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AOK: Mathematics
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Mathematics
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Definition
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The abstract science of number, quantity, and space.
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Mathematics may be studied in its own right, or as it is applied to
other disciplines such as physics and engineering.
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The study of the measurement, properties, and relationships of
quantities and sets, using numbers, and symbols
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Mathematics: The TOK way
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Math is sometimes seen as being on the opposite end of art
(in terms of the necessity of structure)…however…
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Math and art can spill over.
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Math and architecture?
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Math can spill over to artistic realms
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Architecture, engineering, medicine, social sciences
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MATH AND ARTS ARE NOT MUTUALLY EXCLUSIVE
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Framework: Elements to think
about
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Scope and Application
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What is the social function of math?
How many different forms does it encompass?
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What are their separate aims?
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To what extent is math influenced by the society and culture in
which it is pursued?
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Elements to think about:
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Concepts and Language
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How do we use language to express the knowledge found within
mathematics?
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To what extent does this differ according to different forms of
mathematics?
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Are there any central concepts for which we need specific
language before approaching mathematics?
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Elements to think about:
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Methodology
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Which ways of knowing do we use in order to connect with, and
understand, mathematics?
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Which ways of knowing do the mathematicians themselves use in
order to study mathematics and communicate their
understanding of it?
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Elements to think about:
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Historical Development
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How has our understanding and perception of mathematics
changed over time?
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How has the role of mathematics within society developed? To
what extent has the nature of math changed?
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What relationship does today’s mathematical understanding have
with that of the past….”stand on the shoulders of giants”
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Elements to think about:
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Links to Personal Knowledge
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To what extent are you involved with mathematics?
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How is your perception of the world, and your position in it,
affected by mathematics?