Knowledge framework for mathematics
The ‘knowledge framework’ is designed to help students explore, discuss, and form an understanding of each of the eight areas of knowledge. The knowledge framework isn’t a formal element of the TOK essay or presentation (ie, it isn’t directly assessed); instead, it is designed to present various consideration points that that can then be used to compare and contrast the different areas of knowledge, as well as tying them to the ways of knowing.
1. Scope and applications
What is the social function of mathematics? How many different forms does it encompass (eg calculus, algebra, applied mathematics, etc.)? What are their separate aims? To what extent is mathematics influenced by the society and culture in which it is pursued? How important is mathematics?
2. Concepts and language
How do we use language to express the knowledge found within mathematics? To what extent does this differ according to different forms of mathematics? Are there any central concepts for which we need specific language before approaching mathematics?
Which ways of knowing do we use in order to connect with, and understand, mathematics? Which ways of knowing do the mathematicians themselves use in order to study mathematics and communicate their understanding of it?
4. Historical development
How has our understanding and perception of mathematics changed over time? How has the role of mathematics within society developed? To what extent has the nature of mathematics (for example, the different forms of mathematics) changed? What relationship does today’s mathematical understanding have with that of the past? (to paraphrase Newton, does it ‘stand on the shoulders of giants’?)
5. Links to personal knowledge
To what extent are you involved with mathematics? How is your perception of the world, and your position it in, affected by mathematics?