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

1. Students in higher education with mathematical difficulties:The scope & nature of the problems & implications for support J Boyle, M Dunlop, D Finn, M Mattey, C Spickett, I Tulloch & J Wilson University of Strathclyde, Glasgow

3. 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…

4. Dyscalculia or ‘Mathematics Disorder’ • 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. • Developmental… and Acquired • Underlying causes Genetic Neurological Cognitive

5. Dyscalculia: Common 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 – • 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

6. Prevalence of Dyscalculia • Large-scale surveys of school-children suggest a prevalence of around 6-7% with no gender differences • 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%)

7. 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…

8. 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

9. 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

10. What’s missing? • To develop effective support systems for dyscalculic students in HE we need: • 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 • Accessible software to support students in numeric tasks

11. Strathclyde University Dyscalculia Project • Second year 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 • To develop an IT-based intervention, BCalc, to support students experiencing problems with mathematics, including those with dyscalculia • Multidisciplinary project involving Computer Science, Bioscience & Psychology Departments and Special Needs Service

12. 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 2 3 1 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

13. BCalc software • Designed for HP Jornada • Microsoft eMbedded Visual C++ • 7 separate functions are called from main dialog box • 8 person-weeks of development effort (CS graduate)

14. BCalc on the Jornada

15. HP Jornada screen

16. Evaluation • The need for training • Confident with paper conversion tables • More ‘step by step’ help • Scientific notation vs powers of ten: 5.000e-002 vs 5 x 10 • Rounding errors difficult to detect and control -2

17. Future direction of research • Extend the evaluation of software that we have already developed for use by MD students. • Extend our current study to other subjects and organisations • Identify particular areas of need that can be used as a basis for developing systems to help with particular problems. • To improve the user-interface of our pilot software support system and assess its value to students with MD; • To investigate the feasibility of scalable software solution.

18. Pocket PC and PalmOS versions

19. Future direction of research • Extend the evaluation of software that we have already developed for use by MD students. • Extend our current study to other subjects and organisations • Identify particular areas of need that can be used as a basis for developing systems to help with particular problems. • To improve the user-interface of our pilot software support system and assess its value to students with MD; • To investigate the feasibility of scalable software solution.

20. Towards a scalable solution <LABEL> <NAME>Vol 2</NAME> <TEXT>Vol 2:</TEXT> </LABEL> <LABEL> <NAME>Vol2</NAME> <TEXT>??</TEXT> </LABEL> <BUTTON> <NAME>CalcVol2</NAME> <ACTION> <TYPE>divide</TYPE> <TRIGGER>CalcVol2</TRIGGER> <MEMBERS>Numerator, Conc2</MEMBERS> <TARGET>Vol2</TARGET> </ACTION> </BUTTON>

21. Conclusion: two conflicting viewpoints Some students have fundamental difficulties that prevent them from ever developing mathematical ability necessary for a science course. Providing a prosthetic to enable to them overcome these difficulties is the equivalent of destroying the integrity of the course for these individual students. This is far more than a 'reasonable adjustment'. A student might be capable of understanding theoretical concepts without being able to carry out consistently and accurately the mathematical processes that underlie these concepts. If we can provide the maths element with an effective aid and this aid can continue to be used once the student enters employment then a prosthetic is a reasonable adjustment to make.