‘Maths anxiety’ is a condition in which children experience real distress either anticipating a maths lesson or whilst being in one. One pupil I taught, I will call her Mary, had become so over wrought by the mere thought of maths that at school she had started to ask to go to the lavatory and stay there for as long as possible to avoid maths lessons. Or she would say she felt sick and ask to go home. She said when I asked her about it that ‘all my thinking stops when I am in maths lessons. I see everyone else writing lots of numbers down, and I don’t know where to begin.’ After I carried out a full assessment of Mary’s processing skills, the reason why she was struggling with maths became clearer. She is a very articulate child, with high expressive and receptive verbal ability and above average general visual perception and yet her anxiety during maths lessons was so extreme, that she was filled with a sense of dread and failure. This was not due to ‘dyscalculia’ which is an intrinsic difficulty with understanding numerical operations, but it was due to her having real difficulty keeping up with the pace of the verbal instructions in class due to the fact that she has a below average verbal memory and difficulty linking verbal and visual instructions. The key to alleviating her stress was to go back to the beginning and slowly take her through the early mathematical processes at her own pace.
Having written two spelling workbooks, and saying that I would never put myself through that level of stress again… I found myself creating my first maths workbook ‘Times Tables, It’s a doddle’ as a result of seeing the stress students like Mary were and will experience, if not taught in a way that works for them. Many pupils I had tutored or assessed had said that they found learning the times tables almost impossible. And this is because expecting students with verbal memory difficulties to learn the times tables by rote learning is not going to work very well. But encouraging these students to find the correct answer from a choice and to recognize the patterns in numbers, whilst they do this, does work and also develops the student’s understanding of numbers simultaneously. This also crucially minimises anxiety levels. The hard work that went into the book has been well worth it, it has been very well received by students and tutors, not just here in the UK but students have worked through the book in places as far away as Singapore, Australia and America.
As discussed above being an assessor as well as a tutor gives me access to tests which highlight specific areas of difficulty with Maths. I have found that students of all ages, and particularly students who have working memory difficulties tend to struggle with fractions. When this difficulty is brought up, with the student, they will invariably say ‘I can’t do fractions’ whilst crossing their arms and looking downcast, in order to convey a general sense of, so that’s that, hoping that we will move swiftly on, and act as though fractions don’t exist…
But as with learning the times tables, these students can get to grips with fractions, if they are taught in a steady, structured way, using imagery where necessary. And linking fractions to real life problems, makes them more relevant. I created a longer version of the times table book which included a section about fractions which was well received and decided to create a separate fraction book as a result. This book, ‘Fractions, Step by Step’( you try and think of a snazzy title…) takes students through understanding how to identify a fraction of a shape or a group of objects, right through to working out how to multiply fractions with different denominators, and how to divide a fraction by a fraction, in a steady, sequential way, building on what has already been learnt. And as students with working memory difficulties often say that they have to have a digital watch because they can’t tell the time using an analogue watch, there is a section in the workbook which explains fractions of an hour.
Sarah Cowell Dip SpLD, SpLD APC, January 2021
Why ‘Zebras Spells Really Well 2’ is focused on teaching children to read and spell words with Double Vowels
There are many different combinations of double vowels within words and as the same letters can be sounded out differently they can cause specific problems for dyslexic children. As dyslexic children typically find it hard to distinguish and manipulate the specific speech sounds in words this then impacts on their ability to turn speech sounds into the letters that represent them. As different sets of double vowels can make the same sound, this makes the whole already complex process, even more demanding. And as the same sound can be created using different double vowels ‘homophones’ have evolved such as, ‘paws’ and ‘pause’ and ‘threw’ and ‘through’.
There is a maxim often used to guide the spelling and reading of double vowels in words which is, ‘When two vowels go out walking the first vowel does the talking.’
Unfortunately this only works some of the time; words such as ‘bead’ follow this rule, the first vowel is pronounced and the second sound is silent. When the ‘first vowel does the talking’ it takes its ‘long vowel’ sound, this is its capital letter sound, in this case ‘E’.
But there are lots of words containing double vowels in which the sound is split and the second vowel is not silent, as in the words: ‘dual’ and ‘fuel’. There are also lots of words in which the double vowels in the words do not represent the sound in the word at all, such as the word ‘eight’ which sounds as ‘long a’ + ‘t’. Reading this article it seems amazing that the majority of us acquire literacy skills relatively easily! We gradually develop our skill over time. A lot of this happens as we start to intuit words from contextual clues and subliminally register the subtle differences in letter groups as we read.
Dyslexic children typically struggle to read and so their attention is distracted by the task itself and this is part of the reason why they struggle to spell words accurately. Focusing on the spellings themselves and placing words which include the same letter groups which create the same sounds into specific worksheets, takes away competing words and accelerates learning. And being tasked with selecting the correct words within the word group to complete sentences reinforces the meanings of the words alongside their spellings.
Sarah Cowell, June 2020
The JCQ Access Arrangements Regulation 2019-2020 document starts by stating that, ‘Access arrangements are the principal way awarding bodies comply with the Equality Act 2010. The Equality Act 2010 requires an awarding body to make reasonable arrangements where a candidate who is disabled within the meaning of the Equality Act 2010, could be at a disadvantage in comparison to someone who is not disabled. The awarding body is required to take reasonable steps to overcome that disadvantage. Evidence of need: The evidence of need will vary depending on the disability and access arrangement being applied for.’
Being given a diagnosis of, for example, dyslexia, does not automatically bring with it a qualification of need for ‘Access Arrangements’, although dyslexia is a recognised disability in terms of the Equality Act 2010.
But it is very unlikely that an individual who has been assessed as being dyslexic will not have one standard score below 84, in a standardised test that is relevant to being given an Access Arrangement. Every dyslexic student is all too aware of the difficulties they face assimilating the meaning of text without rereading it, or writing facts down at the same pace as their peers. The underlying reason why dyslexic students process words and often numbers
slowly will be due to underdeveloped working memory skills, maybe visual or verbal or both. But this will only be evident if these skills have been formally assessed.
It is important that parents, carers and guardians of students with a specific learning difficulty, make sure that they push for extra help at school as early as possible for the student they care for. This is because the rules re, Access Arrangements, state ‘that a history of need, and a normal way of working’ must be evident in the years leading up to the student taking, for example their G.C.S.Es, if they wish to apply for access arrangements.
It is also relevant for parents and carers to note that, historic, full diagnostic assessments, even written a week before an access arrangement application are not now allowed to be used when applying for an access arrangement.
In terms of an access arrangement report, the carer must first ask if the school is willing to accept an independent assessor’s report, and be willing to fill out the first part of what is called Form 8, which covers the pupil’s history of need, and then send that report to the independent assessor. The assessor is then asked to assess the student and write their assessment in the ‘light of the evidence supplied by the school.’
All this seems to fly in the face of the SEND ACT, page 100, clause 6.45 which states that ‘schools should take seriously any concerns raised by a parent, these should be recorded and compared to the settings own assessment and information on how the pupil is developing.’
This is probably why the JCQ regulations state that, ‘The JCQ recommends that SENCOs and assessors working within the centre should carefully consider any privately commissioned assessment to see whether the processing of
gathering a picture of need, demonstrating a normal way of working and ultimately assessing the candidate themselves should be instigated. (JCQ, page 7)
Sarah Cowell, August, 2019©
‘Zebras Spell Really Well, Phonics and Spelling Rules’
The predominant reason why people with dyslexia find processing letters and words demanding is that they have difficulty processing speech sounds, this is described as ‘phonological processing’ skill. They may also have an underdeveloped verbal memory, and more general working memory difficulties which affects the overall speed of their linkage of letters to sounds and vice versa. This slow processing then goes on to inhibit their reading fluency which impacts on their recall of the text they have just read.
‘Problems in learning to use the regular patterns of letter-phoneme correspondence in words as an aid in identifying new words have been referred to as the single most important defining feature of specific learning difficulties.’(Lyon, Shaywitz, & Shaywitz, 2003)
A tried and tested way of developing phonemic decoding skill is to teach the spelling rules alongside teaching letter to sound correspondences starting at alphabet level.
The pupil should be taught step by step beginning with single-letter sounds linked to letter names and letter shapes and working through stages through simple one syllable words to complex multi-syllabic words.’ (Beve Hornsby, 1995)
‘Zebras Spell Really Well’ is a cumulative sequential spelling programme that takes the learner on a journey starting at letter to sound level, right through to exercising their skill at reading and writing words in sentences. Imagery is used throughout and the learner is continually, being engaged by a variety of tasks, in order to learn a specific spelling rule, prior to moving on to the next one.
Lyon, G.R., Shaywitz, S.E., & Shaiwitz, B.A. (2003) A definition of Dyslexia. Annals of Dyslexia, 53(1-14)
Hornsby, B (1995) Overcoming Dyslexia, 73, Vermillion Press
‘Times Tables?’ It’s a Doddle’
‘Phonological processing skills play a critical role in learning to read write and spell, particularly for alphabetical writing systems. They also appear to be involved in mathematical computation’
(Wagner, Torgesen and Rashotte, 1999)
The ability to rapidly ‘name’ or read both letters and digits is a fundamental part of phonological processing tests. ‘Rapid naming of objects, colours, digits or letters requires efficient retrieval of phonological information from long term or permanent memory.’(Wagner, Torgesen and Rashotte, 1999)
And the ability to recall digit strings in forward order is a fundamental aspect of phonological memory tests.
‘It is clear that phonological coding in working memory is potentially more useful when attempting to code new words, particularly new words but by bit, as a means of storing intermediate sounds.’(Wagner Torgesen and Rashotte, 1999)
It would be sensible to conclude that low scores in both rapid digit naming tests and digit memory span tests would predispose the individual to having difficulty performing mathematical operations. Processing numbers slowly will place strain on the individual’s working memory and this will impact on their ability to perform calculations with integral steps and also to recall the different steps involved.
‘Long term retrieval abilities are important to math and calculation skills. For example students with deficits in long–term retrieval may have difficulty recalling basic addition, subtraction, multiplication, and or division facts when encountered within a math problem.’ (Korkman, Kirk, and Kemp, 1998)
It is perhaps not surprising then that Dr Beve Hornsby, speech therapist, clinical psychologist and specialist teacher, lead at the ‘Dyslexia Clinic’ in St Bart’s Hospital from 1971-1981,and who also set up the ‘Hornsby International Dyslexia Centre’ stated in her book ‘Overcoming
Dyslexia’, ‘Around 60% of dyslexics have difficulty with basic mathematics.’ (Hornsby, 1995)
The ‘Times Tables? It’s a doddle!’ work book has been created to support children with dyslexia who have co-existent difficulty with recalling maths facts, leading to a real difficulty conquering the myriad facts in the twelve basic times tables. The workbook uses imagery and multi-tasking to support learning and includes textual problems to exercise the learner’s ability to turn number problems into words and vice versa. The learners have to select the correct answer to the times tables from a non-sequential set of answers, thus there is no rote learning.
The reader is engaged from the outset in working the facts out for themselves from given clues.
Sarah Cowell© Dip SpLD, SpLD APC, 2020
Wagner, R.K., Torgesen, J.K., Rashotte, C.R (1999) The Comprehensive Test of Phonological Processing, 2, pro-ed
Wagner, R.K., Torgesen, J.K., Rashotte, C.R (1999) The Comprehensive Test of Phonological Processing, 6, pro-ed
Wagner, R.K., Torgesen, J.K., Rashotte, C.R (1999) The Comprehensive Test of Phonological Processing, 6, pro-ed
Korman, M., Kirk, U., Kemp. S.,(1998) The NEPSY Manual, The Pysch Corp
Hornsby. B., Overcoming Dyslexia, 27, Vermillion Press
Sometime ago a delightful nine year old boy, I shall call Sam, came to see me with his mother, with a very specific set of issues that Sam was very aware of and concerned about.
Sam could not work out why he found it so hard to remember multiple verbal instructions and why he could not pronounce certain single speech sounds and blends very well. He found being around noise really stressful to the point that he had left the music room and sat in the corridor at school, because the noise to him was overwhelming. In the classroom he had moved to another table for the same reason on many occasions. He also felt he could not hear certain sounds either close to or from a distance. My initial thought was that this sort of hypersensitivity to sound can be associated with sensory neural deafness, which would also account for his hearing difficulty related to certain sounds. But Sam had passed a hearing test when he was four years old and he did not have a family history of progressive hearing loss and he had not had a bout of ear infections or illnesses over the following years that would trigger, this response.
The assessment results showed that Sam had above average numeracy skills and conversely below average phonological processing skills results, echoing Sam’s description of his difficulties. Sam’s spelling skill and untimed word reading skill were almost inevitably at the low average level. He had an above average expressive and receptive vocabulary, and this supported his reading in context which was at the mid-average level. Sam had secure attention
and concentration skill overall, but he had real difficulty reversing a list of letters dictated to him, he simply could not recall the letters well enough to re-order them. The ‘Object Recall’ sub test in the ‘Test of Memory and Learning 2’ Verbal Memory Index, also produced a below average result. The test required Sam to recall in sequential order the names of a set of objects. Images of the objects were displayed to Sam as they were named. This task disturbs the ease of recall of individuals with learning difficulty as the mixed visual to verbal cue, interferes with their recall as opposed to supporting it.
Sam had a history of speech and language difficulty, he found it hard to pronounce certain speech sounds and he wrote at a slow rate and he achieved a low average result for the ‘Beery Visual Motor Integration Test V1’, which is a test which assesses the individual’s ability to draw shapes. All this pointed towards Sam having fine motor dyspraxia, which also affects formation of speech, as it is in part a muscular process and Sam had said, ‘I know what I want
to say I just can’t get it out of my mouth.’
So what to do?
My recommendations included: Sam having support directed at developing his discrimination of letter sounds, using multi-sensory learning techniques, which would simultaneously develop his spelling, reading and continuous writing skill. To experiment with using ergonomic pencils and pens. To visit the local speech and language team for re-assessment and to have his hearing re-assessed across all the frequencies required to hear speech sounds both with and without background noise.
I was pleased to see an email in my inbox from Sam’s mother recently. She told me that Sam’s hearing assessment had due to her persistence, led to him being referred to a specialist audio-neurologist in London. Sam has as a result been diagnosed as having ‘auditory processing disorder’. This explains Sam’s hyper sensitivity to noise. Sam is not deaf as such, his difficulty is that his neural processing of sounds he has heard, is underdeveloped. Fortunately, our
auditory processing skills gradually develop until we are around fifteen years old. With the right support Sam can gradually develop his discrimination of speech sounds and his ability to distinguish general sounds and this will help him to cope with noisy situations and to feel less assaulted by sound. One relatively simple but useful intervention which can help students at school is the teacher’s voice can be amplified through a microphone connected to a headset worn by the student, this cuts out any extraneous distracting noise. Each child has their own pattern of need and so must be assessed by a specialist at an auditory processing clinic such as the one at Great Ormond Street Hospital in London. They take NHS referrals and will also see children privately.
Currently if a student wants to be considered eligible for a Disability Support Allowance (DSA) due to for instance Dyslexia, whilst in Higher Education, they have to provide an assessment carried out beyond the age of sixteen. As of February 2019 this has changed, they can provide a report carried out at any age, as long as it has been carried out by an assessor qualified to do so. This means that the assessor has to have the ‘SpLD APC’ qualification or be an HCPC registered psychologist. I will update this post as more information becomes available.
Over the years I have often tutored Dyslexic children who have struggled with mathematics, and one massive causal factor is their inability to learn the times tables.
They become distressed by the mere thought of tackling the times tables because they find the task overwhelming. And it is probably unsurprising that this difficulty with numbers accompanies Dyslexia as one key indicator of Dyslexia is a difficulty with different aspects of phonological processing (that is the processing of speech sounds) and phonological processing skills,
‘Play a critical role in learning to read, write and spell, particularly for alphabetical writing systems. They also appear to be involved in mathematics.’ Wagner, Torgesen and Rashotte, 1999)
Expecting children with poor phonological processing skills to not only assimilate verbal information readily but also to go on to recall this information precisely, is asking too much of them, they need to be taught a different way.
And having difficulty learning the times tables by rote is not the sole difficulty children with dyslexia may struggle with. They often find re-ordering numbers mentally impossible because they cannot readily visualise digits to re-order them. This disables the ease by which they can move from step to step when calculating sums. This is also why some children still count using their fingers well into their teenage years.
Writing integral steps down on the paper is a huge help to all people who have working memory difficulties. And a child recently stood up and hugged me when I suggested she wrote down the times tables answers for the six times table and then go back and count them, to work out how many times the 6 had been multiplied by to get to 36. She had finally assimilated the answers, but simultaneously recalling how she got there was a step too far, for her working memory. And another pupil has to write digits from 1-20 down at the side of the paper to do basic addition and subtraction steps, she cannot do this mentally despite being of average intelligence. And this same girl can happily work out simple algebraic equations.
I set out to try and create a times tables exercise book that was not simply a rote learning tool as clearly this approach will not work for children with working memory problems. I wanted to make the children create their own times tables, as they go. My approach has been to start off with the underlying structure of numbers. Odd and even numbers are highlighted at the outset. Multiplying two even numbers produces an even answer: 2 x 4 = 8. And two odd numbers multiplied together: such as 5 x 3 produces the odd number answer 15. But an even number multiplied by an odd numbers produces an even answer: 3 x 6 = 18. The learner is thus already starting to engage with processing numbers and being a detective not a dispirited observer. The book immediately moves on to focusing on the fact that zero is zero whatever it is multiplied by because children can be very confused about this. Zero is not an odd or an even number it is nothing! The exercise book has two pages devoted to each times table and the learner is initially tasked with selecting the correct answer from a non-sequential list of the answers. They then move on to supplying a missing factor that creates an answer. They are not simply given the answers. Each times table has an image, the two times tables image is a pair of trainers, the nine times tables image is a cat. And the book also includes questions related to the times table involved. What is a three sided shape called? What is 32? What is 36 divided by 12? What is the highest common factor of 36 and 12? What is the square root of 9? Worksheets teaching shape names, square numbers and square roots, highest common factors and lowest common multiples are also in the book. The exercise book also highlights number patterns in the answers to the times tables particularly the: 3, 6, 9 and 12 times tables. Most children are quite fascinated by the way the patterns repeat. And hopefully by the end of the workbook they have learnt not just the times tables facts but learnt how to apply these facts in various ways and why the facts matter.
This study discusses the neurological differences that underlie Dyslexia and the most effective ways of assessing the effects of Dyslexia. Local Authorities are tasked by the SEND Code of Practice 2015, with identifying young people struggling with this learning difficulty when schools or parents request an ‘Educational Health Care Plan’. If assessments diagnose a specific causal factor, such as Dyslexia, Local Authorities should then fund remedial support outlined in the child’s EHC plan. Schools will only go to the Local Authority if the child is persistently underperforming in literacy skills tests and if their own remedial support has proven to be ineffective. But are all young people being assessed thoroughly and are some authorities using outmoded definitions of Dyslexia which affect the assessment tools used?