Supporting Bioscience Students with Mathematical Difficulties in Higher Education: DDIG Conference Loughborough University 13 April, 2005 C Spickett, J Boyle & J Wilson University of Strathclyde

Difficulties in Mathematics  Concern about Standards (e.g. Smith, 2004)  Dyscalculia or ‘Mathematics Disorder’ (DSM-IV) “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 versus Acquired…  Genetic  Neurological  Cognitive

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 1 st and 2 nd Year Bioscience students of around 10% (42/400, with response rate of 21%)

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…

Compensatory Support in HEI  Practical support includes: extra time in examinations use of a calculator access to notes/formulae and 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  ‘Reasonable adjustments’: how should these be determined…

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 Better understanding of accessibility issues for dyscalculic students (and dyscalculic/dyslexic students) Development of best practice teaching and assessment materials/methodologies A better understanding of the scale and nature of the problem Accessible software to support students in numeric tasks

Strathclyde University Dyscalculia Project  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 problems also in working memory  Advice sought from Computer Science Department…  Multidisciplinary project involving Computer Science, Bioscience & Psychology Departments and Special Needs Service

Primary Aims A. To explore the prevalence and nature of mathematical difficulties experienced by Bioscience students B. To develop an IT-based intervention, BCalc, to support Bioscience students experiencing problems with mathematics, including those with dyscalculia

A. Survey of Mathematical Difficulties  Questionnaire devised by course tutor to identify nature of mathematical difficulties in Bioscience students in Strathclyde University  Items reflected mathematics requirements of calculations test in Practical Bioscience credit (BB206) in 2 nd Year  All of these require fairly simple mathematical tasks, such as fractions, powers, manipulating equations, and logarithms  Nevertheless, a significant number of students struggle with these calculations, and fail the credit because of it  Questionnaire distributed to st and 2 nd year Bioscience students in lecture theatres

(a)If the original E.coli culture contains 5.4 x 10 9 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 (b)If bottle 5 is found to contain 1.9 x 10 4 cfus ml -1, what is the number of cfus ml -1 in the original culture E coli culture 0.1 ml 9.9 ml9.0 ml 1 ml Sample Bioscience Exam Question

Format of Questionnaire  Problems (Y/N) with credits involving numerical calculations, mathematical functions [in 8 areas]  Rate confidence [1 to 5] in Algebraic functions Manipulating equations Logs Powers of 10 Decimal places Fractions Mental arithmetic Moles & Molarity Conversions between units Drawing graphs Dilutions

Findings from the Strathclyde Survey - 1  86 respondents (response rate 21%) 60 1 st Year, 24 2 nd Year and 2 did not disclose year 66 F, 17 M & 3 gender undisclosed Mean Age years (SD 1.94) (range years)  42 reported mathematical difficulties 32 F, 9 M & 1 gender undisclosed 29 1 st year, 12 2 nd year & 1 year undisclosed Mean Age years (SD 2.30) (range years) Average no. of difficulties reported: 2.57 (range 0-8), SD=1.80 Lower-bound prevalence rate of mathematical difficulties of at least 10% amongst 1 st and 2 nd year Bioscience students

Findings from the Strathclyde Survey - 2  Students who reported difficulties in maths were significantly less confident than those who did not report problems in the following areas: Algebra (X 2 = 6.28, p< 0.05) Logarithms (X 2 = 6.62, p < 0.01)  76% of those reporting difficulties were female: links with mathematics anxiety? (Ashcraft, Kirk & Hopkins, 1998; Woodard, 2004)  Backward logistic regression for N=81 with no missing data revealed that difficulties with algebraic functions significantly discriminated 75% of those reporting problems and 68% of those reporting no mathematical difficulties  Odds are around 4:1 that a student reporting maths problems will have problems with algebraic functions

Coventry & Liverpool Hope Universities…  Strathclyde Questionnaire administered to Bioscience Students at Coventry (N=59 returned: 58 1 st Year & 1 2 nd Year) and Liverpool Hope Universities (N=39 returned: 20 1 st Year & 19 3 rd Year)

Strathclyde + Coventry & Liverpool Hope - 1

Strathclyde, Coventry & Liverpool Hope - 2

Strathclyde, Coventry & Liverpool Hope -3  Combined dataset (N=170, with no missing data): 67% of those reporting difficulties were female Backward logistic regression revealed that lack of confidence with algebraic functions significantly discriminated 77% of those reporting problems and 58% of those reporting no mathematical difficulties Odds are 4.5:1 that a student reporting maths problems will have problems with algebraic functions  Coventry & L’Hope dataset (N=89, with no missing data): Moles & Molarity only significant predictor (p <0.05)  Differences between institutions…

B. Development of BCalc Aug 2002The first version of BCalc was written and installed on an HP Jornada Oct 2002Application to the university’s Research & Development Fund for support to enhance BCalc Dec 2002Funding obtained and BCalc was adapted to run on PCs and Palm OS systems

BCalc Demonstration

BCalc Demonstration (cont.)

Evaluation  Scientific notation in ‘unusual’ format eg 5 x vs 5.000e-002  Add / remove some details  Confident with paper conversion tables  More ‘step by step’ help  Need for early identification and training

Future Directions for Research  To improve the user-interface of our pilot software support system and further assess its value to students with MD/Dyscalculia  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