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Questioning the Value of Mathematics Is mathematics harmful? Can it be damaging to the human spirit? These may sound like strange and unprovoked questions. But let me explore these possibilities in the context of some of the acknowledged positive value of mathematics. Mathematics is often claimed to have different types of value: 1. Extrinsic or social value because of all of its uses and applications in society, technology and other areas including the sciences; 2. Personal value because of its empowerment of individuals via their understanding and ability to use and apply mathematics, as well as enabling some to develop and express their creativity through mathematics; 3. Intrinsic value as a wonderful exploration of pure thought and ideas for its own sake. But are these untrammelled goods? Does promoting these aspects of value lead to solely beneficial outcomes? What are the actual, including unintended, outcomes and the opportunity costs of privileging mathematics in education and society? Mathematics provides the foundation for banking, commerce and indeed money itself. But is mathematics implicated in the global disparities in wealth and life chances? Mathematics underpins instrumentalist thinking and governmentality, but is mathematics responsible for the growing dehumanization in the treatment of people in the modern world? Mathematics is a core subject in the school curriculum and virtually a sine qua non for university education. However, many school leavers have negative attitudes towards mathematics and feelings of inadequacy. Is overvaluing mathematical achievement to blame for this? In the presentation I explore some of the deeper reasons underpinning these problems. By better understanding the limits to its value I believe we can be wiser in teaching, applying and creating mathematics. I conclude that although mathematics itself is neutral, it is its misapplications that are to blame for problems like those listed above. My recommendation is that to avoid such problems we need to teach philosophy and ethics to mathematics students at college, and also need to reform the school mathematics curriculum in an holistic way. Here's the link in case you want to see the talk itself http://www.youtube.com/watch?v=RCngE2hZyMg
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Valuing of Mathematics
As mathematics professionals we greatly esteem and value mathematics
Mathematics is valuable in several waysMathematics has:1. Intrinsic value2. Extrinsic and social value3. Personal value
Questioning the Value of Maths
• But is mathematics an untramelled good?• Does promoting mathematics lead to solely
beneficial outcomes? • What are the actual, including unintended,
outcomes and costs of privileging mathematics in education and society?
• Dare we question the unquestionable and ask: • Does mathematics cause harm?
1. Intrinsic value of mathematics
• Mathematics has intrinsic value – for its own sake
• Powerful exploration of pure thought, truth and ideas for their own sake
• A wonderful and rich language for describing and modelling the world
The beauty of pure mathematics• A wondrous world of
beautiful crystalline forms that stretch off to infinity in richly etched exquisiteness
• Like painting and poetry mathematics has permanent aesthetic value (Hardy)
• Mathematics possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture (Russell)
The Characteristics of Mathematics
Calculation is central – it dominates history and schooling
• Rule based procedures in which meaning is ignoredAlgebra is central – the language of mathematics• Variable based – specific meanings are detached
(noted by Berkeley 1710)Unique linguistic move from meanings to rules • This enables the miracle of electronic computing• But has costs too
Costs of mathematics
The mathematical way of thinking promotes• Detachment of meaning• Ethical neutrality• Separated values• Dehumanizing outlook
Seeing the world mathematicallyReplaces beautiful complexity of nature with simplified models
Separated Values of Mathematics
Separated values (Gilligan 1982) promote: • Rules, • Abstraction, • Objectification, • Reason, • Dispassionate analysis, • Impersonality These values intrinsic to mathematicsBut inculcating these values fosters a dehumanized
outlook
Separated values in mathematics
• Separated values may be necessary by the nature of mathematics
• Within mathematics they are necessary and beneficial
• Beyond mathematics they are unnecessary and potentially harmful
2. Extrinsic / Social Value of Maths
MATHEMATICS ESSENTIAL FOUNDATION FOR • Much of knowledge – especially science• Information and communication technology –
computing wholly based on maths • Applications in engineering, technology and
throughout society• Economic, fiscal and commercial basis of
modern society• Work, study and everyday life
Mathematics is Basis for Modern Life
MATHEMATICS
Science
Technology & Material basis
for life
Computing
Media & Knowledge
systems
Money
Social Organisation &
Trade
We live in a mathematized social world
Characteristics of MathematicsSchool, university and research mathematics presented in sentences where predominant verb form is imperative (Rotman)Imperatives instruct or direct actions - either inclusively (Let us …, Consider…) or exclusively (Add, Count, Solve, Prove, etc)Operating mathematically is to follow imperatives, follow orders, to carry out instructed procedures following rules unquestioningly Many procedures on signs carried out with deferred meaningGood training for calculative or instrumental reasoning (Frankfurt School) – conducting procedures with no thought of external impact or ethical considerations
Negative Outcomes of Maths in Society
• Objectivism and simplistic epistemology• Instrumental reasoning in management and
governmental thinking – ethics free thought• Mathematics examinations a sifting / filtration
device – fractional distillation of population via school – class reproductive
• Sexism supported by maths (diminishing)
Mathematics promotes objectivism and simplistic epistemology
• In the world things are not just absolutely
True or False• Decisions are complex and need to take
account of context & human consequences
Instrumental reasoning
Mathematics provides training in instrumental reasoning for management, business and governmental thinking
• Convergent rule following thought• Inculcating separated values • Training in ethics-free and value-free thinking
Instrumental reasoning• Mathematics is essence of
instrumental reason - focus on means to ends and not on underlying values (Frankfurt School critique)
• Instrumental reasoning underpins management, corporate and governmental thinking
• Standardization, routinization, and dehumanization lead to unethical treatment of persons (Kelman 1973)
People are viewed as objects
Maths as Fractional Distillation
PROFESSIONALS
SKILLED WORKERS
UNEMPLOYED UNDERCLASS
UNSKILLED WORKERS
CHILDREN
MATHEMATICS ASSESSMENT SYSTEM
Mathematics success highly correlated with career outcomes
Social views of maths were sexist
ADVERTS
Mathematics as basis of money
• Mathematics is the basis of money
• The tool for the distribution of wealth
• As a tool mathematics implicated in the global disparities in wealth and life chances
3. Personal value of mathematics
There are great benefits: Mathematical knowledge empowers individuals to
• Gain understanding, skills, reasoning and problem solving abilities
• Gain qualifications for employment• Be able to use mathematics in life and work• Express creativity through mathematics • Gain foundation for further study
Costs: Negative attitudes to mathsMany learners and adults• Are labelled as maths failures• Lack confidence• Fear mathematics• Have reduced opportunities
False image of mathematics
• Stern, unforgiving, joyless, authoritarian subject
• Meaningless, formal, learned by rote
• Mathematics ability inherited gift -- not due to own effort
Stereotyped images persist
• Modern child’s view of mathematician
• Bad images of mathematics persist
Mathematics has two Faces
BAD FACEHarm • Dehumanized
thinking• Instrumentalism
ethics-free governance
• Social reproduction• Negative attitudes
& Image
GOOD FACEBenefit & Value• Intrinsic• Social• Personal
Harm comes from mis-application
Mathematics not intrinsically harmfulBut its applications can be detrimental to manyHow can we rectify this?• Include philosophy of mathematics with
mathematics• Add the ethics of mathematics• Reform school mathematics teaching,
curriculum and assessment
Teach philosophy of mathematics
Include philosophy of mathematics in mathematics degree courses
• Teach the limits of mathematical knowledge - its certainties do not apply to the world – there is always a margin of error
• Teach limits of mathematical thinking – true/false dichotomies do not apply to the world
Teach the ethics of mathematics
Add the ethics of mathematics to mathematics degree courses
• Teach the limits and dangers of instrumental thinking – it dehumanization of people and institutions
• Mathematics must be applied responsibly– it is wrong to ignore ‘incidental’ outcomes or ‘collateral damage’ in social impacts
Reform mathematics teaching
• Humanize mathematics teaching - duty of care for learners: their maths attitudes and images matter
• Don’t demonize errors – they are inevitable steps in learning – not sins or failures
• Teach critical thinking – look critically at social applications and mathematics-based claims
• Add mathematical appreciation (10%) to mathematical capability i.e. ‘doing maths’ (90%)
Teach Appreciation of Maths
Maths more than calculating, solving and provingSchool maths needs a broader appreciation of• Maths in culture, art and social life• History of mathematics and maths in history• Mathematics as a unique discipline• Proof and how maths knowledge validated • Controversies in philosophy of maths• Introduce big ideas of mathematics
pattern, modelling, symmetry, structure, equivalence, invariance, proof, paradox, recursion, randomness, chaos, infinity, etc
End of Talk
