Working Effectively with All Learners

Stage: 1, 2, 3, 4 and 5
Article by Jennifer Piggott

This short article offers some questions and prompts to encourage discussion about what experiences you want to give learners to help them develop their full potential in mathematics.

Why not use the questions in the first section as a stimulus for discussion in a team meeting or when you wish to reflect on your own practice? They ask you to think about what experiences learners have in your classroom and what your expectations are of them.

The second section gives some ideas for opening up lessons to encourage more discussion and mathematical activity. There are many questions and prompts you can use as a teacher to engage learners in thinking more deeply and communicating their mathematics (See references to the "Questions and Prompts" and "Thinkers" books).
 

Questions to ask as you reflect on the experiences you offer in your classroom:

 

What are we trying to encourage when we ask our learners to "do mathematics"?

What sort of mathematics appeals to them?
What do good problems look like?
What sorts of thinking do we want to encourage?
What kinds of questioning would help?
What can you do to change things?

 

Ideas to consider when you wish to encourage mathematical discussion with your learners:

 

'Analyses of the kinds of questions that teachers ask in classrooms have shown that many teachers ask questions that test the ability of pupils to recall facts and procedures (often called lower-level questions), rather than the ability of pupils to apply, synthesis or explain their knowledge (often called higher-level questions).'
Askew and Wiliam

Why not select one of the sub-headings below and work with colleagues on how you might integrate that idea into a particular lesson?
 

Exemplifying and 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 and Conjecturing

Of what is this a special case?
What happens in general?
Is it always, sometimes, never true?
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 and 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 ...

This will help you to think about your learners' classroom experiences.

For more information on effective questioning look at Questions and Prompts for Mathematical Thinking, an excellent and thought-provoking book with lots of practical ideas.
 

References and other useful material:

 

Askew, M. Wiliam, D. (1995) Recent Research in Mathematics Education 5-16, HMSO.

Bills, C. Bills, L. Mason, J. Watson, A. (2004) Thinkers: A collection of activities to provoke mathematical thinking, ATM

Watson, A. & Mason, J. (1998) Questions and Prompts for Mathematical Thinking, ATM.

Jeffcoat, M. Jones, M. Mansergh, J. Mason, J. Sewell, H. Watson, A. (2004) Primary Questions and Prompts, ATM.