Mathematics knowledge questions
Knowledge questions (KQs) form the heart of the TOK course, and provide us with the opportunity to discuss, explore, and sometimes argue about the way in which we acquire, use, and evaluate our knowledge about the world.
Although the mathematics knowledge questions that you see here link primarily to this area of knowledge, many of them link to other AOKs, and themes, so one of the first things to consider is how they relate to, and impact on, other aspects of the course.
Knowledge questions on the nature and scope of mathematics
- These KQs on the mathematics relate to Big Question 1, our first BQ unit for TOK
- They also link to the nature and scope of mathematics, part of the IB’s knowledge framework
- Good KQs ask how we know about the world (second-order knowledge), rather than what we know about the world (first-order knowledge)
- Being able to tell the difference between first and second-order knowledge can be difficult, but it is the most important attribute of successful TOK thinking
Is mathematics the most ‘fundamental’ of all the areas of knowledge?
Does mathematics provide us with certain knowledge?
Are mathematical axioms the same as truth?
Is the term ‘mathematical proof’ different from other types of proof?
Is mathematics defined by its content or method?
How does mathematical reasoning differ from other forms of reasoning?
Is mathematical knowledge always abstract?
Why is mathematics so highly esteemed?
Is mathematics based on ‘unproven truths’?
Knowledge questions on the relationship between mathematics and values
- These KQs on mathematics relate to Big Question 2, our second BQ unit for TOK
- They also link to mathematics and ethics, part of the IB’s knowledge framework
- Good KQs ask how we know about the world (second-order knowledge), rather than what we know about the world (first-order knowledge)
- Being able to tell the difference between first and second-order knowledge can be difficult, but it is the most important attribute of successful TOK thinking
Are there special ethical responsibilities regarding how mathematical knowledge is produced and used?
Does basing decisions on algorithms create solid ethical knowledge?
Can ethical knowledge be objectively calculated via mathematics?
How different are mathematics and ethics in terms of the evidence used to justify knowledge claims?
Who should create the ethical framework used to produce and use mathematical knowledge?
Knowledge questions on the communication of ideas in mathematics
- These KQs on mathematics relate to Big Question 3, our third BQ unit for TOK
- They also link to methods, tools, and practices of mathematics, part of the IB’s knowledge framework
- Good KQs ask how we know about the world (second-order knowledge), rather than what we know about the world (first-order knowledge)
- Being able to tell the difference between first and second-order knowledge can be difficult, but it is the most important attribute of successful TOK thinking
Does mathematics provide us with the most objective form of language?
How can data visualizations be manipulated in order to spin the knowledge they communicate?
Do mathematical symbols convey the same type of meaning as ordinary words?
How can the intention behind statistics interfere with its objectivity?
How can statistics be used to manipulate people?
Is it possible to present data objectively?
Knowledge questions on mathematics, perspectives, and context
- These KQs on mathematics relate to Big Question 4, our fourth BQ unit for TOK
- They also link to perspectives & context related to mathematics, part of the IB’s knowledge framework
- Good KQs ask how we know about the world (second-order knowledge), rather than what we know about the world (first-order knowledge)
- Being able to tell the difference between first and second-order knowledge can be difficult, but it is the most important attribute of successful TOK thinking
Is mathematics ever aligned to a particular culture or tradition?
How easy is it to establish consensus in mathematics?
Is it a paradox that mathematics is both a human construct, and objectively true about the world?
To what extent do assumptions underpin our understanding of mathematics?
Can we draw on personal experiences to help produce and understand mathematical knowledge?
Knowledge questions on the creation of new ideas in mathematics
- These KQs on mathematics relate to Big Question 5, our fifth BQ units for TOK
- They also link to methods, tools, and practices of mathematics, part of the IB’s knowledge framework
- Good KQs ask how we know about the world (second-order knowledge), rather than what we know about the world (first-order knowledge)
- Being able to tell the difference between first and second-order knowledge can be difficult, but it is the most important attribute of successful TOK thinking
How has the development of technology impacted mathematics?
Does mathematics progress cumulatively, or does new knowledge violently destroy old knowledge?
Is mathematics invented or discovered – or created in some other way?
Why is it so difficult to produce mathematical proof?
Does mathematics develop in the same way as other areas of knowledge?
Is mathematical knowledge driven forward by individual thinkers?
Knowledge questions on becoming a discerning knower about mathematics
- These KQs on mathematics relate to Big Question 6, our final BQ unit for TOK
- They also link to methods, tools, and practices of mathematics, part of the IB’s knowledge framework
- Good KQs ask how we know about the world (second-order knowledge), rather than what we know about the world (first-order knowledge)
- Being able to tell the difference between first and second-order knowledge can be difficult, but it is the most important attribute of successful TOK thinking
To what extent can we use intuition to evaluate mathematical claims?
Is it possible to ‘experience’ mathematics?
Explore these KQs via the latest real-world situations
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