Knowledge in Mathematics
A course likely to offer a window into the processes employed in the discipline to generate knowledge together with a glimpse of the organization and structure of some of the significant mathematics ideas.
Mathematics is often thought of as a science of quantity and space, allowing us to perceive relationships, patterns and structure in different aspects of the world. It is built upon both logic and intuition, analysis and construction, and focuses on both particularities and generalities. It has a particular language consisting of notations and symbols, together with axioms, postulates and definitions on the basis of which the entire structure is built. It is these very characteristics which often contribute to the difficulty in understanding the subject – everything is considered fixed and given. This may be alleviated to some extent if teachers and other professionals working in the area of mathematics education appreciated the nature and methods of the discipline. Such an understanding is likely to promote better judgments regarding worthwhile tasks and activities and choice of appropriate representations and openness to different methods of working on problems.
This course will be offered to the MA Education students who are interested in developing
an understanding of mathematics. This course is likely to offer a window into the processes
employed in the discipline to generate knowledge together with a glimpse of the
organization and structure of some of the significant mathematics ideas. This will done
through a historical study of few selected areas from school mathematics, namely Numbers and Number Systems, Algebra and Geometry, so that the evolving nature and methods of the discipline as a result of human activity is well illustrated. It would aim to consolidate the nature and methods of the discipline by elucidating the nature of abstraction, ‘objects’ of study and the role of symbols in mathematics. This organization of the course would also help them revisit the content and draw connections between various ideas, often seen as distinct. It will also provide opportunities to work on problems requiring school-level mathematical competence to appreciate the nature of mathematical enquiry. It would seek to help students to draw out connections between the nature and methods of mathematics as a discipline and common approaches to teaching and learning of school mathematics.