Working Effectively with All Learners
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 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:
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: