Questioning the value of mathematics: Is mathematics harmful?
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The document explores the multifaceted value of mathematics, highlighting intrinsic, extrinsic, and personal dimensions while questioning its unquestioned status in society. It discusses the potential harms arising from the instrumental reasoning fostered by mathematical thinking, which can lead to ethical detachment and social inequalities. The author advocates for reform in mathematics education to incorporate ethics and a broader appreciation of its cultural relevance, suggesting a more humanized approach to teaching mathematics.
Questioning the value of mathematics: Is mathematics harmful?
- 1. Questioning the Value of Mathematics Paul Ernest University of Exeter p.ernest@ex.ac.uk
- 2. Valuing of Mathematics As mathematics professionals we greatly esteem and value mathematics Mathematics is valuable in several ways Mathematics has: 1. Intrinsic value 2. Extrinsic and social value 3. Personal value
- 3. 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?
- 4. 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
- 5. 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)
- 6. The Characteristics of Mathematics Calculation is central – it dominates history and schooling • Rule based procedures in which meaning is ignored Algebra 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
- 7. Costs of mathematics The mathematical way of thinking promotes • Detachment of meaning • Ethical neutrality • Separated values • Dehumanizing outlook
- 8. Seeing the world mathematically Replaces beautiful complexity of nature with simplified models
- 9. Separated Values of Mathematics Separated values (Gilligan 1982) promote: • Rules, • Abstraction, • Objectification, • Reason, • Dispassionate analysis, • Impersonality These values intrinsic to mathematics But inculcating these values fosters a dehumanized outlook
- 10. 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
- 11. 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
- 12. Mathematics is Basis for Modern Life MATHEMATICS Science Technology & Material basis for life Computing Media & Knowledge systems Money Social Organisation & Trade
- 13. We live in a mathematized social world
- 14. Characteristics of Mathematics School, 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 meaning Good training for calculative or instrumental reasoning (Frankfurt School) – conducting procedures with no thought of external impact or ethical considerations
- 15. 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)
- 16. 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
- 17. 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
- 18. 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
- 19. Maths as Fractional Distillation PROFESSIONALS SKILLED WORKERS UNEMPLOYED UNDERCLASS UNSKILLED WORKERS CHILDREN MATHEMATICS ASSESSMENT SYSTEM Mathematics success highly correlated with career outcomes
- 20. Social views of maths were sexist ADVERTS
- 21. 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
- 22. 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
- 23. Costs: Negative attitudes to maths Many learners and adults • Are labelled as maths failures • Lack confidence • Fear mathematics • Have reduced opportunities
- 24. False image of mathematics • Stern, unforgiving, joyless, authoritarian subject • Meaningless, formal, learned by rote • Mathematics ability inherited gift -- not due to own effort
- 25. Stereotyped images persist • Modern child’s view of mathematician • Bad images of mathematics persist
- 26. Mathematics has two Faces BAD FACE Harm • Dehumanized thinking • Instrumentalism ethics-free governance • Social reproduction • Negative attitudes & Image GOOD FACE Benefit & Value • Intrinsic • Social • Personal
- 27. Harm comes from mis-application Mathematics not intrinsically harmful But its applications can be detrimental to many How can we rectify this? • Include philosophy of mathematics with mathematics • Add the ethics of mathematics • Reform school mathematics teaching, curriculum and assessment
- 28. 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
- 29. 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
- 30. 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%)
- 31. Teach Appreciation of Maths Maths more than calculating, solving and proving School 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
- 32. End of Talk