Dyscalculia in Higher Education

DYSCALCULIA IN HIGHER EDUCATION By Simon Drew A Doctoral Thesis Submitted for the award of Doctor of Philosophy at Loughborough University September 2015 © Simon Drew 2015 Sisyphus by Lacie Cummings Abstract This research study provides an insight into the experiences of dyscalculic students in higher education (HE). It explores the nature of dyscalculia from the student perspective, adopting a theoretical framework of the social model of disability combined with socio-cultural theory. This study was not aimed at understanding the neurological reasons for dyscalculia, but focussed on the social effects of being dyscalculic and how society can help support dyscalculic students within an HE context. The study’s primary data collection method was 14 semi-structured interviews with officially identified dyscalculic students who were currently, or had been recently, studying in higher education in the UK. A participant selection method was utilised using a network of national learning support practitioners due to the limited number of participants available. A secondary data collection method involved reflective learning support sessions with two students. Data were collected across four research areas: the identification process, HE mathematics, learning support and categorisations of dyscalculia. A fifth area of fitness to practise could not be examined in any depth due to the lack of relevant participants, but the emerging data clearly pinpointed this as a significant area of political importance and identified a need for further research. A framework of five categories of dyscalculic HE student was used for data analysis. Participants who aligned with these categories tended to describe differing experiences or coping behaviours within each of the research areas. The main findings of the study were the importance of learning support practitioners in tackling mathematical anxiety, the categorisations of dyscalculic higher education students, the differing learning styles of dyscalculic and dyslexic students, and the emergence of four under-researched dyscalculic characteristics: iconicity, time perception, comprehension of the existence of numbers that are not whole and dyscalculic students understanding of non-cardinal numbers. Acknowledgements I am immensely grateful to my supervisors, Clare Trott and Professor Barbara Jaworski, for their tireless and unending advice, time and expertise throughout my PhD. Without their guidance and constructive criticism I would not have made it through to the end. 3 I would also like to thank everyone within the Mathematics Education Centre for giving me the opportunity to undertake this PhD, and everyone who works there for their invaluable encouragement and assistance throughout this process. I would also like to thank my family and friends, especially Suzie and Joey for their incredible emotional and practical support throughout my journey, and coping with my many periods of PhD blues. I dedicate this thesis to them. 4 Contents List of chapters 1 Introduction ............................................................................................ 16 2 Theory ..................................................................................................... 22 3 Dyscalculia .............................................................................................. 34 4 Neurodiversity ......................................................................................... 57 5 Higher education ..................................................................................... 80 6 Methodology ............................................................................................ 98 7 Implementation ..................................................................................... 109 8 Experiences leading to identification of dyscalculia ............................... 128 9 Experiences of mathematics in higher education ................................... 160 10 Experiences of learning and support in higher education ...................... 219 11 Categorisation of dyscalculic students in higher education ................... 245 12 Fitness to practise ................................................................................. 269 13 Conclusion ............................................................................................. 278 14 Related work ......................................................................................... 285 15 References ............................................................................................ 287 List of chapters and sections 1 Introduction ............................................................................................ 16 1.1 Preface............................................................................................... 16 1.2 Background ........................................................................................ 17 1.3 Research questions ............................................................................ 18 1.4 Outline of thesis ................................................................................. 18 1.5 Glossary of terms ............................................................................... 20 2 Theory ..................................................................................................... 22 2.1 Introduction ....................................................................................... 22 2.2 Epistemology ..................................................................................... 22 2.3 Theoretical perspective ...................................................................... 23 2.3.1 Vygotsky and socio-cultural theory ..................................................... 25 2.3.2 Social model of disability .................................................................. 28 2.3.3 Pollak and dyslexic identity ............................................................... 30 2.3.4 Conceptual and procedural mathematical learning styles ....................... 32 2.3.5 Stroop effect ................................................................................... 33 2.4 Summary ........................................................................................... 33 3 Dyscalculia .............................................................................................. 34 3.1 Introduction ....................................................................................... 34 5 Contents 3.2 History of dyscalculia ......................................................................... 34 3.3 Definitions of dyscalculia ................................................................... 37 3.3.1 Inclusion criteria .............................................................................. 38 3.3.1.1 Mathematical ability ................................................................ 38 3.3.1.2 Numerosity and quantification skills .......................................... 38 3.3.1.3 Age appropriateness ............................................................... 39 3.3.1.4 Intelligence disparity ............................................................... 39 3.3.1.5 Recollection of number facts .................................................... 40 3.3.1.6 Educational and everyday issues............................................... 40 3.3.1.7 Persistence ............................................................................ 41 3.3.2 Exclusion criteria ............................................................................. 41 3.3.2.1 Educational opportunity ........................................................... 41 3.3.2.2 Appropriate motivation ............................................................ 42 3.3.2.3 Absence of unrelated impairments ............................................ 42 3.3.2.4 Alternative neurodiversities ...................................................... 42 3.3.2.5 Emotional well-being ............................................................... 43 3.4 Prevalence of dyscalculia ................................................................... 43 3.5 Characteristics of dyscalculia ............................................................. 45 3.6 Dyscalculia and time .......................................................................... 48 3.7 Definition of mathematics .................................................................. 49 3.8 Cognitive theories on dyscalculia ....................................................... 51 3.8.1 Numerical core deficit model ............................................................. 52 3.8.2 Numerical domain-specific deficit model ............................................. 52 3.8.3 Domain-general deficit model ............................................................ 54 3.9 Summary ........................................................................................... 56 4 Neurodiversity ......................................................................................... 57 4.1 Introduction ....................................................................................... 57 4.2 Memory .............................................................................................. 59 4.2.1 Sensory register .............................................................................. 60 4.2.2 Working memory ............................................................................. 60 4.2.2.1 Central executive ...................................................................

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