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The NQT of Maths Meeting the Challenges of the First Year Chris Olley

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© 2012 Chris Olley Visit: Introductions Who are you? Where and when were you trained? Which school do you work in? What type is it? What teaching groups do you have?

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© 2012 Chris Olley Visit: The 24 game

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© 2012 Chris Olley Visit: The 24 game – two spot

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© 2012 Chris Olley Visit: The 24 game – three spot

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© 2012 Chris Olley Visit: Activity: Design Your Own Devise three 24 game cards: one each of one, two and three spots. Explain how you decide on the difficulty level. How could you devise an algorithm e.g. a software program to generate further sets at different (spot) levels

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© 2012 Chris Olley Visit: The five Part Lesson Starter Activity Exposition Practice Summary

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© 2012 Chris Olley Visit: Anonymous Like the crest of a peacock so is mathematics at the head of all knowledge. [An old Indian saying. Also, “The Crest of the Peacock" is the title of a book by G.G. Joseph]

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© 2012 Chris Olley Visit: Bell, Eric Temple ( ) Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.

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© 2012 Chris Olley Visit: Einstein, Albert ( ) It is nothing short of a miracle that modern methods of instruction have not yet entirely strangled the holy curiousity of inquiry. In H. Eves Return to Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1988.

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© 2012 Chris Olley Visit: What’s the Story? What is mathematics about? What is it for? Is it useful?

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© 2012 Chris Olley Visit: What is a square? Einstein, Albert ( ) As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. In J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.

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© 2012 Chris Olley Visit: Marking and other forms of Assessment Why do you mark students work? When do you do it? When do you feedback the outcome How do you do that? What does it mean? To you To them What effect does it have? How about other assessments?

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© 2012 Chris Olley Visit: Marking Shared and consistent mechanisms Shallow marking Tick marking Mechanical development Deep marking Personal feedback Skills development

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© 2012 Chris Olley Visit: Assessment Regular Consistent with external assessments Consistent with schemes of work Tracking and predicting

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© 2012 Chris Olley Visit: Notes and Examples (Year 7) What I can do with an example from the exercise (Year 8) What I can do with my own example (Year 9) What I can do and how it works with extended examples (Year 10) What I can do and why it works with annotated exemplification (Year 11) What I can do and here’s a proof

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© 2012 Chris Olley Visit: Notes and Examples Supported with writing frames In this lesson I learned how to An example: Part of the assessment: deep marking Writing up time: proper revision Open book tests: (but closed end of year) Individual and group presentations

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© 2012 Chris Olley Visit: The Data Handling Cycle Discovering advanced mathematics, Collins Educational.

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Map of Investigative Skills Exploration Proof Criticise Write up Re-draft Present Extend Using algebra Justify and explain Generalise and test Pattern spotting Organisation Tabulation Breaking down Diagrammatic representation Design

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© 2012 Chris Olley Visit: What is a Square? Kasner, E. and Newman, J. Mathematics is the science which uses easy words for hard ideas. Mathematics and the Imagination, New York: Simon and Schuster, 1940.

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© 2012 Chris Olley Visit: Talking Maths Gauss, Karl Friedrich ( ) You know that I write slowly. This is chiefly because I am never satisfied until I have said as much as possible in a few words, and writing briefly takes far more time than writing at length. In G. Simmons Calculus Gems, New York: McGraw Hill inc., 1992.

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© 2012 Chris Olley Visit: Pascal, Blaise ( ) Words differently arranged have a different meaning and meanings differently arranged have a different effect. W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.

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© 2012 Chris Olley Visit: ICT: Resources Graphical Calculators Specialist Resources (Dynamic geometry, algebra, statistics, graph plotters,....) Generic Resoures (Spreadsheet, Database, Logo) Specific curriculum support (e.g. SMILE, ATM,...) Exercise games (Mathblaster,...) Integrated Learning Systems

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© 2012 Chris Olley Visit: ICT: Teaching Lesson Planning Learning outcomes Structure Assessment Classroom management Furniture Movement Grouping

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© 2012 Chris Olley Visit: Classroom Management Strategies What can you do? What must you not do?

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© 2012 Chris Olley Visit: Keeping them Onside A’s – B’s – C’s – D’s ABCD ABCD

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© 2012 Chris Olley Visit: Douglas Adams Human beings, who are almost unique in having the ability to learn from the experience of others, are also remarkable for their apparent disinclination to do so.

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© 2012 Chris Olley Visit: WOW Lessons Let no one ignorant of mathematics enter here. Plato (429–347 BC) Let no one ignorant of mathematics enter here. Plato (429–347 BC) Progression Context Structure Purpose Mystery, wonder, atmosphere, revelation, theatre, surprise, tangents... Colour and Music Creativity Imagination Tangential thinking Challenge and accessibility Fun Humour History IC T Controvers y Multi-skilled Linkages WOW lessons are …

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© 2012 Chris Olley Visit: Not much, really Structure Planning Purposeful Developmental Coherent Managed WOW!

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© 2012 Chris Olley Visit: Nelson Mandela Education is the most powerful weapon which you can use to change the world.

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© 2012 Chris Olley Visit: Off the Scheme Engaging maths activities for a broader perspective.....

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