether they would recognise pupils with Foetal Alcohol Spectrum Disorder, b) have any experience or relevant training that would help them, and most importantly c) what is their knowledge of teaching strategies and approaches to take. This is in the form of a questionnaire which is included at the end of this article. I am aware that there are many complex and often interrelated learning difficulties which impact how a learner can access the maths curriculum. Although the focus of my research is pupils with Foetal Alcohol Spectrum Disorders (FASD), I know that this will go alongside ADHD, autism and others. My granddaughter, who I mentioned in my last article, has diagnoses of FASD, PDA Autism and ADHD. All of these will not only impact her behaviour and her approach to school and learning but will vary from day to day and who it is who is making the demands upon her. Pathological Demand Avoidance (PDA Autism) is the subject of an excellent book “Understanding PDA: for Kids and Grown Ups” by Stacey Freeman. She illustrates the problem from the perspective of a little boy called Ethan; he says, “Demands can feel very threatening, so even if I want to do something, I won’t always be able to.” You can imagine what implications this has when transferred to the school learning environment. In my previous article, I mentioned the MILE program in the USA. MILE is an abbreviation of Maths Individual Learning Experience and is reported as having some success indicating the level of classroom support required. It also has implications for the type of learning environment that these learners experience, and for the way demand and expectations are made of them. As I mentioned previously, the aim of my research is to explore and understand the current situation and then learn and adapt from others to inform the initial and in-service training of teachers. It is important that we remember there will be a gap between chronological age and developmental age. So the current expectations about all learners achieving GCSE by the age of 18 may not be realistic. As a teacher and head of department I always took the importance of the level of subject knowledge and experience of the teacher together with the teaching materials and resources to be the most important aspect of learning maths. However, I now think for these pupils it’s about the support, the approach and the way the learning environment is organised. I now view the traditional classroom to be a very scary place for these pupils.
Vol. 29 No. 4 Spring 2025 14 A reminder of the words of Professor Barry Carpenter, who gave us this background and laid down the challenge for us to explore, is helpful at this point: “The neuroscience around this tells us that the teratogenic effects of alcohol on the brain in utero significantly affects the parietal lobe, which is the brain’s centre for numeracy and mathematical computation. Whilst there has been some level of progress in the education of children with foetal alcohol spectrum disorders, we still have a long way to go on appropriate adaptations and accommodations within the curriculum. This is particularly so in the area of mathematics.” Update on the work of UK government on SEND Recent announcements suggest that the government has begun to recognise its shortcomings in addressing the needs of many SEND pupils. I’m not convinced, however, they understand either Dyscalculia or FASD and the number of pupils affected. My local MP has forwarded my research proposal to the DFE, as I wish to help them understand why research in this area is essential and the importance of learning from initiatives being implemented elsewhere in the world. As yet I’ve not had a reply! The key documents and legislation by the UK government relevant to SEND provision and school setting for pupils with FASD are: “The Special Educational Needs and Disability (SEND) Code of Practice from 0 to 25 years (Department for Education, 2014). It brings together legislation from the Children and Families Act 2014, the Equality Act 2010 and the Special Educational Needs and Disability Regulations 2014. The code of practice enables parents to request an EHCP with the local authority. (Education, Health and Care plan) if they feel extra support is needed for their child. The Code highlights four broad areas of need: • Speech, language and communication needs • Cognition and learning (including Specific Learning Difficulties) • Social, emotional and mental health difficulties • Sensory and/or physical needs. (Department for Education, 2014) Any diagnosis once obtained will include guidance in at least one of the above areas of need. A reminder of the Problem FASD is a spectrum of disorders that impacts the physical, emotional and intellectual development of the child to a greater or lesser degree. Research has shown Children with FASD encounter learning difficulties in Mathematics. FASD slows development in mathematics, so many children will be working at a different developmental age compared to their chronological age. This is referred to as ‘developmental dysmaturity’. An example would be a young person with chronological age 18 has a maths skills age of 8. One reason for choosing Key Stages 3 and 4 is that any differences in learning needs should be more apparent at this age compared to learners without FASD. It has been shown that there was a 31% gap in maths attainment for pupils with SEND at the end of Key Stage 1 and a wider 49% gap at the end of Key Stage 2. Even though there will be regional variations, development dysmaturity leads us to conclude that this gap will be wider at KS3 and wider still at KS4.
Vol. 29 No. 4 Spring 2025 15 There are no definitive percentages of children affected by FASD as it is not a condition recorded at birth in the UK. So, to have an idea of the size and scale of the problem of how many pupils with a diagnosis of FASD there are currently in schools we have to use estimates. Data from the USA suggests 9.1 per 1,000. However, more recent work suggests that the data model for the UK is 3.2% of the population. Using the latest data from the Department for Education (2023), which gives the number of pupils in each Key stage as; KS 3: 1,947,519 and KS 4: 1,251,567 or 3,199,086 for 11-16 pupils. Using the 9.1 per 1000 estimate, this gives 29,112 pupils. The more recent estimate of 3.2% gives 102,371 pupils. It is suggested that 6% of pupils have Dyscalculia, 3.2% with FASD. Together this represents 9.2% of pupils at KS3 and KS4. The aim of my research is: “To explore how to ensure that teachers and support assistants are fully equipped to recognise a learner with FASD and know effective intervention strategies.”
Vol. 29 No. 4 Spring 2025 16 Where did the idea for brain scanning come from? A recent study conducted on soldiers suffering from PTSD in America lead to a similar study being done with children and adults in Europe and America recently. Originally conducted by Stanford in 2009 - https://med.stanford.edu/news/ all-news/2009/12/brain-imaging-shows-kidsptsd-symptoms-linked-to-poor-hippocampusfunction-in-stanfordpackard-study.html. From this, therapies have been targeting areas that children need intervention with to help brain development as they grow. Which and how many pupils are involved? Unsure I’m afraid the EP (educational psychologists) are studying children from all over the UK. What actually happens and what information do you get back about the pupils? The EP reports help inform any interventions or practises we have in school to help nurture and develop the children’s learnt experiences and help create more positive experiences to replace the emotional reactions to similar experiences. Essentially, we aim to coach children through negative experiences by offering positive ones and modelling safer, happier choices to overcome the same difficulties. This can be done through targeted practise to address specific events and combatted through interventions like, drawing and talking, play therapy, lego therapy, counselling, life skills interventions etc. Interview with Robert Lewis I recently had the pleasure of meeting Robert Lewis Assistant Headteacher at Shenstone Lodge School. Shenstone Lodge is a primary SEMH school taking care of children with complex social, emotional and mental health needs with a large proportion of trauma related behaviours. During our time together I listened with great interest as he described one of the intervention they are involved with as part of the wider support for their pupils. Some of their pupils are taking part in brain scans as part of their commitment to understand the pupils they are seeking to support. Robert describes how this fits within the supportive ethos promoted by the school. This piece is simply an introduction, and the project is still in its very early stages, more information will be shared when it becomes available. Robert has kindly offered to talk about this during SEND November.
Vol. 29 No. 4 Spring 2025 17 How does this inform your practice and support what you already do? Our school ethos is built around regulating before educating and helping to address children’s needs to ensure they are ready to learn. This can be done in a variety of ways but children only then begin to engage with learning once their personal needs are met. Interventions aimed at addressing personalised needs, timetable adjustments, approach in the classroom, resources available etc. What are the outcomes from this? Children are more settled and happier. This helps promote a safe judgement free space that then encourages and supports learning as children have managed to leave their challenges at the door, or have had them addressed head on in the classroom. What is changing as a result of this project? Children are attending school more, less incidents of violent or serious dysregulated behaviours, better engagement from home, academic learning is now able to be a focus. Once settled we find the many pupils make significant progress and begin to meet age expectations in some cases.
Vol. 29 No. 4 Spring 2025 18 New guidance on the assessment of a Specific Learning Difficulty (SpLD) in Mathematics In March 2025, SASC (Specific Learning Difficulties (SpLD) Assessment Committee) published new guidance for assessors for the identification of a specific learning difficulty in mathematics. (SASC.org.uk – downloads). This includes a new definition taking into account recent research on mathematical cognition. A working group was set up by SASC to review the SASC 2019 guidance on assessment of Dyscalculia and Maths Difficulties which considered recent research as well as existing definitions in order to revise the definition. The group brought together key researchers from university departments focusing on maths difficulties and/or maths anxiety as well as those working in the field of dyscalculia/maths difficulties assessment. This highlighted how there are different interpretations of a number of terms between and within research and education. In particular, the term “number sense” and the concept of fluency, neither of which have an agreed definition and can be interpreted very differently. A list of participants can be found at the front of the document. The aim of the group was to bring together a range of experience and to reach consensus (at least 80%) on a definition and how to assess. Once a draft definition was broadly agreed, a series of statements was circulated to a wider group of people with a lived experience or who work in the field of maths difficulties. 30/33 statements reached 80% consensus and were included in the final definition. Whilst the guidance is aimed at assessors identifying maths difficulties and recommending how individuals might be supported, the research behind it may be of interest to teachers in considering how to adapt their teaching. What does the research tell us? It is often reported that there is far less research on mathematics difficulties compared with dyslexia, and that what exists is limited. However, there have been a number of useful papers published, particularly meta-analyses, papers that combine research from a range of studies in order to compare data across a larger cohort and consider common themes. Of particular interest is Bert De Smedt’s paper in 2022 – “A Bert’s eye view”. Through this study, De Smedt identified the key factors that contribute to performance in mathematics. This is categorised into domain-specific (directly related to mathematics) and domain-general factors which are more likely to contribute to performance across the curriculum. Most of the factors are cognitive (e.g. working memory) but environmental factors such as experiences of mathematics at home and school also add to the mix.
Vol. 29 No. 4 Spring 2025 19 Each individual has their own unique profile and the convergence of this range of factors can impact on success in mathematical tasks in education and beyond, both positively and negatively. It is also possible to mitigate for some of these factors through appropriate support. Therefore, it can be helpful for teachers to determine the factors that may be creating barriers in order to consider the best way forwards, in particular to increase an individual’s resilience and reduce or even prevent maths anxiety. Domain specific (maths related) factors Numerical magnitude processing involves the ability to understand, process and represent quantities. This can involve counting, estimating and comparing quantities both physical (non-symbolic) and when represented by Arabic numerals (symbolic). Home maths environment: The quality and quantity of maths-related activities at home as well as parental attitudes and expectations, impact on maths learning, particularly in the early years. Aspects of the school environment (whole-school ethos, staff subject knowledge, confidence and experience) can also contribute. Maths anxiety frequently co-occurs with maths difficulties and often leads to a downward spiral. Those with maths difficulties are also more likely to lack resilience when approaching maths related tasks. The role of language in mathematics Both domain-general and domain-specific language have an impact. General language and communication difficulties impact on maths learning as well as other areas of the curriculum. Receptive language affects the ability to understand instructions and tasks. Expressive language impacts on the ability to express mathematical thinking, particularly verbally. In addition, many people with maths difficulties have a further difficulty understanding language specific to maths. This can include: • meaning of “maths words,” • terms such as ‘measure’, ‘multiplication’, ‘equation’, • linguistic elements that have a mathematical meaning that do not require precise mathematical knowledge, quantitative terms (more, less) or spatial terms (below, under). Domain-general cognitive factors The impact of domain-general cognitive factors is likely to be seen across the curriculum but may have a greater or lesser impact in maths dependent on other contributing factors. Executive Functions • Working memory: The ability to maintain, update, and manipulate verbal or visuospatial information in memory. This has an impact in maths for example when working through a calculation mentally.
Vol. 29 No. 4 Spring 2025 20 • Inhibitory control/inhibition: The ability to inhibit a dominant response or resist interference. This includes ignoring distractions externally (noise in the classroom) or intrinsic thoughts. In maths it can also mean avoiding irrelevant information in word problem. • Shifting: The ability to switch attention between mental sets, tasks or strategies. In mathematics, this can impact on flexibility in using strategies or applying a concept or procedure. In fractions this can impact on the understanding the relative magnitude of fractions. For example, ¼ is smaller than ½ even though the denominator has a larger value. Visual-spatial processing skills: The ability to tell where objects are in space. This can impact across many areas of mathematics not simply shape and space. Mental rotation and visualising concepts are particularly important. Examples include: • Comparing visual quantities • Distinguishing between symbols/ numerals (e.g. 6/9 and +/x) • Aligning columns in workbooks • Using number lines • Interpreting graphs Other cognitive factors may include phonological awareness which has a greater impact on mathematics for younger learners than later on. Risk and resilience factors The impact of maths difficulties is further complicated by a number of risk and resilience factors. An individual may have processing issues that would be expected to have a severe impact on maths learning, but this can be mitigated through environmental factors such as a positive ethos, a teacher’s strong subject knowledge and levels of empathy. Conversely, an individual may have strong processing skills but negative experiences in maths may lead to low resilience resulting in lower attainment levels. Risk and resilience factors include: Biological factors: Certain genetic conditions (e.g. Turner syndrome, Williams syndrome), medical issues, difficulties with vision and/or hearing. Children born prematurely are also more likely to have maths difficulties with the risk increasing by each week before 32 weeks. Environmental factors: Experiences of and attitudes to maths at home. The school environment also plays a key role including attendance; teacher confidence, anxiety; access to support. A Specific Learning Difficulty (SpLD) in Mathematics For consistency, the definition is mapped to the Dyslexia (Delphi) definition published by SASC in March 2025. The full definition can be found at the end of this article. The guidance states that a specific learning difficulty in mathematics is a set of processing difficulties which can include domain-general factors which can also affect other areas of learning and domain-specific that are related to mathematics. A SpLD in mathematics is lifelong
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