Vol. 28 No. 1 Spring 2023 1 Editorial Team: Kirsty Behan Alan Edmiston Peter Jarrett Alison Roulstone Les Staves Nicky White 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, The Old Courthouse, 58 High Street, Maidstone, Kent ME14 1SY Published by the Mathematical Association, 259 London Road, Leicester LE2 3BE Tel: 0116 221 0013 Fax: 0116 212 2835 (All publishing and subscription enquiries to be addressed here.) Designed by Nicole Lane 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. Editors’ Page - Extended editorial 3 The editorial in this edition is far longer than usual. The idea behind this is that both reflects upon our recent conference and serves to highlight its importance in two ways: • How valuable the sessions were in showcasing the role Equals can have in supporting the teaching profession and, • The outcomes in term of the future work and direction of Equals. The 2022 Equals conference 14 The recall of tables – part 3 16 This concludes the of reflections of Mark Pepper on the place and future of tables in the maths classroom. How my army training helped me survive 18 I met Tarun Patel, who began teaching in a PRU, in Coventry during his ECT year and became fascinated by his story. He kindly agreed to share his journey into teaching mathematics and what a story it is!
Vol. 28 No. 1 Spring 2023 2 Teaching can be a lonely experience, we closeour classroomdoorsandhope for the best. If you’re lucky, you work in a MAT where you get to share some of your achievements and experiences. If you’re extremely lucky you are invited to a nationwide wide conference where you get to share your experience and you sit back and watch the ripple effect that your work has. I am one of the lucky ones and I am not going to let this ‘luck’ run away. I want to change the offer we give to our SEND students because I believe that theydeservebetter. Special needs education deserves better education, better funding and better research to ensure that the young people in our care get what they deserve. Rebecca Pack - Conference reflections
Vol. 28 No. 1 Spring 2023 3 Editors’ Page The January 2023 edition of Equals is comprised mainly of articles celebrating the success of our first conference and the resulting ripples it has caused. This editorial will be much longer than usual as it contains lots of information and news as I try to map out and articulate the changes that we are seeking to put in place as a consequence of the conference. This editorial will be followed by a series of reflections from a number of delegates most of whom have never written for Equals before. Changes to the Equals editorial board I would like to take this opportunity to thank Louise Needham for all she has done to support Equals. As a result of her changing role, Louise no longer has the capacity to be as active within Equals as she has been; Louise we wish you all the best! I would now like to introduce two new editorial board members: Alison Rylstone and Les Staves. During the conference they both agreed to join our team and they bring great strengths and qualities to Equals. If you read their short biographies below you can see why I was so keen to involve them in the future direction of Equals. Alison Roulstone is a qualified primary schoolteacher and Special Educational Needs Co-ordinator (SENDCo) with seventeen years of teaching and leadership experience in mainstream schools across the East Midlands, UK. Having taught Mathematics to children from the early years all the way up to Key Stage 2, Alison has a good understanding of the primary maths curriculum and age-appropriate skills progression. Currently a PhD student within the Centre for Mathematical Cognition, based at the University of Loughborough, her research project focuses on understanding and raising awareness of dyscalculia amongst educational practitioners, and developing a screening instrument to identify children who are at risk of dyscalculia. Presently, she is collaborating with researchers from the UK, Vietnam, South Africa, Italy, and Germany to better understand what teachers know about dyscalculia. Les Staves worked as a teacher with children with very special needs in the UK since 1973. He was Head Teacher at an outstanding special school, before becoming an independent consultant, trainer and author. He has worked internationally training teachers and working on curriculum development for special schools, government bodies, and SEN organisations. Though Les is proud of his reputation for curriculum development and writing he is most proud of his reputation as an inspirational teacher and trainer. His school courses are firmly based in practical experience and knowledge of children’s development, and
Vol. 28 No. 1 Spring 2023 4 engaging ways of teaching. His aim is always to provoke your thinking and motivate your teaching, he always hopes to both entertain you and touch your teaching heart. Conference proceedings All of the presentations given on the 25th November will be collated into a conference proceedings publication. This will be distributed amongst all conference delegates by Easter. If you were not present at the conference and would like a copy, please get in touch. Success across all settings I did not use the term success to describe the conference lightly. The term can be used in many ways to articulate what took place at Parliament Hill School on the 25th November 2022. Literally it was a success for we planned for 100 delegates and far more that that turned up, in fact we sold out of tickets. The last two conferences I have tried to run did not take place due to poor numbers. The success of this event in large part is due to the support of the Maths Association and I must thank Alice Onion and Bindu Modi for all their hard work dealing with all of the administration in the run up and on the day. It was also a success as a result of the: • Strength of the presenters, the knowledge they were able to share regarding SEND within mathematics; • Generosity of the staff at Parliament Hill School who could not have been more helpful; • Way the day was able to showcase the SEND work supporting by the NCETM and taking place in many Hubs across England; • Fact that the conference took place at the right time and reflected the growing mood that good teaching for SEND should be to be viewed as good teaching, for all. With regard to this last point I can assure you that we at Equals will continue to do all that we can to help you aspire to the best teaching you can for all your learners regardless of setting. The 2023 Conference Although a venue has yet to be agreed I am delighted to let you know that the 2023 conference will take place in the Midlands at some point during the second half of the Autumn term. The MA website will be updated as soon as the details become available and an outline of the program will be included in the next edition of Equals.
Vol. 28 No. 1 Spring 2023 5 The future of Equals This was the title of the feedback form that was sent to all conference delegates. We felt having so many people in one place would afford a valuable opportunity to gain a sense of both the impact of Equals has and also the direction we should take so that to best meet the needs of teachers and their pupils. This piece summarises the feedback and begins to map out the direction of travel Equals will begin to take before the 2023 conference. Helpfully the feedback confirmed that Equals, in its desire to be research informed whilst providing practical advice that is directly relevant to classroom practice, resonated with the delegates. This finding validates the approach we have taken at Equals but it is also very humbling given the range of SEND contexts we are seeking to support. The following list provides a very brief sample of how wide this range is: SEMH – both mainstream and special, excluded students and medical referrals, lots of ADHD, ASC, undiagnosed dyscalculia and anxiety, dyscalculia, Autism, AHDH, Mild Learning Difficulties and pupils with lack of self-esteem in mainstream education, maths anxiety and providing support to move pupils towards some form of terminal qualification at the end of KS 4. It was clear that the thing that has been most supportive has been the SEND seminars and so we will host two more between now and the Summer break. The first, by popular demand, will feature Les Staves discussing the ‘Roots of Math’s in February. Details of Les’s seminar can be found on page 6. This confirmation provided the validation we needed to move forward in the way we have since the beginning of lockdown in 2020. The feedback was invaluable as it provided as insight into the areas of difficultly that people need most help with and it is this that we will act upon. The following bullet points are a summary of the specific areas that respondents asked for help with: • Dyscalculia. • Using manipulatives to support harder concepts in maths. • Practical suggestions on what we can do to be more inclusive in a mainstream classroom. • “Outdoor maths” (maths outside the classroom). • Engaging older learners who are operating at KS1 level maths – I LOVED that Steve Chinn talked about age-appropriate manipulatives as my students have a social age much higher than their mathematical age and so won’t touch anything they perceive as babyish! • A range of practical strategies I can use to support SEND learners in my classroom. • How to build a bespoke curriculum which would suit pupils who are SEND, EAL and those who have not had a good education previously and so don’t like maths in the mainstream secondary education. • Practical examples on teaching specific topics in maths, e.g. fractions and directed numbers etc. • Developing trajectories for early maths concepts would be useful. The knowledge is both confirming and directive and as a result we will be able to refine the support we can provide during the next stage of our journey.
Vol. 28 No. 1 Spring 2023 Announcing the next Equals SEND seminar Equals Webinar Series: The Root of Maths with Les Staves 15 February 2023 6 Link to book: https://members.m-a.org.uk/Event-registration/Eventid/39 This webinar will delve into the relevance and roots of mathematics for children with very special needs. It will explore what Ofsted have described as the ‘cultural capital’ they need, and the skills and knowledge teachers need to help them engage in developing. It will range from sensory beginnings of learning through to number sense and the beginnings of becoming numerate. Those who attended the Equals conference may recognise this as a session Les recently held. By popular demand we are hosting a webinar to enable those who were not able to attend on the day, a chance to engage with Les. Date: Wednesday 15th February Time: 16:00 Price: MA members FREE / Non members £6
Vol. 28 No. 1 Spring 2023 7 The Equals Metacognition group Kirstin Mulholland and I led a session on metacognition at the conference. The idea for this was triggered by a conversation I had with Wendy Skelton of Fountains School (you can read her piece on metacognition in issue 27.2). Recently I managed to catch up with her to find out how things are going. At this stage they are 12 months into a three-year training programme with Thinking Matters. Not limited to maths the focus is whole school and cross curricular as they seek to develop self-regulation using specific tools such as thinking frames and habits of mind. Wendy was keen to stress that this is very early in the process but a common language for learning and thinking is beginning to emerge across the school. In maths she is using a defining frame at the start of topic to elicit prior knowledge from her pupils. The idea is that the use of a specific frame will trigger recall and enable the students to access prior knowledge. She is very excited about how this is developing and we will follow Wendy on her metacognitive journey and catch up with her in the next edition. Talking to Wendy I realised that the idea of metacognition was something that Equals could champion which is why I involved Kirstin in the conference. Kirstin’s original piece can be found in edition 27.2. During our session, as the discussion flowed and the time began to disappear, it quickly became apparent that a one-hour session could do little more than scratch the surface of such an important concept. It also highlighted the wide range of ideas people bring with them concerning such an apparently ‘well-known’ educational idea. I myself was first introduced to the term 30 years ago with reference to the application of the ideas of Lev Vygotsky. During the session my suggestion that we form some form of metacognition working group was very well received and so the Equals Metacognition group was born. The following email was sent to all who ‘signed up’ prior to its start in January 2023: “It was so lovely to see you in our session on Friday and as promised here is the group email regarding our next moves. As I said at the conference, I think an understanding of metacognition is key to helping pupils and I would like to explore how we can specifically focus upon this concept within mathematics and with SEND students in particular. As a group I would like us to think about how we could do this and also how Equals could become a vehicle to develop our understating of metacognition within mathematics and to disseminate any outcomes. Could you reply to me with your thoughts and after Christmas I can disseminate any finings and next steps including possible remote meetings. To help could you think about what you would like to do and how we could collectively work to develop our understanding and practice. For example you may have written something or have an idea for an article that could be published early next year. Do let me know what you think so we can add some structure to what seemed like a very positive thing to do at the conference.” What this group will look like has yet to be decided and defined and if you would like to join the group then please get in touch in response to the appeal above. The initial outcomes from this group will be shared in the next edition of Equals and the topic itself will form a major strand at the 2023 conference.
Vol. 28 No. 1 Spring 2023 8 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 honor the memory of Ray Gibbons, who founded Equals, we are pleased to open submissions for the 2023 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. 28 No. 1 Spring 2023 9 Conference reflections This section contains a series of delegate reflections on the Conference. They have been included as they serve to give an insight into how important we take our professional role as a subject association in supporting teachers of mathematics. More than that I think they highlight how important it is for teachers to network and share both their stories and expertise. Guy Carpenter 05:30 wake up, three trains and three and a half hours later I finally made it to Parliament Hill School, London. Was it worth it to attend the EQUALS SEND conference: Success Across all Settings? Yes it was!!! Equals laid on an extensive programme of thought-provoking experts in the areas of Dyscalculia, SEND Intervention programmes and resources, Metacognition and Maths Anxiety. The opening address by Steve Chinn, the countries lead on developing Mathematics proficiency in neurodivergent learners was intelligent, sharp, and insightful with a twist of humour. A great way of breaking an audience into the day’s events. How do you follow that? Well, a dive into Designing Interventions with Pete Jarrett, Chair of the BDA Dyscalculia and maths learning difficulties Committee. Here Pete talked passionately about providing access to intervention that utilised some key principles. It was clear that Pete loves an acronym. Knowledge – what do they know already? How can we build on this? Attittude - self efficacy and what stops learners from believing in themselves; Skills - How is the knowledge used, linked to the attitude of self-efficacy (metacognition) and the knowledge of Maths content? Habits - How learners use all the above to make positive decisions about learning to progress. Pete talked extensively about providing a scaffolds and heuristics for learners to access concepts and ideas in the form of the TREE acronym: Tangible - physical movement developing enactive knowledge, or a story that can develop links to prior knowledge in a schema; Representation- exposing the structure visually, pictorially, or abstractly; Efficient - limiting energy and thought process, reduction of cognitive load- process or tool but also looking at the elegance of maths; Effective - does it do the job well? Can it be applied in more than one situation? Is it a future proof strategy? Added to this is C for communication - how do we communicate the Maths we want to expose using language so not to confuse. The language of Mathematics, instruction, and challenge so that learners can articulate what it is that they don’t understand so we can be that person who is the safety net for them.
Vol. 28 No. 1 Spring 2023 10 ‘Sometimes I wish I could borrow someone else’s head so I can explain’. How many learners think this and don’t act upon it? We as adults and teachers are there to be the safety net and provide them with the strategies to free them from this language and thought constraint. Safety nets and strategies were a big theme running through the day and exemplified further by Kirstin Mulholland and Alan Edmiston who talked about Metacognition and self-regulation. As teacher we must model what is ‘hidden in plain sight’; the thought process and thinking of the expert, that leads the learner to seeing the journey to expertise. This modelling of ‘what I am doing and why I am doing it’ gives rise to an improved resilience, high quality classroom discussion and develop learners’ ability to identify knowledge and strategies that will give rise to improved self-efficacy and success. For me the Equals SEND conference delivered exactly what it promised and more. It improved my knowledge, confirmed some thoughts I already had, but also instilled a fire in me to go out there and make a difference. THE BEST TEACHER(ING), SHOULD START WITH SPECIAL NEEDS TEACHING. Alison Roulstone A major highlight of the Equals Conference was listening to the opening keynote presentation by Prof. Steve Chinn, who spoke about practical ways to support learners with specific learning difficulties in reading (dyslexia) and in mathematics (dyscalculia). His methods are pragmatic, highly successful and based on extensive research. Steve’s vast experience in supporting students with specific learning difficulties, both in mainstream and specialist shone through his delivery. He recommends carefully designed visual images and the use of concrete manipulatives, matched to relevant maths vocabulary and concepts to develop mathematical understanding. All the following presentations/workshops were extremely well attended, involving a range of speakers from different specialist fields. One of the first things I noticed about the conference was everyone’s passion and enthusiasm for learning more about effective ways to improve outcomes for learners with specific learning differences. There was no shortage of questions answered in the discussions. The Equals conference confirmed to me the superb work being done across all settings to support education development. The popularity and interest in the Equals Conference was clear for all to see and evidenced by the high levels of attendance and eager participation from all delegates. Les Staves The conference was a great opportunity to network with people who are passionate about maths and teaching. Hearing the perspectives of Steve Chinn was a priceless experience. We owe him much for his real insight into the hidden difficulties that children encounter learning mathematics. The leaning towards understanding children’s special needs was refreshing. It was valued not only by the teachers and support assistants from special schools, who often feel
Vol. 28 No. 1 Spring 2023 11 unsupported in their struggle to make appropriate maths accessible and understood. But also, by mainstream colleagues who need to find avenues of differentiation. Those I spoke to who expressed the value that the SEND information they were gaining would have on their practice. Thanks for the opportunity to hear and spread the word that maths is for everyone’s lives. Razia Latif I thoroughly enjoyed the whole day at the Equals conference. We very rarely get the opportunity to engage with other mathematicians. The different sessions were very engaging and thought provoking, sometimes reassuring personal practice and at times challenging this practice. I loved listening to the range of speakers, as I was able to walk away with a deeper understanding of the topics. Furthermore, it forced me to reflect on my own practice which is always a good thing. I thoroughly enjoyed taking part in my research project, led and guided by Lou Hoskyns. The guidance at each step of my journey was valuable to ensure my research area was trying to “Keep it Simple” I was able to really focus on this with her guidance and felt quite honoured to be able to share my experience and successes at the “Keeping it Simple” workshop. Anon Loved it!!! I’ve been telling all my colleagues about it and have already used so many things in my classroom. I’d be interested in the webinar, I might run some dyscalculia CPD at my school (a PRU). I’m all over games in the classroom and this has really inspired me to up my game (!). Alice Hall Throughout 2021, while the world was in lockdown, the Equals team created a fantastic suite of webinars that promoted SEND topics and help in the classroom. These webinars took off in popularity and the MA saw the number of members and non-members attending these sessions grow month on month. It became clear to the Equals team that the need for a face-to-face event in 2022 was high. Working with Alan and his team, from the office in Leicester, was incredibly easy. There was such a clear vision of what we were aiming towards and the interest in the event was immediate. The job roles of the delegates were so varied. We welcomed teachers, Tas and SENDCOs, Maths curriculum advisors and primary and secondary specialists. The atmosphere for the duration of the conference was one of excitement and interest, a buzz of conversation and colleagues meeting old and new friends. The feedback received post conference has shown us that it was well received and a much-needed event. With this in mind, we now work towards promoting Equals to as big an audience as possible. We also look forward to hosting another conference in 2023 that will encompass the topics and subjects the feedback has asked for.
Vol. 28 No. 1 Spring 2023 12 Rebecca Pack • Do you fancy coming to a conference in London, where we talk about your project? • Why my work – it’s just what I do? • London? • A day out of class? Massively mixed emotions, anxiety, trepidation, excitement and pride. The answer was only ever going to be a positive one – with the approval of SLT obviously. I left the ridiculous workload of mainstream three years ago to be dropped into a massive learning curve of the special sector. It’s been the hardest and scariest move of my life – but I absolutely love it. The Equals conference proved that to me. For the last two years of moving from class teacher to being functional skills lead, I’ve felt like a fraud. Why should my mainstream beliefs and practices work in the special sector? Last year, I signed our school up to the NCTEM readiness within special school group, where I met the amazing Lou Hoskyns-Staples. During the focus groups, Lou shared many concepts, such as subitizing that I have been trying to incorporate into our newly written curriculum. It was a welcome pat on the back that I was on the right track. Our project helped identify the two very different learners within our two sites. Our ASC site decided to focus on adjusting their work tray focus whereas our SLD site focused on using iconic images to support learning. The NCETM project gave us the ‘permission’ to change what we were doing and try something different. Giving some time to trying these changes, the project proved to me that what we were doing was making a massive difference to our pupils and gave actual evidence to support this. To read our project in the Equals journal was an absolute pleasure. There’s something very reassuring about seeing your work in actual print. To go and share this with a group of interested practitioners was like a dream come true – which was not to disappoint. The Keynote from Steve Chinn immediately put my mind to rest; his talk about subitizing and dyscalculia was exactly what I have written in to our new curriculum, yet another reassuring nod to my curriculum. To move from Steve to Lou’s discussion of our project was reassuring. Sitting in a room with a random group or education practitioners, listening to work that I had been part of was daunting to say the least. Lou had given me the heads up that she would be calling on me to add a personal edge to the research that we had carried out. To be able to add a personal perspective to the students included in the project was pure joy. I remember putting my hand to my heart when my particular student was discussed. I’m sure I said out loud ‘he just makes my heart melt’. Other people in the room were able to join in with my joy and pride of the student. After the presentation, the ‘floor’ was opened to practitioners in the room. To be asked about what I do and the work that has been done was amazing. Especially when I found out later than the questions were coming from one of the more renowned Special needs educationalists in the country – Les Staves. I went to his talk next. He recognized me, which was lovely, he
Vol. 28 No. 1 Spring 2023 13 acknowledged me personally and the work that I have been doing, which was wonderful. Teaching can be a lonely experience, we close our classroom doors and hope for the best. If you’re lucky, you work in a MAT where you get to share some of your achievements and experiences. If you’re extremely lucky you are invited to a nationwide wide conference where you get to share your experience and you sit back and watch the ripple effect that your work has. I am one of the lucky ones and I am not going to let this ‘luck’ run away. I want to change the offer we give to our SEND students because I believe that they deserve better. Special needs education deserves better education, better funding and better research to ensure that the young people in our care get what they deserve. The 2022 Equals conference
Vol. 28 No. 1 Spring 2023 14 THE 2022 EQUALS CONFERENCE
Vol. 28 No. 1 Spring 2023 15
Vol. 28 No. 1 Spring 2023 16 The recall of tables – part 3 This concludes the of reflections of Mark Pepper on the place and future of tables in the maths classroom. Reflections on Students unable to rapidly recall multiplication tables are at a considerable disadvantage in exams and in everyday life Parts 1 & 2 In the two most recent editions of Equals Online (vol 27.1 and 27.2 ) I described the initial difficulties of a Year 9 student, Jim, who had poor number fact recall competence and the teaching strategies used to eventually result in a marked improvement in this. In the course of this work with Jim I would sometimes privately consider whether this was an efficient use of teaching time. On a macro level this is a controversy that commonly arises. Opponents of teaching number fact recall object on the grounds that it exclusively consists of rote learning through the memorisation of As his number fact recall improved a great increase in his self-confidence became apparent. palpable. This strongly affected his performance in responding to recall at a significant disadvantage within the non-calculator GCSE paper. Even those students with good number sense would be liable to make computational errors as well as using up valuable time through the use of cumbersome and inefficient methods of computation in tasks such as finding the product of two single digit numbers. The effects of poor number fact recall on general maths attainment If we return to the case of Jim it is interesting to consider the extent to which his initial poor number fact recall adversely affected his general maths attainment. At the outset of our sessions his lack of confidence in his own maths ability was number facts such as multiplication tables and the application of taught algorithms. They believe that an alternative strategy of encouraging the development of autonomy, creative skills and problem solving ability should be used. This approach is commonly termed number sense. Some teachers are likely to be tempted to exclusively use a number sense approach whilst eschewing all aspects of number fact recall. The difficulty with this approach is that it can place the students with poor number fact maths questions and manifested itself in considerable levels of anxiety. As his number fact recall improved a great increase in his self- confidence became apparent. A consequence of his reduced level of anxiety was a notable improvement in his level of success in answering questions including those that required the use of number fact recall. The obligation to teach number fact recall Many teachers may feel that under the current official assessment procedure they are obliged to
Vol. 28 No. 1 Spring 2023 17 teach number fact to those students who have difficulty with it in order to avoid putting them at a considerable disadvantage when taking the non-calculator paper. Nevertheless they may well consider that otherwise there would be no value in teaching number fact recall. There are, however, reasons why it is important for the students to have good number fact competence. Reasons for teaching number fact recall regardless of the non-calculator paper Self-image of young people Many young people are acutely aware of their self-image. This commonly manifests itself in concern about their outward appearance such as the clothes that they wear, body image and their hairstyle. In addition to this it is likely that they would want to come across as being interesting, well-educated and creative. In order to fulfil this ambition they would need to There can be no doubt that a good understanding of mathematical concepts is of far greater value than proficiency within number fact recall. present themselves as being articulate, literate and numerate. In some cases the young person will try to demonstrate proficiency in English but at the outset confess that they lack ability in maths. This is commonly interpreted as evidence of a lack of concern. In reality it is probable that they have feelings of inadequacy and so they pre-empt being “found out”. Without this precursor they would be mortified to be expected to publicly answer questions involving the product of two single digit numbers. Conversely young people who are proficient in mental maths would be able to demonstrate this and this would contribute to a positive self-image. Failings and injustices within the current exam system There can be no doubt that a good understanding of mathematical concepts is of far greater value than proficiency within number fact recall. Despite this being the case the current exam papers both for National Curriculum Tests (NCTs) and the GCSE are predominantly designed to reward evidence of number fact recall. This is due to the fact that the vast majority of questions are closed and commonly require an answer consisting of a single word or number. A consequence of this is that candidates are denied the opportunity to demonstrate their conceptual understanding. This disadvantage is exacerbated by some aspects of the marking scheme. An example of this features in the KS2 NCTs which specifies that an additional mark is available when an acceptable strategy has been used regardless of whether the correct answer has been provided. This will, however only be awarded if the formal method had been used. This means that if a student demonstrates initiative by using their own method the extra mark would not be awarded. Yet a student who regurgitates a taught method will get the mark! Students with poor number fact recall will be at a considerable disadvantage in the non-calculator paper in questions that require number fact recall. This is a particularly unfair situation as there is not an even distribution of such questions in the papers of different years. As noted in Part 1, in
Vol. 28 No. 1 Spring 2023 18 some years such questions hardly feature whilst in other years there can be as many as 7 questions that require the use of number fact recall. This injustice would be eradicated by simply permitting the use of calculators for all papers. It seems reasonable to conclude that the current official assessment system is flawed. There has recently been a groundswell of pressure from groups as diverse as the National Education Union, the Kenneth Baker Think Tank, The Times Education Committee, the publishers Pearson and the Tony Blair Institute for Global Change, calling for reforms including the abolition of exams in both the secondary and the further education sectors. If these reforms do eventually take place then the main pressure to teach number fact recall would be significantly diminished. How my army training helped me survive as an ECT I met Tarun Patel, who began teaching in a PRU, in Coventry during his ECT year and became fascinated by his story. He kindly agreed to share his journey into teaching mathematics and what a story it is! I never thought I would be a teacher; my initial career plan was to stay in the infantry and progress through the ranks of the army. The best teachers I have known are from the army and I strongly believe that the army and teachers should have a closer relationship. Commanders in the army hold countless attributes to developing great soldiers, which include leading by example, encouraging thinking, demanding high performance, using discipline and rewards effectively. However, I choose to pursue teaching after some personal circumstances changed the way I viewed life. After completing my teacher training, I left my CV with an agency stating I am looking to teach maths as a supply teacher locally after having no luck with local schools. Near the end of the summer holidays, a Head Teacher from a school in the west midlands called and was desperate for a maths teacher with an immediate start. I mentioned I was searching locally and as I didn’t want to travel however the head teacher stated that this school was an independent school SEN and the pay would reflect travel. Long story short I applied, had my interview, and received a job offer. Two days later it is my first day and I had no idea what I had signed up for. With no scheme of work and abilities ranging from Entry level to GCSE I knew I had my work cut out for me as an ECT. Students in this school were every mainstream teachers’ nightmare, Constant disruption, fighting, swearing and gang culture. Students did not want to learn, any sort of behaviour management would lead to abuse towards myself and other staff
Vol. 28 No. 1 Spring 2023 19 members in the school. This school required out of the box thinking as methods I learnt during my teacher training did not work. As behaviour management was hopeless, I used instructional coaching techniques I learnt in the army. I was quick to use a technique called PAR, Present, Apply and Review, in which 60% of the lesson composed of the Apply phase. The Apply phase, allows students to work through problems either on paper or in my case together as a class. I spent minimum time presenting and reviewing. Initially I needed to build good relationships with students which was done through story telling of my army career as well as my level of fitness. I started the next few lessons by giving students the cold shoulder and stating to them why I would teach them if they didn’t want to learn. I spent a lesson reading a map with students looking in. They asked me what I was doing, and I explained I was plotting coordinates and figuring out timings. This was a key turning point for them, as it gained interest. I opened up an OS map and asked students if they could name any key features they knew. After a few correct answers I asked if they could then figure out how long it would it take to travel from Point A to Point B. Most of them had no idea until a student mentioned that I would need to measure with a ruler and use the scale on the map. I asked students if they wanted to learn about how we navigate in the army, to which they replied Yes. Although there was still a great deal of behaviour issues I had them engaged and started a series of lessons on speed distance and time. The dilemma I faced is that I can’t relate many mathematical topics to the military, as the only Maths teacher in the school I decided to seek guidance else to which I found out about the Maths hub. I was joined a work group called “Teaching for mastery in AP and SEND schools”. Within my first few weeks of meeting Alan he had helped me develop activities that use story telling in a way that would help students learn about maths. To anyone who is new to SEN maths I strongly recommend using the Maths hub and getting yourself onto a session with Alan. The 2022 Equals conference
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Vol. 28 No. 1 Spring 2023 21 Learners can’t generalise and are overwhelmed when problem solving Learners can’t or won’t revise A: Not with timely practice. By using ✓ bite sized teaching on firm foundations, ✓ 15 min. personalised retrieval practice per lesson, ✓ which allows time for high quality feedback, we help teachers turn learning barriers into steps Free training and use for up to 2 terms in exchange for progress data, thereafter £1 per learner per half term. Learners have poor numeracy skills Low success leads to demotivation Feedback is rarely effective Learning is quickly forgotten Learners find learning difficult Learners have many learning gaps Q: Do these learning barriers: mean that low prior attaining learners will fall further and further behind their peers? Advertisement
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