Thematic mathematics: The combinatorics of prime factorizations

In this article, we use a particular example to illustrate a thematic approach to the teaching and learning of mathematics. Our theme, suitable for undergraduates and able sixth-form students, is the enumeration of mathematical objects associated with the prime factorizations of integers. It is shown in detail how this gives rise to some beautiful mathematics. Potential educational benefits of the theme-driven exploration of mathematics are discussed, as are the possible difficulties that may be encountered when carrying out such activities. The various instructional styles associated with a thematic approach are also considered briefly. © The Author 2009. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications. All rights reserved. For permissions, please email: [email protected].