Dr Patrick William Barmby
Personal Information
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3 Montego Lodge, Victoria Avenue, Little Falls, Roodeport
011 7173468
011 4751905
072 061 0822
patrick.barmby@wits.ac.za
5th March 1968
British
Education
Sep. 2004 – Jan. 2006
Postgraduate Certificate (PGCert) in Higher
Education Teaching, Durham University.
Oct. 1998 – July 1999
Postgraduate Certificate of Education (with
QTS) in Secondary Science Teaching,
University of Sunderland.
Oct. 1991 – Sept. 1994
PhD in Theoretical Semiconductor Physics,
University of Nottingham.
Oct. 1987 – July 1990
First Class BSc (Hons.) in Physics, University of
Nottingham.
Relevant Previous Employment
Lecturer in Primary Mathematics
Sept. 2004 – July 2014
School of Education, Durham University:
Research Associate
Sept. 2001 – August 2004
Centre for Evaluation and Monitoring (CEM),
Durham University
Teacher with Voluntary
Service Overseas (VSO)
Sept. 1999 – Sept. 2001
Kawethei Secondary School, Machakos District,
Kenya
Current Role
Senior Lecturer in Mathematics Education
Sept. 2014 - Present
Wits School of Education, University of the
Witwatersrand
Research background
A particular focus of my research is in mathematics education, and I publish in academic journals
such as Educational Studies in Mathematics, and professional publications such as Mathematics
Teaching. In addition to journal publications, I was also lead author on a text book for experienced
and student teachers Primary Mathematics: Teaching for Understanding, published by Open
University Press (OUP), and on another text book publication Understanding and Enriching
Problem Solving in Primary Mathematics for Critical Publishing. With colleagues, I have also
contributed chapters for text books by Ian Thompson, namely Issues in teaching numeracy in
primary schools and Teaching and Learning Early Number, also published by OUP. I am a
member of the British Society for Research into Learning Mathematics (BSRLM) and I regularly
present at the organisation’s conferences throughout the UK. I am also a member of a group of
researchers convened by Tim Rowland from Cambridge University, specifically looking at
primary mathematics and meeting each term to discuss our work and other issues concerning
primary mathematics. I have also presented my research at international maths education
conferences such as the conferences of the International Group for the Psychology of Mathematics
Education and the International Symposium for Elementary Mathematics Teaching. I also review
maths education papers for journals such as Research in Mathematics Education, Learning and
Instruction and Journal of Teacher Education. In my previous role in the Centre for Evaluation
and Monitoring, working within the Education Evaluation Group, I was involved in a number of
evaluations of initiatives in mathematics education. I was principal investigator on the evaluation
of the Royal Institution’s Secondary Mathematics Masterclasses. I was also co-investigator for the
evaluation of Every Child Counts and co-investigator on the evaluation of the Further
Mathematics Network.
Current research interests
Over the last five years, the main focus of my research has been on the notion of ‘understanding’
in mathematics, and the relationship between understanding and representations of mathematical
concepts. Drawing on the work of Hiebert and Carpenter, I have taken a ‘network’ model of
understanding, involving the idea of connected internal representations of mathematical concepts.
Also drawing on the ideas of Anna Sierpinska, I defined these connections as ‘reasonings’, also in
line with Philip Johnson-Laird’s mental models view of thinking and reasoning as manipulation of
internal representations. This ‘representational-reasoning’ model of understanding has been useful
for outlining implications for practice with researchers, teachers and student teachers for how we
approach the teaching for understanding in mathematics.
Building further on the view that our internal representations are influenced by the external
representations that we experience, my work with colleagues has examined primary pupils’
understanding of diagrammatic representations in mathematics, especially representations of
multiplication. We have also built on this work to examine (a) the impact on student teachers of
working with multiple representations in their teacher training courses, and (b) the impact of a
professional development course on experienced teachers focussing on the use of multiple
diagrammatic representations in both multiplication and fractions. Work in both these areas has
highlighted the benefits that a multi-representational approach can bring to teachers and pupils. In
addition, it has highlighted that teachers also need to consider the progression in representations
that pupils experience, not assuming that the mathematical structure of representations will be
perceived by pupils (as highlighted by Paul Cobb and colleagues).
In terms of further developing the above research and exploring new areas, there are two
avenues that I am currently focussing on. Firstly, I am exploring the use of eye tracking
technology to examine how primary pupils look at diagrammatic representations. Early results
have shown that pupil’s mathematical understanding influences the way they examine these
representations. More importantly perhaps, this work is highlighting the usefulness of this
methodology in the area of mathematics education and working specifically with younger pupils.
At present, there is quite a gap in this area and the work provides a proof of concept of using such
technology with primary pupils. Initial work in this area has been accepted for publication with the
academic journal Educational Research. The second area is a departure from the above, and
returns to some previous work on attitudes. The use of questionnaires to ‘measure’ attitudes
towards mathematics is problematic particularly in terms of the validity of findings. However,
more in-depth qualitative approaches suffer from the difficulty of making any study
representative. Recent work I have carried out involves a mixed methods approach, using
qualitative analysis of statements about mathematics, and using these to develop questionnaires for
quantitative analysis. Interesting initial results have been obtained from pre-service primary
teachers at Durham University and these finding were presented at the PME conference in
Vancouver in July 2014. A great advantage of this method is that by starting with qualitative
comments from teachers, it takes into account differing educational contexts of pupils/teachers.
Therefore, this method would be equally applicable to the various school contexts in other
countries. This work has now been submitted for publication in an international mathematics
education journal.
Publications
Books
Barmby, P., Bolden, D. & Thompson, L. (2014). Understanding and Enriching Problem Solving
in Primary Mathematics. St Albans: Critical Publishing.
Barmby, P., Bilsborough, L. Harries, T. & Higgins, S. (2009). Primary mathematics: Teaching
for understanding. Buckingham: Oxford University Press.
Book chapters
Barmby, P., & Edwards, R. (2013). Developing the potential of all pre-service mathematics
teachers. In R. Hyde & J. Edwards (Eds). Developing mentoring in mathematics (pp. 108122). London: Routledge.
Kind, P., & Barmby, P. (2011). Defending attitude scales. In I. M. Saleh & M. S. Khine (Eds.),
Attitude research in science education: Classic and contemporary measurements (pp. 117135). Charlotte, NC: Information Age Publishing Inc.
Barmby, P., Harries, T., & Higgins, S. (2010). Teaching for understanding/Understanding for
teaching. In I. Thompson (Ed.) Issues in teaching numeracy in primary schools (2nd Ed.),
(pp.45-57). Open University Press.
Harries, A., Barmby, P. & Suggate, J. (2008). ‘What’s in a picture? Understanding and
Representation in Early Mathematics’. In I. Thompson (Ed.) Teaching and Learning Early
Number (2nd Ed.), (pp. 160-175). Open University Press.
Coffield, M., Riddick, B., Barmby, P. & O’Neil, J. (2008). ‘Dyslexia Friendly Primary Schools:
What can we learn from asking the pupils?’ In Reid, G., Manis, F., Fawcett, A. & Siegel,
L. (eds.) SAGE Handbook of Dyslexia. London: Sage.
Rattray, J., Aiston, S. & Barmby, P. (2007). ‘Learning for life not just for exams: The
development of metalearning in higher education students’. In C. Rust (ed.) Improving
Student Learning through Teaching. Oxford: Oxford Centre for Staff and Learning
Development.
Journal articles
Barmby, P., Bolden, D. & Raine, S. (2015). A mixed-methods approach to studying pre-service
teachers’ attitudes towards mathematics. Educational Studies in Mathematics (under
review)
Bolden, D., Barmby, P., Raine, S. & Gardner, M. (2015). How young children view mathematical
representations: a study using eye-tracking technology. Educational Research, 57(1), 5979.
Barmby, P., Bolden, D., Raine, S., & Thompson, L. (2013). Developing the use of diagrammatic
representations in primary mathematics through professional development. Educational
Research, 55(3): 263-290.
Bolden, D.S., Barmby, P.W. & Harries, A.V. (2013). A representational approach to developing
primary ITT students' confidence in their mathematics. International Journal of
Mathematical Education in Science and Technology 44(1): 70-83.
Barmby, P., Bolden, D., Higgins, S. & Tymms, P. (2012). Predicting success on a Bachelor of
Arts Primary Education degree course. Educational Research 54(3): 323-330.
Barmby, P., Harries, T., Higgins, S. & Suggate, J. (2009). ‘The array representation and primary
children’s understanding and reasoning in multiplication’. Educational Studies in
Mathematics, 70(3), pp. 217-241.
Barmby, P., Jones, K. & Kind, P. (2008). ‘Examining Changing Attitudes in Secondary School
Science’, International Journal of Science Education, 30(8), pp. 1075-1093.
Harries, T. & Barmby, P. (2008). ‘Representing multiplication’. Mathematics Teaching, 206, pp.
37-41.
Harries, T. & Barmby, P. (2007). ‘Representing and understanding multiplication’. Research in
Mathematics Education, 9, pp. 33-45.
Kind, P., Jones, K. & Barmby, P. (2007). ‘Developing attitudes towards science measures’,
International Journal of Science Education, 29(7), pp. 871-893.
Barmby, P. (2006). ‘Improving Teacher Recruitment and Retention: The Importance of Workload
and Pupil Behaviour’, Educational Research, 48, 3, pp. 247-265.
Barmby, P. & Defty, N. (2006). ‘Secondary School Pupils’ Perceptions of Physics’, Research in
Science and Technological Education, 24, 2, pp. 199-215.
Barmby, P. & Coe, R. (2004). ‘Evaluating the MEI “Enabling Access to Further Mathematics”
project’, Teaching Mathematics and its Applications, 23, 3, pp. 119-132.
Reports: Official
Barmby, P., Bolden, D.S., Raine, S. & Thompson, L. (2013). Developing the use of visual
representations in the primary classroom. Nuffield Foundation.
Torgerson, C.J., Wiggins, A., Torgerson, D.J., Ainsworth, H., Barmby, P., Hewitt, C., Jones, K.,
Hendry, V., Askew, M., Bland, M. Coe, R., Higgins, S., Hodgen, J., Hulme, C. & Tymms,
P. (2011). Every Child Counts: The Independent evaluation Executive Summary.
Department for Education (DfE).
Torgerson, C.J., Wiggins, A., Torgerson, D.J., Ainsworth, H., Barmby, P., Hewitt, C., Jones, K.,
Hendry, V., Askew, M., Bland, M., Coe, R., Higgins, S., Hodgen, J., Hulme, C. & Tymms,
P. (2011). The Every Child Counts Independent Evaluation Report to DfE.
Wiggins, A., Barmby, P., Kokotsaki, D., Lyth, A. & Torgerson, C. (2009). City GATES evaluation
Phase 1: Existing data analysis. CfBT.
Funded projects
Completed
Principal investigator – Developing the use of visual representations of mathematical concepts in
the primary classroom, submitted to the Nuffield Foundation (£40,808), May 2011 – July
2012.
Co-investigator – Evaluation of the Every Child Counts initiative on behalf of the DCSF
(£135,150), January 2009 – October 2010.
Principal investigator – Evaluation of the Royal Institution Secondary Mathematics Masterclasses
on behalf of the Royal Institution (£20,000), January 2008 – August 2008.
Principal investigator – Evaluation of the Lab in a Lorry initiative on behalf of the Institute of
Physics (£16,846), October 2005 – January 2006.
Principal investigator – Evaluation of the Repayment of Teachers’ Loans Scheme on behalf of the
Department for Education and Skills (£34,060), January 2004 – July 2004.
Co-investigator – Evaluation of the MEI ‘Enabling Access to Further Mathematics’ Project
(£7,000), Completed October 2003.
Conference presentations
2014 PME Conference: Presented a research report entitled ‘A new approach to measuring preservice teachers’ attitudes towards mathematics’ at the PME Conference in Vancouver,
Canada.
2013 (Nov) BSRLM Conference: Presented a paper entitled ‘How young children view
mathematical representations: A study using eye-tracking technology’ at the BSRLM
Conference in Edinburgh.
2012 PME Conference: Presented a short oral report entitled ‘Assessing young children’s
understanding of multiplication’ at the PME Conference in Taipei, Taiwan.
2012 (Nov) BSRLM Conference: Presented a paper entitled ‘Measuring pre-service teachers'
attitudes to mathematics: A mixed methods approach’ at the BSRLM Conference in
Cambridge.
2012 (June) BSRLM Conference: Presented a paper entitled ‘Developing the use of diagrammatic
representations in the primary classroom’ at the BSRLM Conference in Sussex.
2011 PME Conference: Presented a short oral report entitled ‘Primary pupils' difficulties with
fractions: A representational view’ at the PME Conference in Ankara, Turkey.
2011 PME Conference: Presented a research report entitled ‘Pre-service teachers’ use of visual
representations of multiplication’ at the PME Conference in Ankara, Turkey.
2011 (Nov) BSRLM Conference: Presented a paper entitled ‘Evaluating the impact of a Realistic
Mathematics Education project in secondary schools’ at the BSRLM Conference in
Oxford.
2011 (Nov) BSRLM Conference: Presented a paper entitled ‘Assessing young children's
understanding of multiplication’ at the BSRLM Conference in Oxford.
2011 (March) BSRLM Conference: Presented a paper entitled ‘Primary pupils' difficulties with
fractions: A representational view’ at the BSRLM Conference in London.
2011 (March) BSRLM Conference: Presented a paper entitled ‘A representational approach to
primary ITT students’ developing competence and confidence in their mathematics’ at the
BSRLM Conference in London.
2010 BCME Conference: Presented a paper entitled ‘Enrichment and engagement in mathematics’
at the BCME Conference in Manchester.
2010 (June) BSRLM Conference: Presented a paper entitled ‘Working with visual representations
of mathematical concepts’ at the BSRLM Conference in Nottingham.
2009 SEMT Conference: Presented a paper entitled ‘Recognising representations of
multiplication’ at the SEMT Conference in Prague, Czech Republic.
2007 PME Conference: Presented a research report entitled ‘How can we assess mathematical
understanding’ at the PME Conference in Seoul, South Korea.
2007 BERA Conference: Presented a paper entitled ‘The array representation and primary
children’s understanding and reasoning in multiplication’ at the BERA Conference in
London.
2007 AMET Conference: Invited speaker presenting a talk entitled ‘Developing software for
primary school mathematics’ at the AMET Conference in Keele.
2006 (Nov) BSRLM Conference: Presented a paper entitled ‘Representing multiplication’ at the
BSRLM Conference in Birmingham.