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The NQT of Maths

The NQT of Maths. Meeting the Challenges of the First Year Chris Olley chris@themathszone.co.uk. 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?. The 24 game. The 24 game – two spot.

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The NQT of Maths

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  1. The NQT of Maths Meeting the Challenges of the First Year Chris Olley chris@themathszone.co.uk

  2. 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?

  3. The 24 game

  4. The 24 game – two spot

  5. The 24 game – three spot

  6. 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

  7. The five Part Lesson • Starter • Activity • Exposition • Practice • Summary

  8. AnonymousLike 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]

  9. Bell, Eric Temple (1883-1960)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.

  10. Einstein, Albert (1879-1955)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.

  11. What’s the Story? • What is mathematics about? • What is it for? • Is it useful?

  12. What is a square? • Einstein, Albert (1879-1955)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.

  13. 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?

  14. Marking • Shared and consistent mechanisms • Shallow marking • Tick marking • Mechanical development • Deep marking • Personal feedback • Skills development

  15. Assessment • Regular • Consistent with external assessments • Consistent with schemes of work • Tracking and predicting

  16. 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

  17. 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

  18. The Data Handling Cycle • Discovering advanced mathematics, Collins Educational.

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

  20. 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.

  21. Talking Maths • Gauss, Karl Friedrich (1777-1855)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.

  22. Pascal, Blaise (1623-1662)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.

  23. 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

  24. ICT: Teaching • Lesson Planning • Learning outcomes • Structure • Assessment • Classroom management • Furniture • Movement • Grouping

  25. Classroom Management Strategies • What can you do? • What must you not do?

  26. Keeping them Onside • A’s – B’s – C’s – D’s A B C D A B C D

  27. 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.

  28. Let no one ignorant of mathematics enter here. Plato (429–347 BC) WOW Lessons Progression Context Structure Purpose Mystery, wonder, atmosphere, revelation, theatre, surprise, tangents... Challenge and accessibility WOW lessons are … Colour and Music Creativity Imagination Tangential thinking Controversy Multi-skilled Linkages ICT Fun Humour History

  29. Not much, really ...... • Structure • Planning • Purposeful • Developmental • Coherent • Managed • WOW!

  30. Nelson Mandela Education is the most powerful weapon which you can use to change the world.

  31. Off the Scheme • Engaging maths activities for a broader perspective .....

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