Using a Risp: What Can Go Wrong...

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4. "The algebra is getting horrible here..."**

The textbook exercises that our students have grown up on

are generally 'fixed' so that the numbers 'work out nicely'.

This is not quite what happens in real life with mathematics,

but it does have the advantage that students can concentrate on the skill
they are meant to be learning

without grappling with expressions
that do not factorise or with surds that refuse to simplify happily.

However, when we ask our students to take on a risp, there are no
such guarantees of numerical serendipity.

They may well be choosing their
own starting numbers, and given the openness of the problem,
they may head off in all sorts of unexpected directions.

A risp may have a simple solution with judicious early choices,
but if students bark up Tree B rather than Tree A (the one that seems
obvious to us),

they may give themselves an algebraic headache.
Risp 25 is a case in point:

So what is the answer? I would say that the onus is on the risp-writer
to ensure that the weaker students in particular

are given a carefully-structured opening
to the risp that ensures a fairly safe passage through the initial moments.

Maybe the choice of numbers or functions will have to be restricted at the start.

In other words, effective early scaffolding needs to be in place.