3. MEI Conference Three-day event for 14-19 mathematics teachers of all GCSE, Core Maths and A level specifications 25-27 June 2015 at the University of Bath 4 workshop sessions every day, each with 8 choices 3 informative and entertaining plenaries En-suite accommodation available Register online at www.conference.mei.org.ukwww.conference.mei.org.uk

4. A level Maths Development Update keith.proffitt@mei.org.ukUpdated 24/04/2015 This presentation plays automatically and has an audio commentary; adjust your volume if necessary.

5. New A levels: why the delay? Otherwise current Year 10 students would sit old GCSEs and new A levels There are issues to be resolved around problem solving So first teaching will now be September 2017, with first AS exams in June 2018 and first A level exams in June 2019.

6. Intentions of reform Linear qualifications: same grades available AS decoupled – but co-teachable with first year of A level if possible Content chosen by HE Increased emphasis on problem solving No harder than current qualifications ALCAB: A level Content Advisory Board Maths panel members can be found herehere and their reports herehere

7. What do we know? Headlines Four separate linear qualifications: AS and A level in Mathematics and Further Mathematics ALCAB has reported on content; DfE has published final content following consultation.final content Content the same for all AS and A levels in Mathematics: pure + mechanics + statistics A level Further Maths has 50% content defined, mostly pure maths; the remaining 50% has options. (20% + 10% defined for AS F Maths) No coursework

8. What don’t we know? Headlines assessment objectives and weightings how the large data set for teaching statistics will be organised (more on this later) how many question papers, and how long calculator use formula books when we will know Ofqual is convening an A level mathematics assessment working group to advise them on the issues, to report by July 2015

9. Content – in AS Maths y = e x including (informally) differentiating y = e kx use of exponential growth and decay in modelling (continuous compound interest, radioactive decay, drug concentration decay, population growth) differentiation from first principles vectors in 2D, not including scalar product

10. Content – out of AS Maths sequences and series radian measure trapezium rule the remainder theorem (not in A level)

11. Content – in A level Maths specific examples of proof by contradiction (including irrationality of √2 and infinity of primes) small angle approximations for sin, cos and tan knowing some exact values for sin, cos and tan proofs of addition formulae sin(A + B) etc Newton-Raphson method

12. Content – out of A level Maths volumes of revolution vector equations of lines the scalar product

13. Statistics in Mathematics Hypothesis test using Binomial distribution in AS Normal distribution in A level only Emphasis on statistical problem solving Use of a data set

14. Students are required to: become familiar with one or more specific large data set(s) in advance of the final assessment (these data must be real and sufficiently rich to enable the concepts and skills of data presentation and interpretation in the specification to be explored) use technology such as spreadsheets or specialist statistical packages to explore the data set(s) interpret real data presented in summary or graphical form use data to investigate questions arising in real contexts Students should explore the data set(s), and associated contexts, during their course of study to enable them to perform tasks that assume familiarity with the contexts, the main features of the data and the ways in which technology can help explore the data. Students should demonstrate the ability to analyse a subset or features of the data using a calculator with standard statistical functions.

15. Mechanics in Mathematics Motion in a straight line in AS, including motion under gravity suvat equations and kinematics, including using calculus, in AS Projectiles and motion in a plane, friction, resolving forces and simple moments in A level

16. Overarching themes A level specifications in mathematics must require students to demonstrate the following overarching knowledge and skills. These must be applied, along with associated mathematical thinking and understanding, across the whole of the detailed content Mathematical argument, language and proof Mathematical problem solving, using a problem solving cycle Mathematical modelling

17. Use of technology The use of technology, in particular mathematical and statistical graphing tools and spreadsheets, must permeate the study of AS and A level mathematics Calculators used must include the following features:  an iterative function  the ability to compute summary statistics and access probabilities from standard statistical distributions  the ability to perform calculations with matrices up to at least order 3 x 3 (Further Maths only)

18. Further Mathematics Linear qualifications, separate from AS/A level Maths 50% of A level Further Maths content fixed: 50% options AS Further Maths: up to 70% options AS Further Maths must be co-teachable with AS Maths (this is not easy) It is hard to design a coherent AS Further Maths course which depends only on the content of AS Maths

19. Core Content: Further Maths Proof: by induction Complex Numbers: up to de Moivre, nth roots Matrices: transformations, 3 by 3 to solve equations Algebra and functions: summing series using differences, Maclaurin Calculus: improper integrals, mean value, volumes, more partial fractions, inverse trig Vectors: lines, planes & intersections, scalar product, distances Polar coordinates: area Hyperbolic Functions: calculus including use of inverse functions in integration Differential equations: second order, SHM, simultaneous 1 st order, modelling with DEs This is 50% of the A level

20. Core Content: AS Further Maths AS Further Maths must include some complex numbers, some matrices, relationship between roots and coefficients of a polynomial This counts for 20%; exam board chooses another 10% from the core A level content on the previous slide This leaves room for 70% options

21. Optional content What are the rules? –build on mechanics or statistics –new applications –extend the core content ALCAB and Decision maths “There is potentially a place in further mathematics for a serious strand of mathematics based on discrete mathematics and this could be considered as an additional strand alongside mechanics and statistics. However, this will require scrutiny to ensure that it will be perceived as a valuable part of further mathematics.”

22. Development issues What is A level standard? Assessing problem solving Use of technology Use of data set Some notes of caution from ALCAB. https://alevelcontent.files.wordpress.com/2014/07/letter-from-alcab- mathematics-and-further-mathematics-chair-to-dfe-8-july-2014.pdf https://alevelcontent.files.wordpress.com/2014/12/letter-with- annexes-from-alcab-chair-to-secretary-of-state-18-november- 2014.pdf

23. Preparing Department audit – who can teach what: mechanics, statistics … Technology – confidence with spreadsheets Linear scheme of work, combining with Further Maths Problem solving – CMEP? http://www.maths.cam.ac.uk/about/community/cmep/ http://www.maths.cam.ac.uk/about/community/cmep/ AS policy in school/college Can you offer Further Maths – The FMSP can provide support.

24. www.mei.org.ukkeith.proffitt@mei.org.uk