ABSTRACT
To study mathematics is one thing; to learn how to study more effectively and efficiently is quite another. Similarly, to teach mathematics is one thing, but to learn to teach mathematics more effectively and efficiently is also quite another. Neither studying nor teaching is improved simply through experience alone. Both require active intention and directed attention (Eraut, 1994; Moon, 1999). True, habits such as preferences for doing things in a particular order or in a particular manner are picked up along the way, simply through studying or teaching. But habits are not always useful, and if useful for a time, may not continue to be maximally efficient ways of deploying attention or energy. More positively, both studying and teaching can be rich sources of pleasure and fulfilment as domains for lifelong enquiry and development.
