1. Mathematics GCSE Pilot Centre Meetings June 2007

2. ©AQA GCSEMathBP2Aut06 2 Pathways Project GCSE1 with Level 2 Functional Mathematics GCSE2 GCE FSMQ

3. ©AQA GCSEMathBP2Aut06 3 GCSE- AQA Pilot GCSE Mathematics  Modular structure  Includes functional mathematics  The standard qualification for all students

4. ©AQA GCSEMathBP2Aut06 4 Functional Mathematics AQA Model AQA are piloting GCSE with Functional Mathematics at level 2 as an untiered component (35%) with two parts  Straightforward competency test  Extended task to test functionality – involving pre-released data sheets

5. ©AQA GCSEMathBP2Aut06 5 Competency test 30 questions in 40 minutes Short, basic skills questions Limited context Expect high threshold for pass/grade C Ultimately On-line

6. ©AQA GCSEMathBP2Aut06 6 Functionality Test Five questions each on a different context Two with pre-released data Three with data given on the day 75 minutes 60 marks

7. ©AQA GCSEMathBP2Aut06 7 GCSE Units Unit 1 (35%)- Functional mathematics Unit 2 (22%)- Statistics and Number  1 hour  Calculator and non-calculator sections  50 marks

8. ©AQA GCSEMathBP2Aut06 8 GCSE Units Unit 3 (43%)- Geometry, measures and Algebra  Paper 1 – non-calculator – 1 hour, 50 marks  Paper 2 - calculator – 1 hour, 50 marks

9. ©AQA GCSEMathBP2Aut06 9 Availability January 2008 – Units 1 and 2 June 2008 – Units 1,2 & 3 All units available in subsequent January and June series

10. ©AQA GCSEMathBP2Aut06 10 Awarding GCSE certification every series from June 2008 Functional Mathematics certificated separately No terminal requirement 1 re-sit allowed before certification

11. ©AQA GCSEMathBP2Aut06 11 GCSE- AQA Pilot GCSE Additional Mathematics  No additional content  Aimed at a majority of candidates  Will emphasise the holistic nature of the subject  Single examination paper at each Tier  Good preparation for further study

12. ©AQA GCSEMathBP2Aut06 12 Additional Mathematics 2 hour paper at each tier 100 marks Calculator required June only from June 2008 In 2008, may be sat alongside existing GCSE

13. ©AQA GCSEMathBP2Aut06 13 Pilot Centres Invited to enter candidates for these new qualifications Ideally whole cohort working towards two GCSEs Actual entry decisions up to centres to make

14. ©AQA GCSEMathBP2Aut06 14 Question Papers The‘rules’ for setting What is different? What is unchanged?

15. ©AQA GCSEMathBP2Aut06 15 Assessment Objectives AO1 – Demonstrate knowledge, skills and understanding AO2 – Apply knowledge and understanding using appropriate terms, concepts and methods in abstract and real-life contexts AO3 – Demonstrate strategies for problem solving

16. ©AQA GCSEMathBP2Aut06 16 AO1 Questions that are straightforward and do not have any multi-step or using and applying elements. Questions that use standard algorithms or are heavily structured.

17. ©AQA GCSEMathBP2Aut06 17 AO2 Questions that have a multi-step element with only one ‘intermediate step’ Questions with using and applying element with a 1 or 2 mark allocation, such as ‘explain…’ Questions with part (a) providing a ‘clue’ to part (b) which would have a more complex using and applying element

18. ©AQA GCSEMathBP2Aut06 18 AO3 Questions that could have a high mark allocation and which require candidates to plan strategy, provide formal proofs, etc. No structure, no lead ins. These would be complex using and applying or multi-step questions Questions could require some sophisticated thinking

19. ©AQA GCSEMathBP2Aut06 19 Functional Mathematics Paper 1 (competency) – assesses AO1 Paper 2 (functionality) – mainly AO2 Competency paper ensures full coverage of content from standards Functionality paper ensures full coverage of performance standards and process skills

20. ©AQA GCSEMathBP2Aut06 20 Functional Mathematics Assessment targeted at Level 2/Grade C Some marks beyond the standards Plenty for Foundation candidates to do

21. ©AQA GCSEMathBP2Aut06 21 Trial Award Grade Boundaries Boundary Competency Max:30 Functionality Max: 60 Scaled total Max: 210 A2645162 (77%) C1929110 (52%) F81554 (26%) Level 21826101 (48%) Level 181451 (24%)

22. ©AQA GCSEMathBP2Aut06 22 Units 2 & 3 Mainly assess AO1 (72% of marks) All statistics content in Unit 2 All geometry and algebra content in Unit 3 Number split across Units 2 and 3 at Foundation Tier

23. ©AQA GCSEMathBP2Aut06 23 Unit weightings Unit and Content Weightings (%) AO1AO2AO3NGS Unit 1 Functional mathematics 1318420105 Unit 2 16429–13 Unit 3 31842617– Overall weighting of Units (%) 603010552718

24. ©AQA GCSEMathBP2Aut06 24 Division of marks across content - Foundation UnitNumber Manipulative Algebra Non- Manipulative Algebra Geometry & Measures StatisticsTOTAL 1 paper 118126330 1 paper 2272319960 220---3050 315 3040-100 TOTAL8018356542240

25. ©AQA GCSEMathBP2Aut06 25 Division of marks across content - Higher UnitNumber Manipulative Algebra Non- Manipulative Algebra Geometry & Measures StatisticsTOTAL 1 paper 118126330 1 paper 2272319960 2 (total for both sections) 20---3050 3 (total for both papers) -402040-100 TOTAL6543256542240

26. ©AQA GCSEMathBP2Aut06 26 Additional Mathematics: Rationale Papers that are: Accessible Recognisable Challenging Some ‘original’ and/or ‘novel’ questions

27. ©AQA GCSEMathBP2Aut06 27 Additional Mathematics: Weighting of Content (%) NumMA NM A GS Tier F 369162910 Tier H 2326122910

28. ©AQA GCSEMathBP2Aut06 28 Additional Mathematics: Trial award Foundation Tier C58% F25% Higher Tier A48% C25%

29. ©AQA GCSEMathBP2Aut06 29 Marks per Assessment Objective (%) AO1AO2AO3 Tier F205030 Tier H205030

30. ©AQA GCSEMathBP2Aut06 30 Leeds University AEU Support materials for functional mathematics and the problem solving element of the GCSE in ‘Additional Mathematics’

31. ©AQA GCSEMathBP2Aut06 31 Support materials for functional mathematics

32. ©AQA GCSEMathBP2Aut06 32 Functional maths standards (from the current draft of the QCA standards document) Understand routine and non-routine problems in a wide range of familiar and unfamiliar contexts and situations Identify the situation or problem and the mathematical methods needed to tackle it Select and apply a range of mathematics to find solutions Use appropriate checking procedures and evaluate their effectiveness at each stage Interpret and communicate solutions to practical problems in familiar and unfamiliar routine contexts and situations Draw conclusions and provide mathematical justifications

33. ©AQA GCSEMathBP2Aut06 33 Elements of the resource Explanatory pages, including a possible teaching strategy 30 items – data sheets and questions ‘Descriptions’ of 10 of them

34. ©AQA GCSEMathBP2Aut06 34 Features of items in the exam and the resource Description of a broad context (relatively complex but accessible) Ramped questions – first just accessing data, then accessing and operating on data simply, then with more complexity Straightforward mathematics, that is not too demanding

35. ©AQA GCSEMathBP2Aut06 35 A teaching approach using the resource The aim of the approach is for students to be able to ‘read’ context descriptions mathematically, so that they can be functional within that context. The approach may include:

36. ©AQA GCSEMathBP2Aut06 36 A progression towards independent activity First stage - as a data sheet is read through by the students, the teacher supports their engagement with it, by suggesting what to notice, and how the information on the sheet could be worked with, and discussing with the students the key mathematical elements and possible misunderstandings.

37. ©AQA GCSEMathBP2Aut06 37 A progression towards independent activity Second stage - the students are given more opportunity to locate the key elements for themselves, but the teacher then discusses their ideas with them, and offers additional prompts before the questions are attempted.

38. ©AQA GCSEMathBP2Aut06 38 A progression towards independent activity Third stage - the students do all the preparation for themselves, and work with the information without prompting (reviewed with the teacher only after attempting the questions, to see if lessons can be learned).

39. ©AQA GCSEMathBP2Aut06 39 Use of Data Sheets Anticipating kinds of questions but not trying to guess exactly what will be asked  If questions are anticipated, the data sheet is read appropriately, and unsettling surprises are avoided  If questions are guessed, there is an unhelpful temptation to try to remember the answers

40. ©AQA GCSEMathBP2Aut06 40 Features of the item ‘descriptions’ in the resource Initial data  suggested discussion points / possible ‘sticking points’ in the description of the context  Answers for each of the questions

41. ©AQA GCSEMathBP2Aut06 41 Features of the item ‘descriptions’ in the resource Commentary on questions  demands and/or possible issues

42. ©AQA GCSEMathBP2Aut06 42 Elements of the resource Explanatory pages, including a possible teaching strategy 30 items – data sheets and questions ‘Descriptions’ of 10 of them Anything else?

43. ©AQA GCSEMathBP2Aut06 43 Support materials for the problem solving elements of the GCSE in Additional Mathematics

44. ©AQA GCSEMathBP2Aut06 44 Problem solving in the GCSE in Additional Mathematics The GCSE in Additional Mathematics has more questions that call on mathematical processes that are not just a matter of procedural or factual knowledge  more reasoning;  more justification of reasoning in explanations;  more visualisation;  more representation of a situation algebraically;  more manipulation of algebra in unfamiliar contexts;  more problem solving

45. ©AQA GCSEMathBP2Aut06 45 For most of these elements it will be sufficient to do more practice. For problem solving, however, there is a likely need for focused attention on strategies.  Faced with unstructured problems, when there are no easy lead-in steps, many students do not know how to begin to find solutions. Problem solving in the GCSE in Additional Mathematics

46. ©AQA GCSEMathBP2Aut06 46 Problem solving in the GCSE in Additional Mathematics The aim of the resource is to offer the means to equip students with strategies to use for the parts of the GCSE in Additional Mathematics that involve problem solving.

47. ©AQA GCSEMathBP2Aut06 47 Elements of the resource Introductory pages, outlining problem solving strategies that will be useful in the exam, and possible teaching approaches 90 examples of problem solving questions (with answers) ‘Descriptions’ of the features of 30 questions Summary lists linking the questions both to process skills and to content areas.

48. ©AQA GCSEMathBP2Aut06 48 Developing ‘strategies’ Ensuring that each student has in their repertoire of possible actions a set of approaches that would be helpful in this exam. Not direct ‘teaching’ but seeding their active problem solving by making suggestions (“You could …” ; “What do you notice …?”; “Why not try …?”)

49. ©AQA GCSEMathBP2Aut06 49 Two possible teaching approaches (i) Lessons focusing on problem-solving Problems are used that are all susceptible to the same approach, and then in later lessons another set that suit a second approach, and so on.

50. ©AQA GCSEMathBP2Aut06 50 Two possible teaching approaches (ii) Problem-solving within lessons. Problems are used that fit in with the content area, as part of teaching mathematics topics.

51. ©AQA GCSEMathBP2Aut06 51 The particular approaches or ‘strategies’ identified in the resource (Identified from a study of the kinds of questions asked) Set cases out systematically Work back from a value that is given Find examples that fit conditions for the answer Recognise and represent relationships between elements of the problem Find features that can be acted on mathematically, and see where it takes you.

52. ©AQA GCSEMathBP2Aut06 52 Progression in the teaching (either approach) First stage – developing possible approaches As each problem is introduced to the students, and they make their first attempts at engaging with the challenge and devising an approach, the teacher draws attention to possibilities for action by making suggestions, by pointing out a feature of the problem, or by asking eliciting questions.

53. ©AQA GCSEMathBP2Aut06 53 Progression in the teaching (either approach) Second stage – developing awareness of approaches Once a range of possible approaches has been established, as a new problem is introduced there is a discussion with the students about what might be a helpful thing to do on that problem.

54. ©AQA GCSEMathBP2Aut06 54 For all problems in the resource: Problem solving classification - which of the five identified strategies this problem is most susceptible to Content area classification - the content area(s) that it would be reasonable to extend by using the problem Grade level - an approximate indicator of the GCSE grade Answer(s)

55. ©AQA GCSEMathBP2Aut06 55 Progression in the teaching (either approach) Third stage – operating strategically The last stage involves getting students to decide independently on what to do, in effect practising problem solving using examples from the resource.

56. ©AQA GCSEMathBP2Aut06 56 For 30 of the problems: About the question  An overall perspective on the question – how it might be understood in mathematical terms. Problem solving approaches  How students might understand and then ‘attack’ the problem

57. ©AQA GCSEMathBP2Aut06 57 For 30 of the problems: Challenges / Issues  Points of particular demand in the question which might trip students up, or common wrong approaches. Finding an answer  The mathematics that students might follow in moving towards a solution to the problem. Follow up  In some questions, where appropriate, there is a description of some suitable further problem solving activities

58. ©AQA GCSEMathBP2Aut06 58 Elements of the resource Introductory pages, outlining the set of problem solving strategies that will be useful in the exam, and possible teaching approaches 90 examples of problem solving questions (with answers) ‘Descriptions’ of the features of 30 questions Summary lists linking the questions both to process skills and to content areas. Anything else?