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

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