How to Write/Choose a Risp
What follows are my tentative suggestions:
Everyone should be able to see the point of the initial question,
and be able to make a start, regardless of their prior technical knowledge.
An element of student choice at the beginning of the exploration may be helpful:
picking a number, or a curve, or an equation.
Students will then take ownership of their example, and will it to succeed.
It should be possible to extend the risp, so that all students can stay interested
in the situation.
Weaker students should find the risp generates accessible and engaging material throughout,
while stronger students should be able to ask harder and deeper questions as they get into the problem.
In other words, differentiated learning should naturally take place.
A risp should encourage fresh questions,
divergent approaches, and open-ended thinking.
A helpful risp will practice key mathematical skills indirectly,
that is, the key skills are needed to tackle the risp and are not simply practiced for their own sake.
A good risp will stimulate curiosity in the student:What if I do this?
A good risp is often synoptic, calling on the syllabus in its entirity,
and rehearses insights and techniques that the student will not have practiced for a while.
This encourage the formation of links between different parts of mathematics,
which is a great aid to understanding.
It will often be the case that a risp will find ICT helpful in some way, often as a labour-saving device.