CMTP: Changes in Mathematics Teaching Project

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Task types used

For this section we use a similar table to that in which we recorded what teachers said about tasks and this led us to see that the tasks we observed illustrated what teachers said about the purposes of tasks.

Mathematical learning purpose	Specific applications seen in lessons
Learn how to tackle complex tasks	See previous section Using model, diagram, symbols and words at every stage of calculation or algebraic manipulation Making choices and combining choices
Promote thinking Play with concepts from a variety of directions Develop generalities	Offering ideas which get gradually more complex, tackled through whole class discussion Finding 'hidden' objects using efficient questioning to eliminate and focus Engage students physically in mathematics, number line, reflections etc. Comparing observations to theoretical deductions Predicting what will happen if... Giving definition and asking for examples Giving examples and asking students to decide what the definition is Compare and match examples to identify central features Constructing own examples equivalent to given example Devising a generality from empirical evidence Devising a generality from spatial structure
Consolidate 'basic' skills Work reflectively on own Develop memory and adaptation	Practising skills which will be combined later Offer interesting problem and discuss possible methods from students Show work from imaginary student which is not quite finished - what do we have to do to finish it? Emphasise key idea, get students to keep saying what it is
Introduce new ideas based on familiar mathematical knowledge Challenge and extend existing ideas	Introducing new ideas as adaptations or reversals of familiar ideas How is what you did in X like (or unlike) what you did in Y? Create objects which fit sets of characteristics
Memory, fluency, action, speed accuracy	Working on remembering vocabulary Games which reveal mathematical features 'Act out' graphs while describing what they tell you
Let me know what they can do Adapt knowledge	Say what they already know about a new topic, give examples to provide raw material for the teacher to develop further discussion, ideas and examples Peer-teaching: students have prepared 'lessons' about given topics as revision
Compare multiple ways to do things Express ideas Expose contradictions	Experiment with ways of doing things and compare them Students show workings on board Encourage use of self-checking strategies
Make connections and see what maths means	Work on a range of tasks which relate to one resource, but are mathematically varied: number, shape, construction, word problems
Words, writing and language	Suggest meanings of technical words, either from previous lessons or from outside experience - e.g. 'what do I mean by...?', what do you think ... means?', 'what do you know about...?' Deliberately using range of language, e.g. division, goes into, how many, over..
Learning how to do test questions	Discussing how to tackle test questions and categorising made-up different answers