Mathematics GCSE Teaching from Sept 2015 Telford Nov 2014

Background

GCSE going linear All GCSE assessments at the end of the course for awards made from summer 2014 onwards. Mathematics GCSE available in June and November.

November GCSE From Nov 2014, entries for current GCSE Mathematics (and English and English Language) will be restricted to re-sit candidates only. No other GCSE subjects are available in November. For new GCSEs for teaching from 2015, November GCSE is for students who were 16 by previous 31 August – can be first sitting. November 2017 is the first November assessment of new GCSE.

GCSE and school performance tables From September 2013, the grade a student achieves for his/her first entry to GCSE is the one that counts for school performance tables. If students are entered for two examinations on the same day then the best result from the two counts. For examinations in the same month but on different days, the earlier one counts.

Early entry to GCSE DfE report 2011 In summer 2013, 23% of maths entries (170,537 entries) and 10% of English entries (70,134) were from students who were not yet at the end of their key stage 4 study.  2006: performance measure of 5A*-C including maths and English introduced

GCSE Mathematics grade

The Wolf Report 2011 Students who are under 19 and do not have GCSE A*-C in English and/or Maths should be required, as part of their programme, to pursue a course which either leads directly to these qualifications, or which provide significant progress towards future GCSE entry and success. The latter should be based around other Maths and English qualifications which have demonstrated substantial content and coverage; and Key Skills should not be considered a suitable qualification in this context.

16-19 Funding 2014-15 “For the 2014 to 2015 academic year all students, full and part-time, on 16 to 19 study programmes who do not have a grade C or above in maths and/or English and are not studying on either a GCSE or an approved alternative qualification (detailed below), which is a ‘stepping stone’ towards a GCSE, will be removed from lagged student numbers and will therefore not generate any funding in future academic years” (DfE) Stepping stones: FSMQ, Functional Skills, Level 1/2 certificate (IGCSE) – see DfE website for definitive and updated list

16-19 Funding 2015-16 “For the 2015 to 2016 academic year the same conditions apply and in addition all full time students (excluding those on a traineeship) enrolling on a 16 to 19 study programme in 2015 to 2016 and beyond with a grade D in maths and/or English GCSE who are not enrolled on GCSE courses in these subjects, will be removed from lagged student numbers and will therefore not generate any funding in future academic years” (DfE)

Changes to GCSE content from 2015

New GCSEs from 2015 “The new mathematics GCSE will be more demanding and we anticipate that schools will want to increase the time spent teaching mathematics. On average secondary schools in England spend only 116 hours per year teaching mathematics, which international studies show is far less time than that spent on this vital subject by our competitors. Just one extra lesson each week would put England closer to countries like Australia or Singapore who teach 143 and 138 hours a year of mathematics respectively. We announced on 14 October that mathematics, alongside English, will be double weighted in secondary school performance measures from 2016.” Michael Gove 1 Nov 2013

GCSE content An increase in GCSE mathematics content overall. More formulae which students are expected to remember e.g. area of trapezium, volume of prism, cosine rule and quadratic formula.

New for Foundation and Higher Know the exact values of sinθ and cosθ for θ = 0°, 30°, 45°, 60° and 90°; know the exact value of tanθ for θ = 0°, 30°, 45° and 60° Use inequality notation to specify simple error intervals due to truncation or rounding Use Venn diagrams Work with percentages greater than 100%

New for Higher Recognise and use the equation of a circle with centre at the origin; find the equation of a tangent to a circle at a given point Find approximate solutions to equations numerically using iteration Interpret the gradient at a point on a curve as the instantaneous rate of change; apply the concepts of average and instantaneous rate of change (gradients of chords and tangents) in numerical, algebraic and graphical contexts

Now Foundation (was Higher) Using trigonometric ratios Calculating with and interpreting standard form (A x 10n), where 1 ≤ A < 10 and n is an integer Applying addition and subtraction of vectors, multiplication of vectors by a scalar, and diagrammatic and column representations of vectors Factorising quadratic expressions of the form x2 + bx + c, including the difference of two squares Using y = mx + c to work with straight lines on graphs.

Changes to assessment objective

Current Assessment objectives Weighting (%) AO1 „recall and use their knowledge of the prescribed content 45–55 AO2 „select and apply mathematical methods in a range of contexts 25–35 AO3 „interpret and analyse problems and generate strategies to solve them. 15–25   2015 Assessment Objectives Weighting Higher Foundation AO1 Use and apply standard techniques 40% 50% AO2 Reason, interpret and communicate mathematically 30% 25% AO3 Solve problems within mathematics and in other contexts

AO1: Use and apply standard techniques Students should be able to: accurately recall facts, terminology and definitions use and interpret notation correctly  accurately carry out routine procedures or set tasks requiring multi-step solutions

AO2: Reason, interpret and communicate mathematically Students should be able to: make deductions, inferences and draw conclusions from mathematical information construct chains of reasoning to achieve a given result interpret and communicate information accurately present arguments and proofs assess the validity of an argument and critically evaluate a given way of presenting information

AO3: Solve problems within mathematics and in other contexts Students should be able to: translate problems in mathematical or non-mathematical contexts into a process or a series of mathematical processes make and use connections between different parts of mathematics interpret results in the context of the given problem evaluate methods used and results obtained evaluate solutions to identify how they may have been affected by assumptions made

Changes to performance tables

Performance tables 2016 Progress across 8 subjects (Progress 8) Attainment across 8 subjects (Attainment 8) The percentage of pupils achieving a C grade or better in both GCSE or level1/2 Certificate (accredited iGCSE) English and maths The English Baccalaureate 5 of the subjects in Attainment 8 are English, maths and other EBacc subjects English and maths count double for Attainment 8

Progress 8 and new GCSE June 2017 is first assessment of new Mathematics GCSE. The first time Progress 8 applies, current GCSE Mathematics will be used. In 2017 new GCSE Mathematics and English will be used. To assess progress, each pupil’s results will be compared with those with the same prior attainment (KS2 test) in the same cohort.

Calculating Attainment 8 Attainment 8 score for Gillian: Attainment 8 score = (7 + 7) + (8 +8) + 6 + 7 + 6 + 6 +5 +5 = 65 Dividing the Attainment 8 score by 10 gives a pupil’s average grade. In this case it is 6.5, between GCSE grades A and B. GCSE G=1,F=2,…A*=8

Calculating Progress 8 Gillian has an Attainment 8 score of 65. Her KS2 fine level scores were 5.3 and 4.9 in mathematics and English, an average of 5.1. Dividing her Progress 8 score by 10 gives an average score of + 0.6 grades, which means that Gillian has achieved an average of just over half a grade better per subject than other pupils with the same prior attainment.

School Progress 8 School Progress 8 = mean of pupil Progress 8 Pupils without KS2 results (or teacher assessments) do not count towards Progress 8 Floor standard: School Progress 8 of -0.5, unless the school confidence interval includes zero.

Performance tables 2017 onwards The only English and maths qualifications that will count in the 2017 secondary school performance tables will be reformed GCSEs in those subjects or qualifications reformed to meet the same standards and expectations. GCSE Mathematics and English taken early will not count for 2017 performance. Considering moving towards Progress 8 in 2017 being based on expectations from 2016 results so that schools know in advance what students need to do to make progress.

Grading of new GCSEs

Grading and tiering from 2015 Numerical grades for GCSE from 1 to 9, with 9 being the best. “In the new tiered maths GCSE the higher tier will include questions that will stretch the most able, and the foundation tier will focus on core mathematical understanding and skills that all students should aim to master.” Ofqual Foundation tier: grades 1-5 Higher tier: grades 4-9

Tiering Foundation Tier Half marks targeted at grades 1, 2, 3 Higher Tier Half marks targeted at grades 4, 5, 6 Half marks targeted at grades 7, 8, 9   At least 20% of marks common between tiers and targeted at grades 4 and 5.

What will the new grades mean? Broadly the same proportion of students will achieve a grade 4 and above as currently achieve a grade C and above. Broadly the same proportion of students will achieve a grade 7 and above as currently achieve an A and above. Top 20 per cent of those who get grade 7 or above will get a grade 9. The bottom of grade 1 will be aligned with the bottom of grade G. Grade 5 will be positioned in the top third of the marks for a current grade C and bottom third of the marks for a current grade B. Broadly in line with average PISA performance in countries such as Finland, Canada, the Netherlands and Switzerland.

GCSE - compensatory GCSE will continue to be a compensatory qualification where good performance in some areas can balance weaker performance in others. Statistical information and examiner judgement are currently used to set grade boundaries. For summer 2017 statistical information from KS2 tests will continue to be used in setting grade boundaries.

Awarding the grades The first award will be done on the basis of statistical predictions deciding grade boundaries. In future years, the aim will be to maintain standards. Grade descriptions will be improved after the first award. National reference test to be introduced from 2017 (piloting 2016) – a small group of year 11s will take it just before GCSE to provide information about the standard of the cohort.

New question types

Assess the validity of an argument (AO2) Pearson Higher

Evaluate results obtained (AO3) Pearson Foundation

Evaluate methods used (AO3)

Evaluate solutions to identify how they may have been affected by assumptions (AO3) OCR Foundation

Overview of accredited GCSEs Eduqas awaiting accreditation on 26 Oct 2014 Overview of accredited GCSEs

AQA Paper 1 Paper 2 Paper 3 Non-calculator 1 hour 30 mins 80 marks 33⅓% of the GCSE Calculator

OCR Paper 1 Paper 2 Paper 3 Calculator 1 hour 30 mins 100 marks 33⅓% of the GCSE Non-calculator 80 marks

Pearson Paper 1 Paper 2 Paper 3 Non-calculator 1 hour 30 mins 80 marks 33⅓% of the GCSE Calculator

Useful websites Ofqual timeline of changes to GCSE and A level: http://www.ofqual.gov.uk/qualifications-and-assessments/qualification-reform/#timeline DfE timeline of forthcoming changes for schools: http://www.education.gov.uk/schools/toolsandinitiatives/cuttingburdens/b00216133/need-to-know-schools Also MEI’s Feb 14 Monthly Maths http://www.mei.org.uk/?section=news&page=monthlymaths

Any more questions http://www.mei.org.uk/?section=teachers&page=curriculum-changes Stella.dudzic@mei.org.uk