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KQs for Mathematics, Making connections to the core theme, Mathematics -…
KQs for Mathematics
Scope
• Why is mathematics so important in other areas of knowledge, particularly the natural sciences?
• How have technological innovations, such as developments in computing, affected the scope and nature of mathematics as an area of knowledge?
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• Does mathematics only yield knowledge about the real world when it is combined with other areas of knowledge?
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Ethics
• If mathematical knowledge is highly valued, does this place special ethical responsibilities on mathematicians when they are making claims?
• On what criteria could we decide whether mathematicians should be held responsible for unethical applications of their work?
• How are unethical practices, such as “data dredging”, used by statisticians to deliberately manipulate and mislead people?
• Is it ethically justifiable for academic mathematicians to spend time doing research that does not have immediate useful applications?
• Do mathematical judgments and ethical judgments face similar challenges in terms of the evidence available to support them?
• Are mathematicians the people best placed to create codes of ethics for professional mathematicians?
Perspective
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• How significant have notable individuals been in shaping the nature and development of mathematics as an area of knowledge?
• What is the role of the mathematical community in determining the validity of a mathematical proof?
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• If mathematics is created by humans, is it still possible to accept mathematical truths as objective facts about the world?
• Are all of the areas of knowledge in the TOK course themselves embedded in a particular tradition or bound to a particular culture?
Methods and tools
• Is mathematical reasoning different from scientific reasoning or reasoning in other areas of knowledge?
• What is meant by the term “proof” in mathematics, and how is this similar to, or different from what is meant by this term in other areas of knowledge?
• How do mathematicians reconcile the fact that some conclusions seem to conflict with our intuitions?
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• How is an axiomatic system of knowledge different from, or similar to, other systems of knowledge?
• Do mathematical symbols have meaning in the same way that words have meaning? Is personal experience more important or less important in mathematics compared to other areas of knowledge?
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