Areas of knowledge
The areas of knowledge, which are situated within the perimeter of the TOK diagram (figure 1), are subject areas or disciplines into which knowledge is frequently classified. They may be seen as an application of ways of knowing, perhaps shaped by methodology, to particular subject matter. The questions that follow in this section deal with both the rationale for such classification and the interdisciplinary comparisons that clarify or challenge the division of knowledge into areas. Reference to the following linking questions may also be useful.
The students’ own experience as knowers would ideally base many of the questions on their studies in the Diploma Programme. Teachers may find it necessary to supplement the students’ educational experience with additional concepts, but they should be guided always by the aim of stimulating students’ personal reflection on knowledge. The question “How do I know?”, which is implied in the “Ways of knowing” section, interacts in this section with another question, “What do I know?”, or, more specifically, “How do I know that a given assertion is true, or a given judgment is well grounded?”
Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.
Bertrand Russell (1917)From a TOK point of view mathematics is a rather special area of knowledge. On the one hand it seems to supply a certainty often missing in other disciplines. On the other, its methods—for example, the application of strict logical procedures to supposedly self-evident first principles—suggest a subject matter that is removed from the real world. It is hardly surprising then to find a variety of responses to mathematical knowledge, from astonishment at the beauty of some mathematical argument, to wonder at the power of mathematics to solve problems in the sciences or engineering, to frustration in the face of apparently...