Mathematics • Definition • The abstract science of number, quantity, and space. • Mathematics may be studied in its own right, or as it is applied to other disciplines such as physics and engineering. • The study of the measurement, properties, and relationships of quantities and sets, using numbers, and symbols
Mathematics: The TOK way • Math is sometimes seen as being on the opposite end of art (in terms of the necessity of structure)…however… • Math and art can spill over. • Math and architecture? • Math can spill over to artistic realms • Architecture, engineering, medicine, social sciences • MATH AND ARTS ARE NOT MUTUALLY EXCLUSIVE
Framework: Elements to think about • Scope and Application • What is the social function of math? • How many different forms does it encompass? • What are their separate aims? • To what extent is math influenced by the society and culture in which it is pursued?
Elements to think about: • 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?
Elements to think about: • Methodology • 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?
Elements to think about: • 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 math changed? • What relationship does today’s mathematical understanding have with that of the past….”stand on the shoulders of giants”
Elements to think about: • Links to Personal Knowledge • To what extent are you involved with mathematics? • How is your perception of the world, and your position in it, affected by mathematics?