the Further Mathematics network www.fmnetwork.org.uk the Further Mathematics network www.fmnetwork.org.uk Additional Maths (MEI Conference) 3 rd July 2008 Additional Maths Let Maths take you Further Welcome!! Hello, my name is Tim And you are I have just completed my second year teaching Additional Maths to students from four different schools, through the Further Mathematics Network Lessons took place at the University of Warwick on Thursdays after school, 4pm-5.30pm I come from a University background and taught alongside someone with a school background. This worked well What is Additional Maths? Extension to GCSE mathematics Aimed at able year 11 students Level 3 qualification The content of Additional Maths 4 strands of Pure Maths each followed by an application 1. Algebra The binomial distribution 2. Co-ordinate geometry Linear programming 3. Trigonometry 3D Trigonometry 4. Calculus Kinematics How 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! 1
Why did students join our classes? NOT everyone joined our classes to sit the exam Even 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 Level Our 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 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 Resources Homework 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! 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 schools Complete GCSE Maths in year 10 or by January of year 11, then study Add Maths Study alongside GCSE Maths in year 11 (or across Years 10 and 11) Whole group Selected students from a group It is preferable if the decision to enter the students for the exam is delayed for as long as possible Resources Textbook Online resources www.addmaths.mei.org.uk Past papers www.mei.org.uk Handwritten solutions and Powerpoint solutions 2
Professional Development 2-day CPD courses Day 1: introduction to the big ideas in Add Maths In-between: consolidation based on web-resources and textbook Day 2: teaching approaches, student misconceptions and extension work Useful URLs The Further Mathematics Network: www.fmnetwork.org.uk Online resources: www.addmaths.mei.org.uk Past papers and CPD information www.mei.org.uk Specification www.ocr.org.uk see http://www.mei.org.uk/cpd/alevel.shtml UCAS tariff points FSMQ A level AS level 120 A 100 B 80 C 60 D A 50 B 40 E C 30 D A 20 E B 17 C 13 D 10 E 7 Performance table points Grade Points A 45 B 40 C 35 D 30 E 25 Additional Mathematics Statistics candidates A B C D E 2003 2342 77 67 57 48 39 29.10% 44.50% 58.00% 67.40% 76.40% 2004 3466 70 61 52 43 34 27.50% 40.30% 52.70% 63.30% 73.10% 2005 3936 71 61 51 41 32 27.80% 38.30% 47.60% 57.20% 66.40% 2006 4381 79 67 56 45 34 35.2% 48.1% 57.3% 65.7% 75.3% 2007 5500?????????? 28.8% 38.6% 48.1% 57.5% 66.8% What the examiners have said 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] There were some very good comments too! 3
continued the Further Mathematics network www.fmnetwork.org.uk 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 11 th June 2007 University of Warwick the Further Mathematics network www.fmnetwork.org.uk Welcome! Outline of Topics 1. 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. VII. Completing the square Simultaneous equations Question 1 4
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 Question 5 Question 6 Question 13 Algebra III - Polynomials I. Operations with polynomials II. The factor theorem III. The remainder theorem Question 9 5
Question 9 Question 2 Question 10 Algebra IV - Applications I. The binomial expansion II. The binomial distribution Question 6 Question 6 6
Question 11 Question 5 Question 12 Question 9 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 Question 10 7
Question 7 Question 7 Question 1 Question 4 Question 12 Co-ordinate geometry II - Applications I. Inequalities II. Using inequalities for problem solving III. Linear Programming 8
Question 8 Question 5 Question 11 Question 11 Trigonometry I I. 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 Question 12 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 9
Question 4 Question 4 Question 3 Question 5 Question 9 Question 7 10
Question 3 Question 8 Question 2 Question 14 (Part One) Question 14 (Part Two) Trigonometry II- Applications I. Working in three dimensions II. Lines and planes in three dimensions 11
Question 3 Question 8 Question 13 (Part One) Question 13 (Part Two) 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 Question 1 12
Question 2 Question 4 Question 10 Question 14 (Part One) Question 14 (Part Two) Calculus II - Integration I. Reversing differentiation II. Definite integrals III. The area between two curves 13
Question 1 Question 3 dy Question 6 Question 7 Question 2 Question 11 (Part One) 14
Question 11 (Part Two) Question 13 (Part One) Question 13 (Part Two) 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 Question 10 Question 8 15
Question 12 Question 14 Question 13 The End Here s looking at you kids This is a Conference so we ve got to have a few funnies Reminder to me Show Bob Francis Powerpoint exam solutions!! 16
This is a Conference so we ve got to have a few funnies 17