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      ­­­­­What is dyscalculia?

The Diagnostic and Statistical Manuel of Mental Disorders [DSM-5] (American Psychiatric Association [APA] 2013) is used across the world to provide core standards for diagnosis. Their diagnostic criteria for mathematical impairment in specific learning disorder are problems with ‘number sense, memorisation of arithmetic facts, accurate or fluent calculation and accurate math reasoning’ (APA 2013, p. 67). DSM-5 states that if the term ‘dyscalculia’ is to be used then this implies that the diagnosis refers to a ‘pattern of difficulties characterised by problems with processing numerical information, learning arithmetic facts, and performing accurate or fluent calculation’ (APA 2013, p. 67).

Butterworth (2003, p.1) explains that even at a basic level mathematics involves complex abilities, such as: 

Understanding number words […] numerals and the relations between them; being able to carry out mental arithmetic using the four basic arithmetical operations – addition, subtraction, multiplication and division; being able to carry out written multi-digit arithmetic using the four basic operations; being able to solve ‘missing operand problems’ (?+4=6); being able to solve ‘word problems’ which set arithmetical problems in realistic contexts, particularly using money and change.

The Department for Education and Skills (2001, p.2) offer the following definition for dyscalculia:

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.

The Diagnosis of Dyscalculia

In England the diagnosis of dyscalculia is guided by SpLD Working Group 2005/DfES Guidelines. These guidelines were revised in September 2011 which also guides the diagnostic procedure for dyscalculia. The revised guidelines state that ‘initial screening is a useful indicator, although currently, few tests exist for the post 16 population’ (SpLD Test Evaluation Committee [STEC] 2011, p. 5). STEC advise the diagnosis of dyscalculia should be made by a suitably qualified professional, such as an educational psychologist. An assessment of dyscalculia must include: 

1. An initial screening test for dyscalculia.

2. A full assessment of verbal and non-verbal cognitive abilities (including matrices); comparing non-verbal reasoning with age expectation/verbal reasoning and a standardised test of mathematical ability.

3. A standardised test of mathematical ability compared with age expectation, intelligence, and verbal reasoning.

4. A full personal history exploration, particularly with regard to mathematics. This should include mathematical experiences through school and how the student manages with everyday situations in which number/mathematics are used.

5. Observation of test behaviour for indications of mathematical anxiety, tension and/or lack of confidence in tackling mathematical calculations and problems. 

To summarise, there is a consensus that dyscalculia involves difficulties with:  

• Number sense (an intuitive feel for numbers).
• Memorisation and recall of facts that relate to arithmetic.
• Calculation.
• Mathematical reasoning: figuring out number related information.
• Processing numerical information.
• Understanding number in written and numerical form.
• Basic mental arithmetic: addition, subtraction, division and multiplication.
• Basic arithmetic with use of a pen and paper: addition, subtraction, division and multiplication.
• Solving real world problems presented in written form.
• Handling money and change.
• A lack of fluency (speed) when processing number.
• Number difficulties affect academic attainment and everyday life.

Dyscalc

Dyscalc is free to use for personal and commercial use. It is provided by Wadeson Street Dyslexia Centre, the directors of Educational Psychologist Ltd, and a business angel making a social investment. 

Dyscalc is a screening instrument. As with any screen it is not diagnostic and a low score does not provide a diagnosis of dyscalculia.­­­ 

Dyscalc samples

Number sense (an intuitive feel for numbers).
Memorisation and recall of facts that relate to arithmetic.
Calculation.

Mathematical reasoning: figuring out number related information.
Processing numerical information.
Understanding number in written and numerical form.

Basic mental arithmetic, add, subtract, divide and multiply.
Basic arithmetic, add, subtract, divide and multiply using pencil and paper.
Solving real world problems presented in written form.

Money and change.

Mathematical skills/abilities assessed on screen

Q1: Basic mental arithmetic: multiplication; application of number fact; calculation; number sense.

Q2: Memorisation and recall of facts that relate to arithmetic.

Q3: Memorisation and recall of facts that relate to arithmetic; mathematical reasoning: figuring out number related information.
Q4: Use of basic number fact and number sense.

Q5: Understanding number in written and numerical form; solving real world problems presented in written form; mathematical reasoning: figuring out number related information; basic arithmetic with use of a pen and paper.

world number related information.

Q6: Solving real world problems presented in written form.

Q7: Calculation and processing numerically related information and number sense; calculation; mathematical reasoning: figuring out number related information; basic mental arithmetic: addition and multiplication.

Q8: Basic arithmetic with use of a pen and paper: subtraction; Solving real world problems presented in written form; handling money and change; calculation; mathematical reasoning: figuring out number related information.

Q9: Number difficulties affect everyday life; number sense; real world number related skills; managing money.

Q10: Mathematical reasoning: figuring out number related information; memorisation and recall of facts that relate to arithmetic.

Q11: Recall of real world number related information.

Q12: Basic arithmetic with use of a pen and paper: addition and/or multiplication; calculation; mathematical reasoning: figuring out number related information.

Q13: Recall of real world number related information and number sense.

Q14: Processing numerical information; understanding number in written and numerical form; mathematical reasoning: figuring out number related information; solving real world problems presented in written form. 

Q15: Real world knowledge and recall of numerically related information; memorisation and recall of facts that relate to arithmetic.

Q16: Real world knowledge and recall of numerically related information; memorisation and recall of facts that relate to arithmetic.

Q17: Memorisation and recall of facts that relate to arithmetic.

Q18: Memorisation and recall of facts that relate to arithmetic.

Q19: Memorisation and recall of facts that relate to arithmetic; basic arithmetic with use of a pen and paper: multiplication.

Q20: Basic arithmetic with use of a pen and paper: division; memorisation and recall of facts that relate to arithmetic; processing numerical information; calculation; mathematical reasoning: figuring out number related information.

Fluency is estimated by the time taken relative to the control sample. 

 

 

 

Dyscalc design

Dyscalc began as a bank of questions generated during a brain storm by a group of skilled and experienced practising educational psychologists. The bank of questions was written into software and released via social networks. We asked that people only take this test if they were over 14 years old, of average academic ability, as gauged by GCSE grades C and above, NVQ Level 2 qualification or above, graduated from high school, middle groups at school etc., and felt their basic number skills were in line with the rest of their abilities.

The software engineer had programmed a facility to send a short message to us once each test was complete. This was made clear in the opening screen. Once the data was gleaned the message was deleted. The message informed which questions had not been answered correctly and the time taken to complete Dyscalc.

Our analysis identified and removed some of the questions, and set a scoring level that the majority of people should be able to meet or exceed (that are over 14 years of age and of average academic ability). Correspondingly, a time limit was established to help give an estimate of fluency.  We were then able test Dyscalc on students known to have been diagnosed with dyscalculia and compare the results against the control group.

Results

 

Levene’s tests showed that there were unequal variances between the dyscalculia group and control group when comparing test scores, F(1, 302) = 126.23, p < .001, and when comparing test times, F(1, 302) = 26.30, p < .001. As such, unequal variances were controlled for in the subsequent t-tests.

 

The dyscalculia group (M = 62.13%, SD = 18.53) achieved significantly lower scores on the test than the control group (M = 93.31%, SD = 6.13), t(200.12) = 20.19, p < .001 (one-tailed).

 

The dyscalculia group (M = 421.53 secs, SD = 388.75) took significantly longer to complete the test than the control group (M = 269.14 secs, SD = 136.95), t(205.12) = 4.67, p < .001 (one-tailed).

 

These results indicate that Dyscalc is a useful screening tool for students with dyscalculia.

 

Citation:

 

Francis, T., Smith, G., Wareham, J. and Wood, H.  (2013)  Dyscalc http://www.educational-psychologist.co.uk/screening/dyscalculic/.

 

 

 

 

 

References

American Psychiatric Association [APA] (2013) Diagnostic and Statistical Manuel of Mental Disorders (DSM-5), 5^th ed. Arlington: American Psychiatric Association.

Butterworth, B. (2003) Dyscalculia Screener. London: nferNelson Publishing Company.

DfES (2001) Guidance to Support Pupils with Dyslexia and Dyscalculia (DfES 05/12/2001). London: Department for Education and Skills.

SpLD Working Group/DfES (2005) Assessment of Dyslexia, Dyspraxia, Dyscalculia and Attention Deficit Disorder (ADD) in Higher Education.

SpLD Test Evaluation Committee [STEC] (2011) Suitable Tests for the Assessment of Specific Learning Difficulties in Higher Education.