I would describe a rich task as having a range of characteristics, offering different opportunities to meet the different needs of learners at different times. What is also apparent to me is that much of what it takes to make a rich task "rich" is the environment in which it is presented, which includes the support and questioning that is used by the teacher and the roles that learners are encouraged to adopt. That is, an environment in which learners are not passive recipients of knowledge, accepting what is given, but independent, assertive constructors of their own understanding who challenge and reflect. On its own a rich task is not rich - it is only what is made of it that allows it to fulfill its potential. With this in mind it might still be useful to list some of the things I might say when describing a rich task.
The guidance document "Mathematics at Key Stage 4: developing a scheme of work", produced by the Secondary National Strategy in 2007 describe a rich task as:
- accessible and extendable,
- one which allows learners to make decisions,
- involving learners in testing, proving, explaining, reflecting and interpreting,
- promoting discussion and communicatons,
- encouraging originality and invention,
- encouraging 'what if' and 'what if not' questions,
- are enjoyable and contain the opportunity for surprise.
An article on the NRICH website expands further on this idea.
An early definitition of a "rich mathenatical task" was given in Ahmed A (1987) Better Mathematics HMSO:London.
This book has been revised and republished as:
Ahmed, A. and Williams, H (2007) Even Better Mathematics, London: Network Continuum.