Gap Analysis/Dyscalculia

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Description

Dyscalculia is a specific learning disability relating to mathematics. People with dyscalculia have significant problems with numbers and mathematical concepts - but still have a normal or above normal IQ. Few dyscalculics have problems with maths alone, many also struggle with problems being able to learn to tell time, left/right orientation, rules in games and much more.

Researchers have yet to come to a final conclusion with just how many types of dyscalculia exist. David Geary has broken the disability down into 4 main areas (1): - Semantic retrieval dyscalculia - Procedural dyscalculia - Visuospatial dyscalculia - Number fact dyscalculia

It should be noted that this is the opinion of just one researcher and there are many other well established categories for Dyscalculia, one such example is published in the Journal of Learning Disabilities and has arisen from the research of Kosc Ladislav. He has broken Developmental Dyscalculia down into 6 areas; verbal, practognostic, lexical, graphical, ideognostical and operational developmental dyscalculia. (10)

Diana Laurillard (Professor of Learning with Digital Technologies at the Institute of Education, London) - “Although they [dyscalculic individuals] can count, they do not see the relationships between the numbers - e.g. that 5 is made up of 2 and 3. For them it is just a sequence, like the alphabet - we do not see E as made up of B and C, because it's not, it's just later in the sequence”

The UK DfES (Department for Education & Skills) Described Dyscalculia in its National Numeracy Strategy:

"Dyscalculia is a condition that affects the ability to acquire arithmetical 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."

Cognitive functions

Genetic, neurobiological, and epidemiologic evidence indicates that dyscalculia, like other learning disabilities, is a brain-based disorder. Some research suggests that it may be the result of an altered neural substrate.

It has also been suggested that poor teaching and environmental deprivation may compound the condition(9).

Because the neural network of both hemispheres comprises the substrate of normal arithmetic skills, dyscalculia can result from dysfunction of either hemisphere, although the left parietotemporal area is of particular significance according to UCL Institute of Cognitive Neuroscience. The debate as to whether the left or right parietotemporal area is linked with dyscalculia is hotly contested, however there is more research pointing towards a fault in the left parietotemporal area.

There is some research to suggest that Dyscalculia may occur as a consequence of prematurity and low birth weight and is frequently encountered along with a variety of other neurological disorders, such as attention-deficit hyperactivity disorder (ADHD), developmental language disorder, epilepsy, and fragile X syndrome. Developmental dyscalculia has proven to be a persisting learning disability, at least for the short term, in about half of affected preteen pupils. (2) Dyscalculia can also occur later in life as a result of a brain lesion or other traumatic brain injury.

Symptoms

Common symptoms include:

- Normal/Accelerated language acquisition. Good visual memory for the printed word. Good in areas of science, geometry and creative arts (until a level of higher math skill is required and where figures use logic not formulae).

- Mistaken recollection of names. Poor name/face retrieval.

- Difficulty with abstract context of time and direction.

- Poor mental math ability.

- Mistakes commonly made when manipulating numbers.

- Inability to grasp and remember math concepts

- Inability to comprehend or ‘picture’ mechanical processes.

- Poor memory of the layout of things.

- Poor sense of direction.

- Difficulty grasping concepts of formal music education.

- Struggles with spatial orientation.

- Poor athletic coordination.

- Difficulty when playing games.

Their challenges

Memory: Poor long term memory resulting in an inability to remember names (despite recognizing faces). Inability to recall schedules or sequences for example dance steps and musical instrument fingering. Unable to remember rules in sports and other games such as card games, also find it hard to remember whose turn it is.

Numbers: Difficulty with numbers specifically in cases of addition, subtraction, omission, reversal and transposition. Inability to count- especially when asked to begin counting at a number other than 1. Particular difficulty with numbers with zero’s and their relationships to each other such as 10, 100, 1000.

Abstract Concepts: Poor concept mastery resulting in an inability to grasp maths concepts. Lack of ability for visualization such as numbers on a clock face and recognizing geographical locations and where they are in relation to these locations. Limited capability for strategic planning such as in chess. Difficulties with spatial orientation such as distinguishing left from right and north, south, east and west. Inability to grasp the concept of time or direction – frequently lost/late and has trouble telling the time. Difficulty handling money, many dyscalculic adults find themselves overdrawn as a result of this. Difficulty in planning for long term, tendency to focus on the present or near future.

Coordination: Poor athletic coordination resulting in difficulty keeping up with rapidly changing physical directions.

The inability to grasp abstract concepts translates to more practical situations:

Financial Planning: Due to the combination of the inability to grasp the concept of money and poor long term memory, financial planning is particularly challenging for dyscalculics. The actual value of products means very little and dyscalculics can also struggle with purchasing the correct quantities, for example when buying food at the supermarket often far too much or too little is bought. When change is given in shops few dyscalculics are able to correctly calculate how much money they have and how much they should have been given back. As a result of all of this, many dyscalculics are consistently overdrawn and rely heavily on others for help.

Currency: Following on from the inability to grasp the concept of money, foreign currency is particularly difficult to comprehend especially as the exchange rates are often changing and calculations are often involved when trying to convert one currency to another.

Temperature: Temperature is meaningless when told in numbers, especially when both Celsius and Fahrenheit are used.

Travelling: Few dyscalculics learn to drive as it is heavily reliant on numbers (speed limits, petrol gauge, distances, etc.). This means many must rely on buses and trains for transport. Getting the right bus/train at the right time and on the correct platform are all huge problems as each of those instances involves the use of numbers and time.

Some persona with use case that address key challenges

Booking a train ticket online

Scenario A “Jenny” is dyscalculic. She is a mother with 2 young children. She is trying to book train tickets online for herself and her two children. The train journey involves 1 change where she must walk to a different platform and also must ensure that her first train arrives at the change destination with enough time for her to find the correct platform before the train sets off for the second part of her journey. She needs to be able to book the tickets for the correct time and with the appropriate rail card, in order to be able to qualify for discounts. She also needs to be able to remember her password for her bank’s security system in order that she can purchase the tickets; this password is made up of a combination of letters and numbers to fulfil the bank’s ‘secure password’ criteria.

Booking a train ticket online

Step	Challenges
Tick box for ‘return’	no challenges
Type in from and to destinations	no challenges
Select date and time for outbound & return journeys	This step is of particular difficulty as it requires the entry of a date and time for travel. Dyscalculics have a limited ability to grasp the concept of time, therefore may struggle to work out when their train journey is, and also how far away the date and time of their journey is from the current date and time.
Select number of adult & child passengers	This step may prove difficult as dyscalculia can reduce the person’s ability to count- however if the numbers are not too high and the counting begins at 1, usually this is achievable.
Tick box for railcards	no challenges
Select railcard type and number that apply for this journey	This step again involves counting, however as above, if the numbers aren't too high this shouldn't prove too difficult.
Select continue	no challenges
Tick box for outward & return journeys (details to look at: time, price, class & single/return)	In this step, the only challenge is the selection of the time of the journey. As mentioned above, dyscalculics struggle with the concept of time, therefore they may be liable to selecting a return journey that occurs before the outward journey. Fortunately, most if not all online train ticket applications will not allow the transaction to proceed if this is the case- the error will be flagged in red.
Select ‘buy now’	no challenges
Tick box to reserve seat and if so select seating preferences- optional	no challenges
Tick box to collect tickets from self-service ticket machine and select station or tick box to have tickets sent by post	Not directly an issue at the point of purchase however collecting the tickets from a self-service ticket machine can be very difficult for dyscalculics. The ticket collection reference number used in order to validate the purchase is made up of an entirely random mix of numbers and upper & lower case letters. It would be almost impossible to commit this reference number to memory or find a pattern in it, therefore it must copied out which gives rise to sequencing issues resulting in the numbers being inputted in the wrong order and therefore the whole process could take a very long time.
Select ‘continue’	no challenges
Tick box new user	no challenges
Type in personal details (Name, Address, Email, etc.)	no challenges
Tick box payment card type (Visa, MasterCard, etc.)	no challenges
Enter card details (number, expiry date, name, security code)	Although this step does involve numbers, it does not require any manipulation of numbers such as addition, subtraction, etc. therefore the act of typing the numbers from the card into the website should be achievable; however some people may struggle with sequencing and end up typing the numbers out of order.
Type in post code and tick box find billing address	no challenges
Tick box to agree to terms and conditions and select ‘buy now’	no challenges
Enter payment card secure bank password	This step is likely to prove most difficult as it requires the use of the long term memory (LTM), which may be fairly limited in dyscalculics, and also the customer is required to enter their password out of its usual order, for example you may be asked to enter the 3rd, 5th and 7th characters in your password. As dyscalculics struggle with the concept of numbers and sequences this step may only be achievable by having the password written down in front of them, however this then reduces the security of their payment method.
Order complete	no challenges

Using online banking to pay someone new

Scenario B “Emily” is a high school student who struggles to understand many of the topics covered in her maths, science and music lessons. She needs to use her online banking account to transfer some money into a friend’s bank account. She hasn’t transferred money online to this particular friend before so she must set up a new user which requires using a card reader and typing in a code which appears on the card reader only for 30 seconds before it changes to increase security.

Using online banking to pay someone new

Step	Challenges
Type in customer number and select ‘log in’	This step is challenging as the person is required to use their LTM in order to type in their customer number and dyscalculics typically have a poor LTM and difficulty with sequencing, therefore again they may need to have the password written down and this is then a breach of security.
Type in 3 random digits from pin number (e.g. 1st, 3rd & 4th) Type in 3 random characters from password (e.g. 2nd, 5th & 10th)	This requires the user to access their LTM to remember the password and then be able to count up each of the numbers/letters so as to enter the correct characters out of their normal pattern. Counting is hard for dyscalculics especially when it doesn’t begin at 1 which increases the difficulty of these 2 tasks.
Select ‘payments and transfers’ and then ‘go’	no challenges
Select ‘pay someone new’	no challenges
Enter details of payee and select ‘add payee’	This task does require numbers so it may be a challenge; however the numbers need to be copied and not manipulated which reduces the complexity.
Type in amount to transfer	Calculating numbers is particularly difficult for dyscalculics as their grasp of maths concepts and rules is typically quite poor. Therefore this task could be very challenging.
Follow on-screen instructions to verify new payee --> Turn on card reader and select function button --> Insert card into card reader --> Type in pin number to card reader --> Type in numbers on the computer screen into the card reader, select ‘ok’ on the reader --> Type the number that appears on the screen of the card reader into the box online --> Click confirm on the website	This task is likely to be the most challenging of the transaction due to the time constraints that are in place for security reasons. Firstly the user must type their pin number into the card reader which requires the use of the LTM. However this can be achieved as often dyscalculics are able to remember their pin number as a pattern. Then the user must enter the numbers on the computer screen into the card reader, this shouldn’t be too difficult as it only requires copying the numbers. The user must then enter the numbers that appear on the screen of the card reader into a text box on the website. This stage is fairly difficult as the numbers on the card reader change every 30 seconds to increase security therefore the numbers must be typed in fairly quickly. Also many dyscalculics struggle to understand the concept of time and therefore may find it difficult to work out quite how quickly they must enter the numbers before they change.
Payment complete	no challenges

Changing the payment details for an online supermarket shop

Scenario C “George” is an elderly gentleman who doesn't like to leave his house and does his supermarket shop online once a week and gets it delivered to his door. His bank details are stored on the shopping website so he doesn’t have to keep typing them in, however he has just been sent a new bank card as his old one has expired so he must re-enter all the details necessary to complete his shop.

Changing the payment details for an online supermarket shop

Step	Challenges
Select ‘food and drink’ and then ‘buy groceries’	no challenges
Log in with username and password	no challenges
Delete old payment card	no challenges
Select ‘add payment card’	no challenges
Type in the card details	This task should be easily achievable as it does not require any manipulation of the numbers; also the numbers do not need to be remembered as they are printed on the card. However dyscalculics struggle with sequencing and therefore may be liable to typing the numbers out of the correct order.
Tick box ‘make this my preferred payment card’	no challenges
Select ‘save’ and then either continue shopping or log out	no challenges

Online Shopping

Whilst dyscalculics may find it relatively simple to set up an online shopping account, it is far harder to complete the actual task of shopping. This stems from the inability to grasp the concept of money and the amount a product costs in relation to the amount of money they might have in their bank account. As a result of this dyscalculics frequently find themselves overdrawn as the task of calculating the numbers to produce a final figure which has some meaning to them as opposed to being a collection of random numbers is a concept they cannot master. This often leads to active avoidance of the task or strong reliability on others- neither of which is a sustainable solution. Quantities are also an abstract concept with dyscalculics often buying far too much or not nearly enough as it is difficult for them to work out exactly how much they need. Anything that involves weights and measures e.g. 1 kg of potatoes is also almost impossible to understand.

How they use the web and ICT to include: Email, apps, voice systems, IM

There is very little in the way of specific Assistive technologies for dyscalculia. One person reports using Smart sum - more research required.

http://www.dyscalculator.com/ is a talking calculator which is designed with dyscalculia. The Author has not tested this tool yet.

How people with dyscalculia use optimized content and special pages

Many people with dyscalculia report that they enjoy using the internet, and there are quite a lot of people with dyscalculia using social media and online video. There is little if any optimised content available for dyscalculia. The scenarios give examples of where dyscalculia impacts people using products and services on the internet.

Characteristics of content optimized for this group

Assistive Technology Devices for Students Struggling in Mathematics from the Georgia Department of Education

There is further research needed before we are in a position to add descriptions of key features and how it helps users overcome challenges. Very little work has been done on this topic.

Summary Existing research and guidelines

It is widely acknowledged that dyscalculia was first discovered in 1919 by Salomon Henschen a Swedish neurologist who found that it was possible for a person of high general intelligence to have impaired mathematical abilities. At the time it was known as ‘number blindness’. The term Dyscalculia was later coined by Dr. Josef Gerstman in the 1940s. When compared with Dyslexia and other similar learning disabilities, Dyscalculia receives relatively little recognition and there is still limited awareness of its existence.

Although there are many classifications of Dyscalculia it can be broken down into 3 sections; Developmental Dyscalculia- inherited/acquired during prenatal or early developmental period. Post-lesion Dyscalculia- acquired during an incident of traumatic brain injury affecting specific areas of the brain. Pseudo-Dyscalculia- as a result of inadequate instruction.

Formal definition The Department for Education Skills (DfES) defines dyscalculia as: “A condition that affects the ability to acquire arithmetical 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.”

Etiology

Adult neuropsychological and neuroimaging research points to the intraparietal sulcus as a key region for the representation and processing of numerical magnitude (4). This raises the possibility of a parietal dysfunction as a root cause of dyscalculia (4). The following two studies support this research.

Virtual Dyscalculia Induced by Parietal-Lobe TMS Impairs Automatic Magnitude Processing

UCL scientists state that dyscalculia is a result of a malformation in the right parietal lobe in the brain – however the underlying dysfunction is relatively unknown (c.07). The study involved using neuronavigated transcranial magnetic stimulation (TMS) to stimulate the brain and cause dyscalculia, only for a few hundred milliseconds, in non-dyscalculic individuals. The subjects then completed maths tasks whilst under stimulation and produced dyscalculic like behaviour. However when the left parietal lobe was stimulated under TMS this behaviour was not observed and therefore it can be reasonably assumed that there is a causal relationship between defects in the right parietal lobe and dyscalculia. (3)

The above research is supported by the following research study: Impaired parietal magnitude processing in developmental dyscalculia - The study was conducted by Gavin R. Price, Ian Holloway, Pekka Räsänen, Manu Vesterinen and Daniel Ansari. The study shows that in children with developmental dyscalculia the right intraparietal sulcus is not modulated in response to numerical processing demands to the same degree as in typically developing children. This suggests a causal relationship between impairment of parietal magnitude systems and developmental dyscalculia. (4)

Research by Shalev, et al. suggests that some families have a genetic predisposition to dyscalculia resulting in prevalence 10x higher than in the general population. (5) Although Dyscalculia cannot be cured, it is hoped that early detection and remedial teaching can go a long way to reducing the effects of dyscalculia on the individual.

Comorbidity

High comorbidity with ADHA (estimates range between 15-26%) and Dyslexia (estimates range between 17-64%)(6). There is strong evidence to suggest Turners Syndrome and Gerstmann’s Syndrome are associated with Dyscalculia(7).

Guidelines

Although there are no specific guidelines produced by a governing body, there are several ways to help an individual with dyscalculia in order to improve their mathematical abilities.

• Study sheets/summary sheets/outlines of most important facts

• Supplementry aids (vocabulary, multiplication cards, etc.)

• Visual demonstrations

• Instructions/directions given in different channels (written, spoken, demonstration)

• Visual or multisensory materials

• Mnemonic aids/devices

Some more useful guidelines regarding Dyscalculia, specifically for school children are available from Leeds City Council (PDF): Guidelines for Specific Learning Difficulties in Maths/Dyscalculia

Dyscalculia is still a relatively unknown disability with many of those affected by it not being diagnosed until later in life. Often, children in schools especially, those affected are thought to be stupid or lazy as many people are unaware of dyscalculia’s existence. This is analogous to the treatment of people with dyslexia.

Potentials and possibilities

To do: Add ideas for filling gaps 

Prevalence

Studies conducted by Gross-Tsur, Manor and Shalev in 1996 suggest that 6.5% of the population are dyscalculic. Conflicting research done by Lewis, Hitch and Walker in 1994 suggests that 1.3% of the population are dyscalculic while 2.3% are dyscalculic and dyslexic – putting the world population of dyscalculics at 3.6%. (8)

5-6% in school age children. (9)

This gives us the rough estimate that between 3½ - 6½% of the world population is affected by dyscalculia; however no international study has been done on how common it is.

Studies show that the presentation of dyscalculia in male and females is roughly equal; neither gender appears to have a greater predisposition than the other. (9)

References to research.

(1) Geary, D.C., (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345-362. Available from: http://psycnet.apa.org/psycinfo/1994-02259-001

(2) Butterworth, B. (1999). The Mathematical Brain. (London: Macmillan).

(3) Cohen Kadosh, R., et al. (2007). Virtual Dyscalculia Induced by Parietal-Lobe TMS Impairs Automatic Magnitude Processing. Current Biology, 17(8), 689-93. Available from: http://www.sciencedirect.com/science/article/pii/S0960982207010652

(4) Price, G.R., et al. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17(24), 1042-43 Available from: http://www.cell.com/current-biology/retrieve/pii/S0960982207020726

(5) Shalev, et al. (2001). Developmental Dyscalculia is a Familial Learning Disability. Journal of learning disabilities, 34(1), 59-65. Available from: http://ldx.sagepub.com/content/34/1/59.short

(6) Wilson, A.J. (2008). Dyscalculia primer and resource guide. Available from: http://www.oecd.org/edu/ceri/dyscalculiaprimerandresourceguide.htm

(7) Bruandet, M., et al. (2004). A cognitive characterization of dyscalculia in Turner syndrome. Neuropsychologia, 42(3) 288-98. Available from: http://www.ncbi.nlm.nih.gov/pubmed/14670569

(8) www.dyscalculiaforum.com

(9) Shalev, R.S. (2004). Journal of Child Neurology 19 765—771.

(10) Ladislav, K. (1974). Developmental Dyscalculia. Journal of Learning Disabilities. 7(3) 164-177. Available from: http://ldx.sagepub.com/content/7/3/164.short

(11) Clare Trott http://publications.lboro.ac.uk/publications/all/collated/mact2.html