AME Institute for Mathematics (Secondary) Teachers
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Designing Tasks to Promote Mathematical Thinking
In Secondary School
Prof John Mason
Open University (UK) & Oxford University (UK)
May 28-29 2012 @ Academy of Singapore Teachers
Click here to register
Fee per participant $200.
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Abstract
Assuming that as teachers, what we want for our students is that they become independent creative mathematical thinkers, participants will be invited to engage in a range of mathematical tasks which will serve as the data for addressing the question of how to engage students in mathematical thinking and how to sustain that thinking so that they develop both reasonable facility with procedures and reasonable appreciation and understanding of relevant mathematical concepts and practices.
Focus for the Institute
The following indicates probable foci that will be subject to modification as we go along in order to meet participants’ interests and concerns as closely as possible.
Principles
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Teaching takes place in time; learning takes place over time.
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Tasks generate activity which provide experience from which it is possible to learn, with suitable reflection.
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Using your own powers gives pleasure; having them usurped gives frustration; dependency demotivates, independence motivates.
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Interest and engagement arise from alignment of use of own powers and ways of working on and with mathematics to make sense of phenomena.
Range of ‘Topics’
Structure of a mathematical topic
Mathematical themes
Frameworks for refining tasks
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Natural powers to use mathematically
Modes of interaction
Task Structures
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Tentative Programme
Session 1 – Monday 28th May 2012 (9.00 am – 12 noon)
Work on several tasks to elucidate possible mathematical powers, themes and modes of interaction, ending with reflection.
Session 2 - Monday 28th May 2012 (12.30pm – 4.30 pm)
Work on several tasks to elucidate the structure of a mathematical topic and the verbs of mathematics, ending with reflection.
Session 3 – Tuesday 29th May 2012 (9am – 1 pm)
Examples of different task structures and ways of presenting tasks.
Work on tasks brought by participants because they require modification or augmentation in order to be effective, ending with reflection on the whole institute.