additional maths - mathematics in education and...

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the Further Mathematics network

www.fmnetwork.org.uk

Additional Maths (MEI Conference)

3rd July 2008



Additional MathsLet Maths take you Further…

Welcome!!

Hello, my name is Tim…

I have just completed my second year teaching Additional Maths to students from four different schools, through the Further Mathematics NetworkLessons took place at the University of Warwick on Thursdays after school, 4pm-5.30pmI come from a University background and taught alongside someone with a school background. This worked well

FSMQ Additional Mathematics

And you are…What is Additional Maths?

Extension to GCSE mathematicsAimed at able year 11 studentsLevel 3 qualification


The content of Additional Maths

4 strands of Pure Maths each followed by an application

1. Algebra – The binomial distribution2. Co-ordinate geometry – Linear programming3. Trigonometry – 3D Trigonometry4. Calculus – Kinematics

FSMQ Additional MathematicsHow many students did we have?First year:

At first we had getting on for thirty!They all seemed to enjoy the lessons, but sadly a lot dropped off (reasons: perhaps after school, too hard, largely though problems with schools arranging taxis)We finished with about twelve

Second year:Similar but better!


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Why did students join our classes?NOT everyone joined our classes to sit the examEven people who weren’t too confident for the Additional Mathematics exam still recognised that the lessons had improved their confidence in GCSE no end, and had prepared them brilliantly for A LevelOur ‘success story’ was a student who was keen but not one of the best in the class. Over the course of the year he became a top student in his GCSE lessons. The school now wants to send 10+ students to Additional Mathematics next year

FSMQ Additional Mathematics continued

One student even used Additional Mathematics to improve his confidence in his Core A Level Mathematics (and the improvements have been very noticeable)This year we had two Year 10 students sit the exam

Homeworks/Independent Study?All students had access to the Online ResourcesHomework was set though some of the students weren’t very motivated for independent study. It was hard to push this when they were doing this as an extra subject (I’ll be harder next year! [A year on: “I could still be harder!!”])We could cover the course content across the year… but only just!Please ask me any questions at any stage of this hour… or afterwards!

FSMQ Additional Mathematics The feedback"Thanks for all of your help, I know [student's name] didn't take the exam with you but she had a lot more confidence after attending your classes, I think you opened her eyes to a different way of looking at maths, she's chosen to take Maths at AS level this year at school."

"Thanks for all your help - we wouldn't have got those results without you."

"You have been a really great help in helping me to understand Maths a lot better.“

[We had a presentation to parents before the start of the course].

Models of delivery used by schoolsComplete GCSE Maths in year 10 or by January of year 11, then study Add MathsStudy alongside GCSE Maths in year 11 (or across Years 10 and 11)

Whole groupSelected students from a group

It is preferable if the decision to enter the students for the exam is delayed for as long as possible

FSMQ Additional MathematicsResources

TextbookOnline resources –www.addmaths.mei.org.ukPast papers – www.mei.org.ukHandwritten solutions and Powerpointsolutions


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Professional Development

2-day CPD coursesDay 1: introduction to the big ideas in Add Maths In-between: consolidation based on web-resources and textbookDay 2: teaching approaches, student misconceptions and extension work

see http://www.mei.org.uk/cpd/alevel.shtml

FSMQ Additional MathematicsUseful URLs

The Further Mathematics Network: www.fmnetwork.org.ukOnline resources:www.addmaths.mei.org.ukPast papers and CPD information www.mei.org.ukSpecificationwww.ocr.org.uk


UCAS tariff points

7E10D13C17B

E20AD30CE40B50AD60

C80B100A120

AS levelA levelFSMQ

FSMQ Additional MathematicsPerformance table points

25E

30D

35C

40B

45A

PointsGrade


Additional Mathematics Statistics

39485767772342200376.40%67.40%58.00%44.50%29.10%

66.8%57.5%48.1%38.6%28.8%

??????????55002007

75.3%65.7%57.3%48.1%35.2%

344556677943812006

66.40%57.20%47.60%38.30%27.80%

324151617139362005

73.10%63.30%52.70%40.30%27.50%

344352617034662004

EDCBAcandidates

FSMQ Additional Mathematics“Many candidates not only failed to demonstrate any understanding of the extension material but failed to demonstrate … understanding of some Higher Tier topics”[2003]“There were a distressing number of candidates scoring very low marks… This cannot have been a positive experience for them” [2004]

What the examiners have said

There were some very good comments too!

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continued

“… it is still true to say that there are a significant number of candidates who appear to have been entered for a qualification that is not suited to their abilities” [2005]“However, it is still disappointing to find a number of centres for which this specification is clearly not appropriate. The specification clearly states that…[it]… is suitable for those gaining a good grade at GCSE – typically A*, A or B.[It]… is designed to be an enrichment for Higher Tier students” [2006]



Additional Maths Revision Day

11th June 2007

University of Warwick



Welcome!

Outline of Topics1. Algebra I - Review

2. Algebra II - Techniques

3. Algebra III - Polynomials

4. Algebra IV - Applications

5. Co-ordinate Geometry I

6. Co-ordinate geometry II – Applications

7. Trigonometry I

8. Trigonometry II – Applications

9. Calculus I – differentiation

10. Calculus II – Integration

11. Calculus III – Applications to Kinematics

Algebra I - Review

I. Linear Expressions

II. Solving Linear Equations

III. Changing the subject of an equation

IV. Quadratic expressions

V. Solving a quadratic equation that factorises

VI. Completing the square

VII. Simultaneous equations

AM 13th June 2003Question 1

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Algebra II - Techniques

I. Linear Inequalities

II. Solving quadratic inequalities

III. Simplifying algebraic fractions

IV. Solving equations involving fractions

V. Simplifying expressions containing square roots


AM 21st June 2004Question 6


Algebra III - Polynomials

I. Operations with polynomials

II. The factor theorem

III. The remainder theorem


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Algebra IV - Applications

I. The binomial expansion

II. The binomial distribution



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Co-ordinate geometry I

I. Co-ordinates

II. The gradient of a line

III. Parallel and perpendicular lines

IV. The distance between two points

V. The midpoint of a line joining two points

VI. The equation of a straight line

VII. Drawing a line given its equation

VIII. Finding the equation of a line

IX. The intersection of two lines

X. The circle


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Co-ordinate geometry II - Applications

I. Inequalities

II. Using inequalities for problem solving

III. Linear Programming

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Trigonometry II. Using trigonometry in right-angled triangles

II. Trigonometric functions for angles of any size

III. The sine and cosine graphs

IV. The tangent graph

V. Solution of equations using graphs of trigonometric functions

VI. Identities involving sin θ, cos θ, and tan θ

VII. Using trigonemetric identities to solve equations

VIII. The sine rule

IX. The cosine rule

X. Using the sine and cosine rule together


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AM 13th June 2003Question 14 (Part One)

AM 13th June 2003Question 14 (Part Two)

Trigonometry II- Applications

I. Working in three dimensions

II. Lines and planes in three dimensions

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Calculus I - Differentiation

I. The gradient of a curve

II. Finding the gradient of a curve

III. Differentiation using standard results

IV. Tangents and normals

V. Stationary points


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Calculus II - Integration

I. Reversing differentiation

II. Definite integrals

III. The area between two curves

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dy





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Calculus III – Applications to kinematics

I. Motion in a straight line

II. The constant acceleration formulae

III. Motion with variable acceleration: the general case

IV. Finding displacement from velocity and velocity from acceleration



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The End

Here’s looking at you kids…

This is a Conference so we’ve got to have a few funnies…

FSMQ Additional Mathematics Reminder to me…

Show Bob Francis’ Powerpointexam solutions!!

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This is a Conference so we’ve got to have a few funnies…


additional maths - mathematics in education and...

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