© 2012 Chris OlleyVisit: www.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?
© 2012 Chris OlleyVisit: www.themathszone.co.uk
The 24 game
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The 24 game – two spot
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The 24 game – three spot
© 2012 Chris OlleyVisit: www.themathszone.co.uk
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
© 2012 Chris OlleyVisit: www.themathszone.co.uk
The five Part Lesson
Starter Activity Exposition Practice Summary
© 2012 Chris OlleyVisit: www.themathszone.co.uk
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]
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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.
© 2012 Chris OlleyVisit: www.themathszone.co.uk
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.
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What’s the Story?
What is mathematics about? What is it for? Is it useful?
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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.
© 2012 Chris OlleyVisit: www.themathszone.co.uk
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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Marking
Shared and consistent mechanisms
Shallow marking Tick marking Mechanical development
Deep marking Personal feedback Skills development
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Assessment
Regular Consistent with external
assessments Consistent with schemes of
work Tracking and predicting
© 2012 Chris OlleyVisit: www.themathszone.co.uk
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
© 2012 Chris OlleyVisit: www.themathszone.co.uk
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
© 2012 Chris OlleyVisit: www.themathszone.co.uk
The Data Handling Cycle
Discovering advanced mathematics, Collins Educational.
1: S p ec ify theP ro b lem
4: S o lve theM athem atic al
P ro b lem
5: Interp ret theS o lutio n
6: C o m p are w ithR eality
3: F o rm ulate theM athem atic al
P ro b lem2: S et up the M o d el
Map of Investigative
Skills
Exploration
Proof
Criticise
Write upRe-draftPresent
Extend
Using algebra
Justify and explain
Generalise and test
Pattern spotting
OrganisationTabulation
Breaking down
Diagrammatic representation
Design
© 2012 Chris OlleyVisit: www.themathszone.co.uk
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.
© 2012 Chris OlleyVisit: www.themathszone.co.uk
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.
© 2012 Chris OlleyVisit: www.themathszone.co.uk
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.
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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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ICT: Teaching
Lesson Planning Learning outcomes Structure Assessment
Classroom management Furniture Movement Grouping
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Classroom Management Strategies
What can you do? What must you not do?
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Keeping them Onside
A’s – B’s – C’s – D’s
A B C D
A B C D
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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.
© 2012 Chris OlleyVisit: www.themathszone.co.uk
WOW LessonsLet no one ignorant of mathematics enter here.Plato (429–347 BC)
Let no one ignorant of mathematics enter here.Plato (429–347 BC)
ProgressionContextStructurePurposeMystery, wonder,
atmosphere, revelation, theatre, surprise, tangents...
Colour and MusicCreativityImaginationTangential thinking
Challenge and accessibility
FunHumour
History
ICT
Controversy
Multi-skilledLinkages
WOW lessons are …
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Not much, really ......
Structure Planning Purposeful Developmental Coherent Managed WOW!
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Nelson Mandela
Education is the most powerful weapon which you can use to change the world.
© 2012 Chris OlleyVisit: www.themathszone.co.uk
Off the Scheme
Engaging maths activities for a broader perspective .....
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