Anne Watson East London Maths Forum June 2008 Trigonometry 26 cm 68 mm θ A B C Trigonometry Triangle properties not names right angle orientation anglesum Labelling conventions vertex letters are not algebra lengths are not accurate ID: 432275
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Slide1
The choirs and orchestras of secondary mathematics
Anne Watson
East London Maths Forum
June 2008Slide2
Trigonometry
2.6 cm
68 mm
θ
A
B
CSlide3
Trigonometry
Triangle properties (not names): right angle; orientation; angle-sum
Labelling (conventions): vertex letters are not algebra; lengths are not accurate;
θ
is ‘theta’ and often used for angles; what is the curved line?
Concepts: ratio; inverse function; transforming equations etc. …Slide4
What prior knowledge is helpful? What is unhelpful?
Images
Language
Methods
Contributory concepts
AssumptionsLimitations
………………. etc.Slide5
Whole school approaches to creating the orchestraSlide6
Straight line graphsSlide7
Internet images of straight line graphs
Nearly all positive
Negatives go through zero or are about fitting lines to data points
Key Maths says ‘top left to bottom right’Slide8
Straight line graphs
Graphs: represent a quantitative relationship; relation between line and coordinate pairs (conventions and meaning)
Reading a graph: axes; continuity; (conventions and meaning)
Dimensions of variation & range of possible changes
etc.Slide9
What prior knowledge is helpful? What is unhelpful?
Images
Language
Methods
Assumptions
Limitations………………. etc.Slide10
Whole school approaches to creating the orchestraSlide11
Calculus
y = (x
2
+ 1) e
-xSlide12
CalculusSlide13
Calculus
Use of letters: variables; unknowns; parameters; constants
Functions: expressions; relations between functions
Graphs: …
Similarity: …etc. …Slide14
What prior knowledge is helpful? What is unhelpful?
Images
Language
Methods
Assumptions
Limitations………………. etc.Slide15
Whole school approaches to creating the orchestraSlide16
Vertical integration of key ideas in the curriculum
Continuity
How to read mathematics
Different meanings of letters
Ratio
Similarity
Functions and graphsetc.Slide17
Algorithm …
Algorithm – you can use it
Algorithm – why teach anything more?
Algorithm – don’t abuse it
Algorithm – why teach anything more?
I will test you
To see if you know itThen I’ll give you
Your next targetSlide18
Thankyou for thinking
anne.watson@education.ox.ac.uk
www.education.ox.ac.uk/people/academics
Anne Watson:
Raising Achievement in Secondary Mathematics
, Open University Press
8th Annual Institute of Mathematics Pedagogy
July 28th to 31stCuddesdon near Oxford
s.elliott@shu.ac.ukJohn Mason, Malcolm Swan, Anne Watson