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**Mathematics Difficulties in Higher Education: The Strathclyde University Dyscalculia Project**

Jim Boyle, C Spickett, I Tulloch, J Wilson, M Mattey & D Finn University of Strathclyde

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**Difficulties in Mathematics**

Concern about standards of attainment in mathematics Reason for apparent fall in standards is unclear Class size; calculators; lack of ‘drill and practice’; class organisation; teaching methods; individual maths schemes Anxiety about mathematics, lack of experience and poor motivation Sub-set of those experiencing difficulties in mathematics will have problems resulting from dyscalculia… Concern about standards of attainment in mathematics (Assessment of Achievement Programme, SEED, 2000; Smith Report, 2004) Reason for apparent fall in standards is unclear Class size; calculators; lack of drill and practice; class organisation; teaching methods; individual maths schemes (Logan & Starritt, 1999) Anxiety about mathematics, lack of experience and poor motivation (Ashcraft & Faust, 1994; Levine, 1987) Sub-set of those experiencing difficulties in mathematics will have problems resulting from dyscalculia…

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**Dyscalculia or ‘Mathematics Disorder’**

“A. Mathematical ability, as measured by individually administered standardized tests, is substantially below that expected given the person’s chronological age, measured intelligence, and age-appropriate education. B. The disturbance in Criterion A significantly interferes with academic achievement or activities of daily living that require mathematical ability. C. If a sensory deficit is present, the difficulties in mathematical ability are in excess of those usually associated with it.” (DSM-IV, APA, 1994) Developmental… and Acquired Geriatric patients Stroke patients Traumatic Brain Injury Dyscalculia or ‘Mathematics Disorder’ (DSM-IV) (APA, 1994) “A. Mathematical ability, as measured by individually administered standardized tests, is substantially below that expected given the person’s chronological age, measured intelligence, and age-appropriate education. B. The disturbance in Criterion A significantly interferes with academic achievement or activities of daily living that require mathematical ability. C. If a sensory deficit is present, the difficulties in mathematical ability are in excess of those usually associated with it.”

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**Common Presenting Problems**

Counting – reciting the number words in the correct order and being able to count a number of objects Reading and writing numerals – being able to understand that a number is a symbol that represents a value Number seriation – placing numbers in order of size Number facts – being able to understand that 2+2=4 or 7x10 =70 Numerical procedures – counting on to add, borrowing and carrying to subtract Principles, concepts and laws of arithmetic – understanding that addition is cumulative and subtraction is not Telling the time and judging elapsed time Calculating prices and handling change Measuring (e.g. temperature or speed) Problems with ratios, fractions, decimals, place value, changing units

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**Underlying Causes of Dyscalculia**

Genetic Neurological Cognitive Genetic: familial prevalence some 10 times higher than would be expected for the general population (Shavlev et al, 2001), with at least one other family member and 50% of first-degree members also having the problems Neurological: neuro-imaging studies reveal that procedural deficits and a form of retrieval deficit appear to be associated with functioning of the prefrontal cortex, while a second form of retrieval deficit appears to be associated with the functioning of the left parieto-occipito-temporal areas & several subcortical structures (Geary & Hoard, 2001) Cognitive: visuospatial deficits (Rourke and Strang, 1978); problems with the reading and writing of numbers (Kosc, 1974); difficulties retrieving arithmetic facts from long-term memory (Jackson and Warrington, 1986); visual-motor integration (White, Moffitt and Silva, 1992); deficits in short-term working memory (Geary, 1993; McLean & Hitch, 1999)

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**Prevalence of Dyscalculia**

Large-scale surveys of school-children suggest a prevalence of around 6-7% with no gender differences (c.f. dyslexia) Half of those with dyscalculia have problems with number only and the rest have comorbid problems with reading Prevalence of dyscalculia in adults and in students in higher education is unknown Strathclyde University Survey: lower bound prevalence rate of self-reported mathematical difficulties in 1st and 2nd Year Bioscience students of around 10% (42/400, with response rate of 21%) Large-scale surveys suggest a prevalence of around 6-7% (Badian, 1983, 1999;Gross-Tsur et al., 1996; Kosc, 1974; Russell & Ginsburg, 1984;Weinstein, 1980), with no gender differences However, stringency of cutoffs used will determine prevalence: (e.g. Lewis et al. (1984), who report prevalence of 3.6%in 9-10 year-old students in UK) Around half of those with dyscalculia have problems with number only and the rest have comorbid problems with reading (Ackerman & Dykman, 1995; Geary & Hoard, 2001; Jordan et al., 2003) But how distinctive from ‘garden variety’ problems with number (Gonzalez & Espinel, 2002)…

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**Recognition of the Need for Support**

Increasing awareness and concern at low levels of mathematical competence for students entering HE programmes in science and engineering Emerging awareness of the presence of dyscalculic students in HE, though little understanding of the obstacles faced Disabled Students’ Allowance is available to dyscalculic students with study support needs But we need to identify the most effective support methods…

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Compensatory Support Compensatory support is typically provided in acknowledgement of a permanent area of difficulty, not susceptible to improvement through remedial programmes For dyscalculic students, it can include: extra time in examinations use of a calculator access to notes/memory aids alternative formats for questions and answers Use of a calculator can assist with computational inaccuracies, but still requires considerable mathematical and conceptual understanding

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**Compensatory Support (cont.)**

Not all types of compensatory support are regarded as academically valid, depending on core learning and assessment criteria Software to support specific academic/professional calculations could allow dyscalculic students to succeed in key tasks, but may be controversial Learning support staff can negotiate accommodations for a disabled student, but this requires clarity on core learning/assessment criteria Dyscalculic students are eligible to apply for disabled students allowance (DSA) to support purchase of assistive software and associated hardware

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What’s Missing? To develop effective support systems for dyscalculic students in HE we need: Accessible software to support students in numeric tasks More understanding of the obstacles/solutions for dyscalculic students in HE, so we can develop guidance for HEIs Better understanding of accessibility issues for dyscalculic students (and dyscalculic/dyslexic students) Development of best practice teaching and assessment materials/methodologies

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**Strathclyde University Dyscalculia Project**

‘AB’: 2nd year university student with difficulties in coping with the mathematics content of Biosciences courses Long-standing history of problems in number at school which necessitated tutorial support Assessment confirmed marked problems in both mathematical reasoning and numerical operations and roblems also in working memory Advice sought from Computer Science Department… Multidisciplinary project involving Computer Science, Bioscience & Psychology Departments and Special Needs Service 2nd year university student referred for assessment due to difficulties in coping with the mathematics content of her Biosciences courses Long-standing history of problems in number at school and received tutorial support Assessment using the Wechsler Objective Number Dimensions (WOND) confirmed marked problems in both mathematical reasoning (Age Equivalent Score 10y 6m) and numerical operations (Age Equivalent Score 11y 9m) Digit Span (Backwards) sub-test of the WAIS-RUK was also below the level that might be expected from an undergraduate (SS 8)

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**Primary Aim of the Project**

To develop an IT-based intervention, XCalc, to support students experiencing problems with mathematics, including those with dyscalculia

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Development of XCalc Aug 2002 The first version of XCalc was written and installed on an HP Jornada Oct 2002 Application to the university’s Research & Development Fund for support to enhance XCalc Dec 2002 Funding obtained and XCalc was adapted to run on PCs and palm systems Feb-Apr 03 Surveys of 1st and 2nd year Bioscience students carried out to investigate incidence of mathematical difficulties

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**Mathematical Demands: Sample Bioscience Exam Question**

0.1 ml 1 ml 1 ml 1 ml 1 ml 9.9 ml 9.0 ml 9.0 ml 9.0 ml 9.0 ml E coli culture 1 2 3 4 5 If the original E.coli culture contains 5.4 x 109 cfus ml-1 calculate the number of cfus ml-1 in bottle 5 after the serial dilution of the original culture, which was performed as described in the diagram above If bottle 5 is found to contain 1.9 x 104 cfus ml-1, what is the number of cfus ml-1 in the original culture

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XCalc Software Calc-Converter (subsequently Bcalc/XCalc) for HP Jornada Microsoft embedded Visual C++ MFC AppWizard to create dialog-based project 7 separate functions are called from main dialog box

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**Future Direction of Research**

To improve the user-interface of our pilot software support system and assess its value to students with MD To investigate alternative representations of mathematical operations to identify those that MD students find most appropriate; To develop a family of support systems appropriate to different disciplines To identify features and requirements for a help and tutoring system that will accompany the support software

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