Working Mathematically with Students:

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Presentation transcript:

Working Mathematically with Students: The Open University Maths Dept University of Oxford Dept of Education Promoting Mathematical Thinking Working Mathematically with Students: John Mason PGCE Oxford May 2018

Conjectures Everything said here today is a conjecture … to be tested in your experience The best way to sensitise yourself to learners … is to experience parallel phenomena yourself So, what you get from this session is what you notice happening inside you!

Outline Some mathematical tasks Some pedagogic reflection Some mathematical powers & themes Some pedagogical actions The role and nature of attention My focus Attention: its role and nature Meta-Task for you What pedagogic actions do you notice me initiating? The role of pedagogic reflections Slogan It is not the task that is rich, but whether the task is used richly

Calleja Spiral

Another & Another Draw a circle and divide it into four congruent pieces Do it another way What does experience of the task contribute to mathematical thinking? Negotiating ‘same & different’ What could be varied? What seems to be invariant? What constrains variation? Personal Narrative Self-Explanation

Increasing Constraints Draw a quadrilateral Draw a quadrilateral with one pair of opposite sides perpendicular Draw a quadrilateral with both pairs of opposite sides perpendicular What does experience of the task contribute to mathematical thinking? Revealing Awarenesses Enriching accessible example space

Patterns from 2 SVGrid

Patterns from 2 What does experience of the task contribute to mathematical thinking? Discerning Details Recognising Relationships Perceiving Properties Imagining & Expressing Conjecturing & Convincing Specialising & Generalising SVGrid

Multi-Level Initiating of Tasks In how many ways can a unit fraction be expressed as the difference of two unit fractions? Notice that Notice that Ways of initiating activity through presentation of a task Purposeful Practise (recent ATM publication)

Over Flow Imagine a bucket containing water (not necessarily full) Imagine an empty open-topped can being immersed in the bucket. Imagine what happens to the water. What variations might make a difference? What questions might be asked? What might work on the task contribute to mathematical thinking?