Mathematical Cultures

Lead Research Organisation: University of Hertfordshire
Department Name: Social Sciences Arts and Humanities RI

Abstract

Highlight notice: Science in Culture

Mathematics is shaped by its history and segmented by content, by professional and institutional differences, by geography and by political boundaries. Thus it is suitable for study as a culture, or better, as a constellation of cultures. Its value is cultural as well as practical. Mathematics is an expression of the human capacity to transcend our material interests and find satisfaction in exercising our intelligence. Further, mathematicians assess and direct research in mathematics using standards and values that are embedded in their research culture. However, the cultural benefits of mathematics are hard to disseminate because appreciation of mathematics requires relatively detailed understanding (compared with fields like the discovery of exoplanets, where the results can be given with little or no technical apparatus). This raises a third theme: the cultural standing and reputation of mathematics. It is a long-standing goal of UK governments to raise attainment in numeracy and STEM disciplines. A major obstacle is the reputation of mathematics among students as forbiddingly difficult and remote.

This project will host three conferences.
The first (Easter 2012) will explore and map the variety of and connections among contemporary mathematical cultures. These can be research cultures, but may also include practitioner cultures (e.g. among engineers, economists, social scientists, etc.) and mathematical cultures among instructor and student groups (e.g. primary/secondary/tertiary teachers, school pupils, mathematics students at all levels).

The second (Easter 2013) conference will articulate and classify mathematical values. What do mathematicians mean when they use terms such as 'deep', 'elegant', 'explanatory', etc.? What is the rational structure of the deliberations mathematicians use to reach value judgments? This conference will build on the first conference by referring these questions to the various mathematical cultures identified at that first event.

The third conference (September 2013) will discuss mathematics in public culture. Amongst other topics, it will explore the question "why should I study mathematics?". This third meeting will build on the first conference by identifying the contributions from and audiences in the various mathematical cultures. It will build on the second conference by drawing on the articulations and explorations of mathematical values.

These meetings will be recorded and edited for publication on the project website. The project will invite to all three conferences (and pay reasonable expenses for) individuals whose interest might be thought to lie solely in the final meeting (such as mathematics popularisers and science journalists).

At every conference there will be space in the programme for postgraduate students to present their work (if they are in parallel sessions, they will not be timetabled against established researchers) and funds to support their attendance.

The network will be managed by the Principal Investigator, aided by an administrative assistant who will organise the meetings, coordinate publication of the outputs and develop and maintain the website.

The PI will share responsibility for inviting participants, judging abstracts of proposed talks and choosing contributions to the outputs with a panel consisting of:

Prof Jeremy Gray, Professor of the History of Mathematics (Open University)

Dr. Matthew Inglis, Lecturer (Maths Education Centre, Loughborough University); Honorary Research Fellow (University of Notts); Royal Society Worshipful Company of Actuaries Research Fellow.

Prof. Benedikt Löwe, Universitair Docent (Universiteit v. Amsterdam); Privatdozent (Universität Bonn); Professor (Universität Hamburg); Lead Investigator of the PhiMSAMP programme.

Dr. Alison Pease, Centre for Intelligent Systems and their Applications (University of Edinburgh)

Planned Impact

Who will benefit from this research?

This network offers direct benefits to mathematics educators, and thus indirect cultural and economic benefits to the UK public.

This network offers policymakers a unique opportunity to consider the cultural value and appeal of mathematics.

This network offers authors of popular mathematics books and science journalists opportunities to meet researchers in various aspects of mathematical culture and hear about their latest work.

This network offers mathematics educationalists opportunities to access researchers on mathematical cultures, mathematical learning and cognition, the history and philosophy of mathematical practice.


How will they benefit from this research?

Raising mathematical literacy is agreed to be necessary for the UK's economic and social development. This perception motivates reports such as "The Demand for Science, Technology, Engineering and Mathematics (STEM) Skills" (Department for Innovation, Universities and Skills, January 2009) and initiatives such as STEMNET. Such initiatives face a widespread public perception that mathematics is a set of useful but uninteresting calculating techniques. This network will develop a discourse and a body of examples that demonstrate the cultural value and appeal of mathematics. This in turn will offer educators and policymakers resources to encourage more people (and especially school pupils) to choose to study mathematics.

This network offers authors of popular mathematics books and science journalists resources for developing new themes and stories.



What will be done to ensure that they have the opportunity to benefit from this research?

The programme panel includes a senior and well-connected mathematics educationalist (Dr. Inglis), who will ensure that the activities of the network are well publicised to educationalists. In addition, we will invite senior representatives of the National Centre for Excellence in the Teaching of Mathematics (NCETM) and the British Society for Research into Learning Mathematics (BSRLM).

We will invite officials from the relevant government departments (i.e. Education; Culture, Media and Sport), mathematics popularisers and science journalists to all three events. Leading authors of popular mathematics books will be invited as speakers and reasonable expenses paid.

Publications

10 25 50
 
Description We learned that the best conception of culture for thinking about mathematics education is this:

A culture is a set of values expressed in practices and artefacts.

This is better than ethnographic or geographical conceptions (e.g. Navajo culture, British culture) because the mathematics classroom is multicultural, even if everyone is a member of the same ethnographic group. There is a staff-culture, a pupil-culture and a disciplinary culture, in addition to whatever cultural riches people bring with them from outside the school. We saw examples (like Finland) where these cultures combine to produce positive outcomes, and other cases (Brazil, Western Canada) where native peoples experience state education as colonialism.

We also learned that there is relatively little work on the cultural significance of mathematics for pupils. Most work on motivation treats it as a psychological condition, rather than as an indicator of alignment between the several value-systems present in the classroom.
Exploitation Route We have already secured funding from ICSU (Eu30k) to develop a research project on Cultures of Research Training, i.e. to investigate and ameliorate the cultural barriers to participation in mathematical research.
We are planning an application for follow-on funding to turn our findings into a resource for school mathematics teachers.
There are some promising leads re. the place of mathematics in cultural understandings and narratives of risk, both in the lay population and among finance and actuarial professionals.
Sectors Education

URL https://sites.google.com/site/mathematicalcultures/home
 
Description Influenced curriculum design in maths teacher training course, Bath Spa University
First Year Of Impact 2014
Sector Education
Impact Types Cultural

 
Description Module in maths teacher training course at Bath Spa University
Geographic Reach Local/Municipal/Regional 
Policy Influence Type Influenced training of practitioners or researchers
 
Description ICSU grants programme
Amount € 30,000 (EUR)
Organisation International Council for Science (ICSU) 
Sector Learned Society
Country France
Start 07/2014 
End 06/2015
 
Description Santander Partnership - Research Collaboration Support
Amount £5,000 (GBP)
Organisation Santander Bank 
Sector Private
Country United States
Start 07/2013 
End 07/2014
 
Description LOGIC and PHILOSOPHY of MATHEMATICAL PRACTICES (VUB) 
Organisation Free University of Brussels
Country Belgium 
Sector Academic/University 
PI Contribution In return for a year's sabbatical, I will travel regularly to Brussels, participate in the meetings of the Centre, teach postgraduates and write two or three collaborative papers with local staff.
Collaborator Contribution Payment of costs, collaboration in writing, environment of the leading European centre for the philosophy of mathematical practice
Impact Collaborative papers projected. Contributions from philosophy, logic, maths education, history of maths and possibly cognitive science
Start Year 2014