the nqt of maths

The NQT of Maths

Meeting the Challenges of the First Year

Chris Olley

[email protected]

© 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?


The 24 game


The 24 game – two spot


The 24 game – three spot


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


The five Part Lesson

Starter Activity Exposition Practice Summary


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]


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.


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.


What’s the Story?

What is mathematics about? What is it for? Is it useful?


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.


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?


Marking

Shared and consistent mechanisms

Shallow marking Tick marking Mechanical development

Deep marking Personal feedback Skills development


Assessment

Regular Consistent with external

assessments Consistent with schemes of

work Tracking and predicting


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


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


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


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.


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.


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.


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


ICT: Teaching

Lesson Planning Learning outcomes Structure Assessment

Classroom management Furniture Movement Grouping


Classroom Management Strategies

What can you do? What must you not do?


Keeping them Onside

A’s – B’s – C’s – D’s

A B C D

A B C D


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.


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 …


Not much, really ......

Structure Planning Purposeful Developmental Coherent Managed WOW!


Nelson Mandela

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


Off the Scheme

Engaging maths activities for a broader perspective .....

the nqt of maths

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