In the process of working with some groups of teachers on this topic, discussed in an earlier article , the following table was developed. It provides examples of generic questions that can be used to guide children through a mathematical investigation, and at the same time prompt higher levels of thinking. Adults and experienced investigators naturally ask these questions of themselves, but children, being inexperienced (formal) investigators do not. Thus, the interaction with the teacher becomes a crucial factor in promoting mathematical achievement.

LEVELS OF THINKING	GUIDE QUESTIONS
Memory: recalls or memorises information	What have we been working on that might help with this problem?
Translation: changes information into another form	How could you write/draw what you are doing? Is there a way to record what you've found that might help us see more patterns?
Interpretation: discovers relationships	What's the same? What's different? Can you group these in some way? Can you see a pattern?
Application: solves a problem - use of appropriate generalisations and skills	How can this pattern help you find an answer? What do think comes next? Why?
Analysis: solves a problem - conscious knowledge of the thinking	What have you discovered? How did you find that out? Why do you think that? What made you decide to do it that way?
Synthesis: solves a problem that requires original, creative thinking	Who has a different solution? Are everybody's results the same? Why/why not? What would happen if....?
Evaluation: makes a value judgement	Have we found all the possibilities? How do we know? Have you thought of another way this could be done? Do you think we have found the best solution?