Effective Learning & Teaching in Mathematics & Its Applications

John Mason

One thing we do not seem to learn from experience, is that we seldom learn from experience alone.

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.

This chapter concentrates on the role of reflection in learning from experience as a lecturer or tutor. After considering some reasons for engaging in active reflection in the first section, some suggestions are made concerning effective ways to use memories of incidents as the basis for methodical reflection with a view to improving student and tutor experience. This then raises the question of how you know that things are improving, and for whom. Such a focus on improvement is important given the encouragement evident in other chapters to introduce new practices.

One important consequence of such reflection is that it is possible and valuable to assist students in becoming more efficient and effective learners, and one of the

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