Working Effectively with

Young Mathematicians with High Potential

What are we trying to encourage?

What sort of mathematics appeals to them?

What would the problems look like?

What thinking are they encouraging?

What kinds of questioning would help?

Mathematical Thinking and Questioning

Exemplifying, Specialising

Give me one or more examples of…

Describe, demonstrate, tell, show, choose, draw, find an example of…

Is … an example of …?

Find a counter-example of…

Are there any special examples of…?

Completing, Deleting, Correcting

                                                                                             

What must be added/removed/altered to ensure/allow/contradict?

What can be added/removed/altered without affecting …?

Tell me what’s wrong with …?

What needs to be changed so that…?

Changing, Varying, Reversing, Altering

Change something to see an effect.

What if …?

If this is the answer to a similar question, what was the question?

Can you do this another way?

Which way is the quickest, easiest, …?

Change … in response to imposed constraints

Generalising, Conjecturing

Of what is this a special case?

What happens in general?

Is it always, sometimes, never …?

Describe all possible … as succinctly as you can

What can change and what has to stay the same so that … is still true?

Explaining, Justifying, Verifying, Convincing, Refuting

Explain why …

Give a reason (using or not using…)

How can we be sure that …?

Tell me what is wrong with …

Is it ever false/always true that …?

How is … used in …?

Explain role or use of …

Convince me that …

Comparing, Sorting, Organising

What’s the same and what’s different about …?

Sort the following according to  …

Is it or is it not …?