Learning and teaching mathematics: A study of a multiple-strategy approach to locating the centre of a circle

Problem-solving plays a crucial role in mathematics education. One of the aims of teaching through problem-solving is to encourage students to refine and build their own processes over time as their experience allows them to discard some ideas and makes them aware of other possibilities (Carpenter, 1989). In addition to developing their knowledge, students also acquire an understanding of when it is appropriate to use particular strategies. Emphasis is placed on making students responsible for their own learning rather than letting them feel that the methods that they are using are the inventions of others. Considerable importance is placed on exploratory activities, observation and discovery, and trial and error. Students must develop their own ideas, test them, discard them if they are not consistent, and try something else (National Council of Teachers of Mathematics [NCTM], 1989). Students become more involved in problem-solving by formulating and solving their own problems, or by rewriting problems in their own words to aid their understanding. Crucially, students are encouraged to discuss the processes that they are using to improve their understanding, gain new insights into the problem, and communicate their ideas (Thompson, 1985; Stacey & Groves, 1985). Copyright © 2012 Association for Mathematics Education of South Africa (AMESA).