Bill Barton

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Bio and Research | Publications | Teaching | Supervision | Seminars and other talks | Previous positions | Qualifications | Awards and Research funding | Professional Societies and other service

Associate Head of Department - Academic

President, International Commission on Mathematical Instruction (ICMI) 2009-2011

Old webpage


Inaugural Lecture

The Pleasure Principle in Undergraduate Mathematics Mathematicians speak like addicts about their subject: deep mathematical knowledge is a source of intense and intimate pleasure. What would the undergraduate experience look like if we directed our efforts at getting students addicted? Relying on research rather than tradition to guide practice, I propose a design for tempting undergraduates into deep mathematical engagement.

ICM Public Lecture

Where is mathematics taking me? An Exciting Ride into the Future Delivered to 1200 secondary students in Hyderabad in 2010--a talk about some mathematical topics and applications, mostly inspired from colleagues in The University of Auckland. ICM public lecture

Research profile

My PhD topic and main research area is Mathematics & Culture, more recently specialising in Mathematics and Language. This includes fifteen years of research and development of the Maori mathematics vocabulary, which has developed into a consideration of communicating mathematics in non-Indo-European languages. In recent years I have become involved in Undergraduate Mathematics Education, developing a theoretical framework with colleagues in the UK, leading a New Zealand project that re-visions mathematics education for 16-19 year-olds, and heading the IMU/ICMI Klein Project.

Fields of interest

Current projects

Pipeline project data
Data sample

The Klein Project

Recent publications

  • BARTON, B. (2011). Designing Alternative Undergraduate Delivery: Oil and Massage. In E. Swoboda (Ed), Proceedings of the 7th Conference of European Researchers in Mathematics. Rzeszow, Poland: European Society for Research in Mathematics Education
  • WATSON, A. & BARTON, B. (2010). Teaching mathematics as the contextual application of mathematical modes of enquiry. In K. Ruthven & T. Rowlands (Eds.) Mathematical Knowledge in Teaching. Cambridge University Press.

BARTON, B. & SHERYN, L. (2009). The mathematical needs of secondary teachers: data from three countries, International Journal of Mathematical Education in Science and Technology, 40(1) January 2009, 101-8.

  • BARTON, B. (2008). The Language of Mathematics: Telling Mathematical Tales. Mathematics Education Library, Vol. 46., New York: Springer.
  • BARTON, B. & GORDEAU, F. (2008). Disciplinary Mathematics and School Mathematics: Report of Working Group 1. In M. Menghini, F. Furlinghetti, L. Giacardi, & F. Arzarello, (Eds.) The First Century of the International Commission on Mathematical Instruction (1908-2008). Reflecting and shaping the world of mathematics education, Roma: Istituto della Enciclopedia Italiana, p.253-64.
  • BARWELL, R., SETATI, M. & BARTON, B. (2007). Multilingual Issues in Mathematics Education: Introduction, Educational Studies in Mathematics, 64(2), 113-119
  • BARTON, B., CHAN, R., KING, C., NEVILLE-BARTON, P., & SNEDDON, J. (2005). EAL Undergraduates Learning Mathematics. International Journal of Mathematical Education in Science and Technology, 36(7), 721-729.
  • BARTON, B. (2009). Revisiting Felix Klein’s Elementary Mathematics From An Advanced Standpoint: An IMU/ICMI Project. In M. Kourkoulos & C. Tzanakis (Eds.) Proceedings of 5th International Colloquium on the Didactics of Mathematics (Vol.1.), Department of Education, University of Crete, Rethymnon, Greece. 17-19th April, 2008, p.511-520 (427-438 in the Greek Edition (Vol.2.))


I was born in New Zealand, and throughout my childhood moved around the country as my father moved from school to school. At the age of 14 we went to Khartoum where my father had a UNESCO position and so began my love for travel and interest in other cultures. I learned to sail on the Nile, and continued my NZ schooling by correspondence. I returned to finish schooling in Auckland, and then entered The University of Auckland where I majored in mathematics, first for a BSc, then a Masters. During this time I again visited my parents, now in Tripoli, Libya, and taught for a short time, developing a love for teaching that has never paled.

Returning to New Zealand I completed a post-graduate teaching Diploma and began several years secondary school teaching while also studying for a Masters degree in Education. Fifteen years in this career included three important periods. One was a period of four years teaching at the University College of Botswana, Lesotho and Swaziland (I was based in Swaziland, and my daughter was born there)—this taught me about the importance of language. The second was producing two series of public television programmes—this taught me about popularising mathematics. The third was being involved in a project to develop the indigenous Maori language of New Zealand so that it could be the language of instruction for mathematics—this taught me about the joys of research.

I moved from my final secondary teaching position (in a Maori-English bilingual Unit) into teacher education, and began my PhD in Ethnomathematics. Thence, in the early nineties, I moved to the Department of Mathematics at The University of Auckland where the senior professors had determined that they should have mathematics education represented in the Department—an unusual circumstance, but one which suited me perfectly: I could teach undergraduate mathematics, and postgraduate mathematics education.

Remaining in this Department, I have just finished my turn as Head of Department, continue to teach, and maintain my research activities. As part of these I have been editor of both the Australasian regional Mathematics Education Research Journal, and an Assistant Editor of Educational Studies in Mathematics. My research interests are two-fold. Following my interest in the Maori language and studies in Ethnomathematics I have investigated the way widely different languages express mathematical ideas. A book on this subject will be published at the end of 2008. With a topologist colleague, I have also undertaken a study of the ways in which language affects the mathematical thinking of research mathematics. Other language research concerns the experiences of those learning mathematics in English when it is not their first language (this is joint work with my wife who is an English language lecturer).

My second research interest is with the development, particularly the mathematical development, of senior secondary teachers. I am delighted to be currently working with Dr Anne Watson in Oxford and with Professor Deborah Ball in Michigan, and their teams, thinking about mathematical knowledge for teaching.

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