Why are mathematics taught?
From Aristotle, Plato, Al-Khawarizmi, and Al-Kindi, to John Allen Paulos (Temple U.), Paul Ernest, (U. of Exeter), and Eleanor Robson (U. of Oxford), maths thinkers have stated three types of reasons: emotional, cognitive and practical.
From Aristotle, Plato, Al-Khawarizmi, and Al-Kindi, to John Allen Paulos (Temple U.), Paul Ernest, (U. of Exeter), and Eleanor Robson (U. of Oxford), maths thinkers have stated three types of reasons: emotional, cognitive and practical.
Setting aside the emotional and cognitive reasons, let’s discuss the
implications of the practical reasons. Mathematical understanding is crucial
for high performance in our personal, public, and work lives. At home, we may
want to understand the results of a medical test, or rekindle our child's love
of math. As citizens, we may want to judge the rise in carbon-dioxide levels in
the air, or the proportion of tax dollars that should go to health, education,
or war. At work, we may need to estimate the money, time, and employees for a
large project. Finally, mathematics underlies our science, technology, and
engineering. OECD countries spend $236 billion per year on mathematics
education yet most countries report shortages in Science, Technology,
Engineering and Maths (STEM) talent.
How is the breadth of mathematical application reflected in PISA?
There are four contexts assessed: personal (self, family and peer groups), societal (one's community), occupational (the general world of work) and scientific (application to science and related issues and topics). These contexts are outstanding choices. Furthermore, by weighting them equally, PISA ameliorates the misconception that mathematics is useful only in the scientific context.
How do we make maths relevant for all occupations, and for new occupations?
The synthesis of research by the OECD and the Royal Society highlights the need to rebalance traditional mathematics (geometry, algebra and calculus) with new branches (statistics and probabilities, applied maths and discrete maths) which are relevant for a wide swath of occupations.
The OECD Global Science Forum Report on Mathematics in Industry describes the needs for different types of mathematics: statistics & probabilities; complex systems; computational maths. Additionally, the Royal Society’s ACME 2011 “Mathematics in the workplace and higher education” highlights requirements such as: mathematical modelling (e.g. energy requirement of a water company; cost of sandwich); use of software and coping with problems (e.g. oil extraction; dispersion of sewage); costing (allocation; dispute management) (e.g. Contract cleaning of hospital; management of railway); performance and ratios (e.g. Insurance ratios; glycemic index); risk (e.g. clinical governance; insurance); and quality/SPC control (e.g. furniture; machine downtime; deviation of rails).
How are maths used in personal and societal contexts?
Again, personal and societal uses highlight the need to rebalance traditional mathematics (geometry, algebra and calculus) with new branches (statistics and probabilities, complex systems) and deepening the understanding of basic arithmetic (number sense and proportionality).
John Allen Paulos, Mathematician at Temple University, and Author of “A Mathematician reads the newspaper“ has stated: “Gullible citizens are a demagogue’s dream… almost every political issue has a quantitative aspect”.
In PISA, Personal uses, mostly arithmetic and spatial, encompass: personal finance, proportional reasoning, understanding technical documents (plans, charts, etc.), mental maths (percentages, four operations, mental calculating including estimating, etc.), estimation (measures/references/distances such as navigation, etc.), basic geometry (billiards, parking, etc.), and spatial reasoning.
Societal uses - related to data, logic, scale, chance, relationships – are defined in PISA as: structured logical arguments, understanding data (statistical), chance/risk/uncertainty (probabilities), visualization and presenting data, magnitude of numbers (budgets, taxes, etc.), rate of change (exponential, logarithmic, S-curve, etc.), understanding systems and scale (ecology, etc.) including identifying relations between objects.
How can we achieve a more numerate society?
Shockingly perhaps, none of this is particularly new! A 1982 US National Science Foundation report stated:
“more emphasis on estimation, mental maths…
“less emphasis on paper/pencil execution…”
“content in… algebra, geometry, pre-calculus and trigonometry need to be… streamlined to make room for important new topics.”
“discrete mathematics, statistics/probabilities and computer science must be introduced”.
The Center for Curriculum Redesign’s Stockholm Declaration has stated:
“We call for a far deeper and reconceptualized understanding of mathematics by the entire population as a critical right, requiring:
How is the breadth of mathematical application reflected in PISA?
There are four contexts assessed: personal (self, family and peer groups), societal (one's community), occupational (the general world of work) and scientific (application to science and related issues and topics). These contexts are outstanding choices. Furthermore, by weighting them equally, PISA ameliorates the misconception that mathematics is useful only in the scientific context.
How do we make maths relevant for all occupations, and for new occupations?
The synthesis of research by the OECD and the Royal Society highlights the need to rebalance traditional mathematics (geometry, algebra and calculus) with new branches (statistics and probabilities, applied maths and discrete maths) which are relevant for a wide swath of occupations.
The OECD Global Science Forum Report on Mathematics in Industry describes the needs for different types of mathematics: statistics & probabilities; complex systems; computational maths. Additionally, the Royal Society’s ACME 2011 “Mathematics in the workplace and higher education” highlights requirements such as: mathematical modelling (e.g. energy requirement of a water company; cost of sandwich); use of software and coping with problems (e.g. oil extraction; dispersion of sewage); costing (allocation; dispute management) (e.g. Contract cleaning of hospital; management of railway); performance and ratios (e.g. Insurance ratios; glycemic index); risk (e.g. clinical governance; insurance); and quality/SPC control (e.g. furniture; machine downtime; deviation of rails).
How are maths used in personal and societal contexts?
Again, personal and societal uses highlight the need to rebalance traditional mathematics (geometry, algebra and calculus) with new branches (statistics and probabilities, complex systems) and deepening the understanding of basic arithmetic (number sense and proportionality).
John Allen Paulos, Mathematician at Temple University, and Author of “A Mathematician reads the newspaper“ has stated: “Gullible citizens are a demagogue’s dream… almost every political issue has a quantitative aspect”.
In PISA, Personal uses, mostly arithmetic and spatial, encompass: personal finance, proportional reasoning, understanding technical documents (plans, charts, etc.), mental maths (percentages, four operations, mental calculating including estimating, etc.), estimation (measures/references/distances such as navigation, etc.), basic geometry (billiards, parking, etc.), and spatial reasoning.
Societal uses - related to data, logic, scale, chance, relationships – are defined in PISA as: structured logical arguments, understanding data (statistical), chance/risk/uncertainty (probabilities), visualization and presenting data, magnitude of numbers (budgets, taxes, etc.), rate of change (exponential, logarithmic, S-curve, etc.), understanding systems and scale (ecology, etc.) including identifying relations between objects.
How can we achieve a more numerate society?
Shockingly perhaps, none of this is particularly new! A 1982 US National Science Foundation report stated:
“more emphasis on estimation, mental maths…
“less emphasis on paper/pencil execution…”
“content in… algebra, geometry, pre-calculus and trigonometry need to be… streamlined to make room for important new topics.”
“discrete mathematics, statistics/probabilities and computer science must be introduced”.
The Center for Curriculum Redesign’s Stockholm Declaration has stated:
“We call for a far deeper and reconceptualized understanding of mathematics by the entire population as a critical right, requiring:
- a new vision of mathematics education that anticipates needs and reinforces the role of mathematics in society, economies, and individuals, and strengthens gender equity,
- changes to existing Mathematics standards as presently conceived, through a significant rethinking of what branches, topics, concepts and subjects should be taught in Mathematics for human, economic, social and career development…”
Humanity has a very large stake in making these goals
happen, and to do so very soon.
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