7/19/2011
KS4
KS5
Mind the gap
Push from
KS4
Line up the gap and build the
last part of the bridge
Pull in
KS5
Mind the gap
Mind the gap
2007 Evaluation of Participation in GCE Mathematics ‐ QCA
• ‘Many students spoke of a ‘big jump’ from GCSE mathematics to AS mathematics.
• Mathematics loses one third more students at the end of AS than English.
• A significant number of students commented that, ‘Mathematics is harder than other subjects’
Reasons for taking up mathematics
• Girls top three reasons (1) Previous success (2) Enjoyment of the subject (3) University and career plans • Boys top three reasons (1) University and career plans (2) General benefit (3) Previous success
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Mind the gap
Mind the gap
• The Ofsted Report : ‘Evaluating mathematics provision for 14‐19 year olds’
• ‘Over half the students dropping mathematics at A level said that they felt that different teaching methods could have helped them to continue’
‘The best teaching gave strong sense of the coherence of mathematical ideas; it focused on understanding mathematical concepts and developed critical thinking and reasoning. Careful questioning identified misconceptions and helped to resolve them, and positive use was made of incorrect answers to develop understanding and to encourage students to contribute. Students were challenged to think for themselves, encouraged to discuss problems and to work collaboratively’
Mind the gap
• Pressures from SLT re GCSE results
• Emphasis is being shifted away from A*
• Different reasons for taking up maths between genders
• Issue regarding teaching methods
• Mixed ability teaching
Series and sequences
(one of Jonny Griffith’s RISPs)
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Mind the gap
KS4
KS5
Divergent
Convergent
Periodic
Other
Always
increasing
Always
decreasing
Oscillating
‘Flat’
Push from
KS4
Line up the gap and build the
last part of the bridge
Pull in
KS5
Careers
the nth term =
• + plus magazine
n
-
+
/
(
)
1
2
3
4
²
• MathsCareers • Royal Statistical Society
x
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Mind the gap
KS4
Push from
KS4
Mind the gap
KS5
Line up the gap and build the
last part of the bridge
Pythagoras Theorem
Pull in
KS5
Mind the gap
KS4
Push from
KS4
KS5
Line up the gap and build the
last part of the bridge
Pull in
KS5
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7/19/2011
Pulling by Intervention
How can we close the gap?
FSMQ Add Maths
• Advantages
– Well structured – Reasonably straight forward to deliver
– Excellent preparation for KS5 and A* GCSE
• Disadvantages
– Challenging for the students
– A bit too similar to KS5 content and approach
FSMQ Add Maths
• Algebra – including remainder/factor theorem and binomial expansion
• Co‐ordinate geometry – including circles and linear programming
• Trigonometry – including simple trig identities and equations
• Calculus – including differentiation, integration and app. to kinematics
Add Maths Teachers’ Quotes
• Keen, quick and responsive students
• I like the way we teach Core and then apply it, i.e. inequalities then LP, calculus then kinematics.
• Students who have taken their GCSE in year 11 can keep their maths going
• Huge overlap with C1 and C2
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Questions?
6
Functions challenge
The function f(x) = 2x + 4 can be written using a function machine like this:
x
x2
+4
f(x)
You can reverse this by undoing the operations like this. This is called finding the
inverse.
f-1(x)
-4
÷2
x
We say the inverse function is
Can you find the inverses of these functions? Use the function machines if you want.
1. f(x) = 3x+5
2. f(x) = 4x+7
3. f(x) =
5. f(x) = ⅔x + 3
6. f(x) = 3 – 2x
7. f(x) = x2
4. f(x) =
8. f(x) = sin x
Draw a graph of a function and its inverse – on the same pair of axes
– what do you notice?
What is different about numbers 7 and 8 – why do you think this
happens?
Function machines