DyscalculiUM: A First-Line Screener for Dyscalculia in Higher Education Clare Trott and Nigel Beacham Mathematics Education Centre, Loughborough University September 2006 Neurodiversity Conference DeMontfort University

There is currently no accepted definition of dyscalculia A number of different definitions exist Numerically based Cognitive based Neuroscience based Definition

The DSM-IV document, used by educational psychologists, defines Mathematics disorder in term of test scores: "as measured by a standardised test that is given individually, the person's mathematical ability is substantially less than would be expected from the person’s age, intelligence and education. This deficiency materially impedes academic achievement or daily living"

Two Important Features 1.Mathematical level compared to expectation 2.Impedance of academic achievement and daily living

More precise specification (Mahesh Sharma) “Dyscalculia is an inability to conceptualise numbers, number relationships (arithmetical facts) and the outcomes of numerical operations (estimating the answer to numerical problems before actually calculating).” The emphasis here being on conceptualisation rather than on the numerical operations

The National Numeracy Strategy The DfES (2001) " 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."

Currently used by the BDA Perhaps more applicable to education in the early years In H.E. emphasis is less on basic computation and more on the application and understanding of skills and techniques

Our Working Definition “Dyscalculic students have a low level of numerical or mathematical competence compared to expectation. This expectation being based on unimpaired cognitive and language abilities and occurring within the normal range. The deficit will severely impede their academic progress or daily living.

Dyscalculia is therefore an inability to effectively connect with number and mathematics. It may include difficulties recognising, reading, writing or conceptualising numbers, understanding numerical or mathematical concepts and their inter-relationships.

It follows that dyscalculics may have difficulty with numerical operations, both in terms of understanding the process of the operation and in carrying out the procedure. Further difficulties may arise in understanding the systems that rely on this fundamental understanding, such as time, money, direction and more abstract mathematical, symbolic and graphical representations.”

Statistics Geary (2004)5 - 8% Desoete et al (2004)3 - 8% Butterworth (1999)4 - 6% Kosc (1974)6.4% Gross-Tsur (1996)6.5%

Kerry Sent to MLSC by her tutor, suggesting dyscalculia Detailed interview and look at work folder Very basic difficulties with understanding simple % LHS of the formula did not co-exist with the RHS

Dyslexia screening - negative result However, fundamental problems still remained Much discussion Kerry sent to Educational Psychologist who confirmed dyscalculia (no dyslexia) Highlighted urgent need for screener

number conceptual operational number comparative conceptual inferential verbal visual-spatial graphical symbolic abstract symbolic graphs tables Spatial- Temporal Direction Time Cognitive Model for Dyscalculia

Cognitive Model Conceptual –understanding of number, place value Comparative –relative size Verbal Symbolic Visual-Spatial

Operational Conceptual –conception of correct operation to achieve required outcome reverse a process Inferential –given an operational definition make comparative inferences about an outcome, without realising the outcome Infer an operational relationship

Abstract Symbolic Spatial-Temporal –Understanding Visual-Spatial diagrams Time Graphical –Reading and Interpreting Graphs Tables

Phase One Developing the Dyscalculia Screening Test

Development of the screener

Available in both paper and electronic versions Electronic version produced on CD-ROM Electronic version developed in Perception

Electronic version

Phase Two Initial Trials

19 students Dyscalculic only, dyslexic only, no SpLD Showed no difference between paper and electronic versions

Further Analysis Sensitivity –The probability that a dyscalculic student performed below the acceptable threshold –How good is the screener at correctly including individuals who are dyscalculic Specificity –The probability that a non-dyscalculic student performed above the acceptable threshold –How good is the screener at correctly excluding individuals who are non-dyscalculic

Dyscalculic v control Percent Sensitivity83.3% Specificity92.3% Percent Sensitivity83.3% Specificity85.7% Dyslexic v Non-dyslexic Dyscalculic v Dyslexic Percent Sensitivity50.0% Specificity87.5%

Background colour Removed timer Scrolling and layout Submit button Modifications

Phase Three Further Trials

Phase Three Trials Involved 30 participants Organised into three equal groups –Dyscalculic –Dyslexic –Control Covered a range of academic subjects Observation carried out Covering 4 HEIs

Dyscalculics v Control Threshold = 87% (changed from 89%) Current trialInitial trial sensitivity100%83.3% specificity100%92.3%

Dyscalculics v Control graph participant percent O dyscalculic O control

Dyscalculics v Dyslexics Current trial Initial trial Sensitivity100%83.3% Specificity70%85.7%

Dyslexics v Control Current trialInitial trial Sensitivity30%50% Specificity100%87.5%

Percentage Scores for 3 Groups percent O dyscalculic O dyslexic O control

Examples from DyscalculiUM Decimals Direction Bar graph Interval bisection Towards abstraction

Decimals Compare 3.59 with % correct

Decimals Compare 0.71 with 0.17 % correct

“It makes for interesting travel as I've missed countless trains and buses or got on the wrong train on the wrong platform at the wrong time. Travel directions have to be written in minute detail as I have no understanding of the motorway network and anything more than 'take the next left' goes in one ear and out the other. I can get lost in a box." J. Blackburn “Damn the Three Times Table” Direction

Direction Following a set of directions involving left and right turns. % correct

Direction

Direction Using clockwise and anti-clockwise % correct

Bar Graph

Reading off the vertical axis on a bar chart. % correct

Between which years the “smallest increase” occurred % correct

Interval Bisection Which number is half way between 2.8 and 3.2? % correct

Towards Abstraction

% correct

Subtest Takes ≤ 48 minutes Use for screening process with other tools Eliminate items with poor discrimination Eliminate items that impede students with dyslexia Subtest consists of 61 items and takes approx mins

Graph: percentage scores on the subtest percent O dyscalculic O dyslexic O control

Phase Four More Trials

Phase 4 Trials 137 students 4 HE institutions 3 FE colleges Large groups/small groups/individuals

Trials: Screening 16 out of 137 identified “at risk” –8% prevalence Geary (2004) 5 - 8% Desoete et al (2004) 3 - 8% Butterworth (1999) 4 - 6% Not post-16

Further Issues English not first language –2 out of 5 “at risk” –Mathematical or language difficulties? Neurodiversity –Dyslexia, Asperger’s Syndrome, ADHD, Dyspraxia More research needed

Summary Provides an effective screening tool for HE Discriminates dyscalculia from dyslexia Easily accommodated into screening process Large or small groups or individuals Future Extensive trials in Autumn 2006 Profile reporting, based on cognitive model

Profiler Conceptual Operational Conceptual Graphical Tabular Symbolic Abstraction Comparative Visual-Spatial Spatial Directional Total Score Comparative Symbolic Comparative Verbal Operational Relational Spatial Temporal Time Taken: 25 Minutes Threshold

References Beacham, N. and Trott, C. (2006) Project Update, Widening the use of DyscalculiUM: A first-line screening test for dyscalculia in Higher Education, MSOR Connections, Vol 6 No 1. Beacham, N. and Trott, C. (2005) Screening for Dyscalculia within Higher Education, MSOR Connections Vol 5 No 1. Butterworth, B. (1999) The Mathematical Brain. London: Macmillan. Desoete, A., Roeyers, H. & De Clercq, A. (2004) Children with Mathematics Learning Disabilities in Belgium, Journal of Learning Disabilities, 37, DfES (2001) The National Numeracy Strategy, Guidance to support pupils with dyslexia and dyscalculia DfES 0512/2001 Geary, D.C. (2004) Mathematics and Learning Disabilities. Journal of Learning Disabilities, 37, 4-15 Gross-Tsur, V., Manor,O. and Shalev R.S. (1996) Developmental Dyscalculia: prevalence and demographic features. Developmental Medicine and Child Neurology. 38, Kosc, L. (1974) Developmental Dyscalculia. Journal of Learning Disabilities, 7, Sharma, M. (1997) Dyscalculia.