


Dyscalculia:


Students who present themselves with a condition that affects the ability to process language are
referred to as dyslexic. Similarly, students who present themselves with number processing difficulties
are referred to as dyscalculic. Often parents and teachers refer to the difficulty with maths as Dyslexia
Maths.
Definition:
Difficulties in production or comprehension of quantities, numerical symbols or basic arithmetic operations that are not consistent with the person’s chronological age, educational opportunities or intellectual abilities.
Multiple sources of information are to be used to assess numerical, arithmetic, and arithmeticrelated abilities, one of which must be an individually administered, culturally appropriate, and psychometrically sound standardized measure of these skills.
Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers and have problems learning number facts and procedures. Even if they produce a correct answer or use a correct method, they may do so mechanically and without confidence.
Students with learning difficulties with maths often, in our experience, present themselves with more than one difficulty such as dyslexia, dyspraxia, auditoryprocessing weaknesses and working memory impairments. This is referred to as having cooccurring difficulties.
For a student with cooccurring difficulties the process of acquiring the fundamental and foundational
skills of learning maths becomes even more challenging. To add to this difficulty, when a student’s
brain network cannot process the significant and important stages required to make a head start with
numbers, the challenges they experience with maths feel greater. Typically they tend to use basic and
inefficient counting procedures for extended periods, make frequent errors and lag behind their peers.
They may experience difficulty with bonds of 10, times tables and retaining number facts; may possess insufficient mathematical vocabulary, struggle with number line accuracy and estimating and generally have a weak number competency.
Neuroscience research suggests that dyscalculics use different brain networks when carrying out
simple number maths and that by exercising the particular brain area using a range of learning styles and stimuli, a student with dyscalculia can be supported!

Brain in dyscalculia: 

The core number areas in the left and right parietal lobes of learners with dyscalculia have fewer nerve cells and/or fewer connections among them.
These areas also activate differently in dyscalculic learners: usually they are less active and in number tasks they respond differently from typical learners. Brian Butterworth (2012).

Parietal Lobe

Dyslexia: 



Dyslexia is a condition that affects the ability to process language. Dyslexic learners often have difficulties in the acquisition of literacy skills and, in some cases, problems may manifest themselves in mathematics. It is not surprising
that those who have difficulties in deciphering written words should also have difficulty in learning the sets of facts, notation and symbols that are used in mathematics. This pattern of abilities and weaknesses is known as ‘specific
learning difficulties’.
Problems often occur with the language of mathematics  sequencing, orientation and memory  rather than with the mathematics itself. Dyslexic learners find it difficult to produce mental or written answers quickly, and the need to ‘learn by
heart’ for pupils who have poor memory systems may well result in failure and lack of selfbelief. Some dyslexic learners will enjoy the flexibility of approach and methods while, for others, choice creates uncertainty, confusion and anxiety. 

Dyscalculia Symptoms: 
How do pupils with dyscalculia learn mathematics differently?
Our research has shown these are some of the difficulties with dyscalculic learners (a longer list has been considered in the development of the Dynamo Maths programme):



often have difficulty counting objects.
This affects basic ‘number sense’. They need clear instructions on how to count in an organised, meaningful way. Numbers need to have a meaning, magnitude and a relationship. They should first of all learn the skill of subitising before moving to counting. 


may have difficulty processing and memorising sequences.
Dyscalculic learners may be slow to learn a spoken counting sequence. Counting backwards is particularly difficult. They need additional practice in counting orally and need to continue oral counting into higher value sequences. Support can be provided by presenting sequences such as 0.7, 0.8, __, __, as 0.7, 0.8, __, __, 1.1, 1.2. The use and recognition of patterns is important and can be used to circumvent some of the problems with memory. Dyscalculic learners need support counting through transitions, e.g. 198, 199, 200, 201 or 998, 999, 1000, 1001, and practice structuring from one count to another, e.g. from counting in tens to counting in ones. 


need extra support in counting forwards and backwards.
Use a clearly labelled number line, or counters placed in recognisable clusters, as on dominoes. Teen numbers are an example of the inconsistencies of our number system. For example, thirteen should be ten three, but it is said and written as three and ten. By contrast, the word twentythree is in the same order as the digits, even if twenty is an irregular word (compared to two hundred). Careful teaching can minimise these difficulties as well as introduce the more regular pattern of larger numbers – sixtysix, seventysix, etc. Dyscalculic learners may find the transfer of a learned sequence, say 90, 80, 70 ..., to a modified sequence 92, 82, 72 ..., challenging. Base ten blocks or coins may help illustrate which digit changes and which remains constant. 


often have difficulties understanding place value.
Language uses names to give values when counting (ten, hundred) while numerals use the principle of place value – the relative places held by each digit in the number (10, 100). Pupils who have not mastered the name value system may say that nine hundred and ninetynine is bigger than one thousand. Language demands are greater in writing numbers in words. Numbers that feature zeros, such as 5006, will need careful teaching, using practical materials and focusing pupils on the ‘top value’ word: five thousand and six has four digits because the top word is ‘thousand’. A place value chart might be useful. Place value cards can also demonstrate the structure of numbers at a more symbolic/abstract level. 


find it difficult to learn number facts ‘by heart’,
but they can usually work within a manageable target and can learn to use strategies. Number bonds to 10 are fundamental and the key to so many more facts that they should form the focus of quick recall. Patterns need to be taught using multisensory approaches. Use memory hooks to help relate new facts to learned facts. Visual imagery, e.g. showing the links between 5 + 5 and 5 + 6 with coins or counters, will also support nondyscalculic pupils in the class.
Facts that may be accessed through rapid mental recall are stored as verbal associations in exact sequences of words, such as ‘8 plus 5 equals 13’ or ‘7 times 8 is 56’. Dyscalculic learners find it difficult to remember such verbal associations. Facts that have been successfully stored as verbal associations may be accessed very slowly. Learners should be encouraged to maximise the use of key number facts, e.g. ‘10 ×’ facts can be used to deduce ‘9 ×’ facts, as in 9 × 7 = (10 × 7) – 7. Short sequences of step counting from ‘5 ×’ can lead towards a ‘partial products’ approach in which, for example, 7 × 8 is seen as (7 × 5) + (7 × 3). 

fail to remember the variety of factderived strategies or mental calculation methods.
The sequence of steps in a calculation is difficult to remember for dyscalculic pupils because of a poor working memory. Weak number concepts and a lack of flexibility hinder multipath reasoning and learners may become confused or feel overburdened. Some see too many methods to learn and remember. It is important to concentrate on strategies that can be generalised, such as partitioning, rather than ‘one off’ methods, as these skills can then be more widely used across a range of calculations. 


may experience counting difficulties that will lead to subtraction errors.
Teaching ‘counting up’ is helpful, e.g. 9 – 7 = ; 7 + = 9. Many dyscalculic pupils gain valuable learning support from the triad method of recording number facts. Dyscalculic learners also benefit from learning to bridgeupthroughten to work out calculations such as 13 – 8. 


find that mental arithmetic may overstretch the working memory.
Through careful differentiated questioning, support can be builtin to overcome this difficulty. For example, when adding 9 as + ‘10 – 1’, the question could be asked in a structured way using the two steps. A key question may act as a prompt, e.g. ‘Have you remembered to adjust the answer?’. Encourage learners to use jottings to support mental calculations. 


have problems recording calculations on paper.
Learners who have performed well in mental mathematics may fail to cope with written methods of calculations. This is due to the increased load on the working memory of having to remember a more formal written procedure, plus difficulties in writing the calculation. Mental calculations often favour working with the most significant digit first. It may be useful for some to continue this approach with written calculations.
Working with base ten materials should support the introduction of written calculations, as these can illustrate the written method. Area, using squared paper, is a good model for multiplication. 

may need more clues to recognise, develop and predict patterns to help them solve problems.
Word problems are likely to be a source of difficulty. Teach the use of a ‘problemsolving frame’: – read the problem; – identify the key information and write it down or draw pictures; – decide which calculation is necessary; – use an appropriate calculation method: mental, written or calculator; – interpret the answer in the context of the problem.
Pupils may learn how questions are constructed if they invent their own word problems. The use of materials or images to interpret word problems can increase success. 

may be unsettled by the insecurity of estimation.
Estimation requires risktaking and insecure learners avoid risk. Visual models may help pupils see ‘closeness’. 


find the sequencing of time difficult.
Sequences of days of the week or months of the year are not easy to learn, and the introduction of simple clock time may also be a problem. The language of time is potentially confusing, with deceptively simple changes such as saying 7.10 as ten past seven (reverse order) creating problems. Using a clock face with pupils moving the hands and specifically
relating the language to the image may help. The introduction of digital representations may be supported, in the first instance, by a set of personal sequencing cards. 





