1. Mathematics: the language of physics and engineering Professor Peter Main Maths in the Science Curriculum University of Southampton 29 July 2014 peter.main@iop.org, www.iop.org

2. Overview l Background l Mind the Gap l SCORE analysis of maths in the sciences l Examples of assessment l IOP Curriculum Committee l Some suggestions for the future

3. Overview l Background l Mind the Gap l SCORE analysis of maths in the sciences l Examples of assessment l IOP Curriculum Committee l Some suggestions for the future

4. 1 English63838 2 Psychology41308 3 Biology35664 4 Art and Design subjects34523 5 Mathematics34301 6 History26491 7 Sociology23514 8 Chemistry23260 15 French8593 16 Economics8037 17 Law7994 18 Physics7361 19 Design and Technology7298 20 Political Studies6591 24 Spanish4871 25 ICT4284 26 Mathematics Further 3972 27 Music 3790 36 Irish 203 1Mathematics51413 2Biology27410 3Physics27148 4Chemistry25974 5English25800 6History25161 14Physical Education11030 15Design and Technology9807 16Mathematics Further9251 17Political Studies8669 18Sociology7843 19Religious Studies7298 20ICT6804 24Drama4763 25Other modern languages4020 26French3918 27Computing3512 36Irish101 A-level subjects for female students 2012 A-level subjects for male students 2012

6. Source: DfE

7. A-level entries in Physics and Maths

8. Observations l Grades are rising inexorably l Large increase in numbers that take maths and physics together (now ~86% of physicists take maths) l Essentially all students with A-level physics go to university, the vast majority to use their physics

9. Overview l Background l Mind the Gap l SCORE analysis of maths in the sciences l Examples of assessment l IOP Curriculum Committee l Some suggestions for the future

10. Mind the Gap (2011) Rationale: l To understand the extent to which students are prepared to deal with the maths aspects of physics and engineering undergraduate courses l Transition from A-Level to degree l Reactions to mathematical aspects of degree courses l Most and least challenging mathematical aspects l Gaps in preparation l To understand reasons for not pursuing physics to degree level http://www.iop.org/publications/iop/2011/page_51934.html

11. Further Maths: 38%; No Further Maths: 57% Variation in extent to which expectations around mathematical content were met, both in terms of amount…

12. Further Maths: 36%; No Further Maths: 56% …and difficulty

13. Academics (40) *Base: 36 academics Vast majority of academics also agreed that students joining their course lacked fluency in Maths “They don’t usually admit that they’ve got a problem. They don’t quite understand what problem they’ve got. They know they are not quite understanding it but they can’t pin point where the problem lies” Engineering academic

14. Specific areas of difficulty according to students and academics

15. 92% academics felt a lack of mathematical fluency could be an obstacle to achieving full potential 85% academics felt this affected their departments’ ability to deliver an optimal programme of study Many academics believed there could be long-term consequences

16. Observations l Despite grades in physics and maths increasing, academics and students do not feel students are well prepared l The lack of mathematical fluency is holding most students back l Some students reported that they they did not choose physics because they did not see it as mathematical at A-level

17. Overview l Background l Mind the Gap l SCORE analysis of maths in the sciences l Examples of assessment l IOP Curriculum Committee l Some suggestions for the future

18. Amount of mathematics http://www.score-education.org/publications/publications-research-policy

19. Type of maths and coverage Physics 5g. Rate of change 5h. Tangent 5d. Log graphs 5f. y = mx + c 3f. Solve e.g. y=k/x 1e. Trig. F’ns in calculators 2c. Means 2d. Percentages

20. Difficulty - steps in calculation

21. Observations l Substantial difference between awarding bodies l Parts of stated mathematical requirements of specifications are not examined l Very little in terms of multi-step calculations

22. Overview l Background l Mind the Gap l SCORE analysis of maths in the sciences l Examples of assessment l IOP Curriculum Committee l Some suggestions for the future

23. Typical A-level question in 2013

24. An atypical A-level question 2013 →

25. Typical question from 1978 l Comparable with harder A-level questions now – note have to set up diagram and write down equation to be solved l This was an O-level question

26. Typical GCSE question 2013 l Not only given the formula to use but in a box and in words l No physics required to answer question

27. Overview l Background l Mind the Gap l SCORE analysis of maths in the sciences l Examples of assessment l IOP Curriculum Committee l Some suggestions for the future

28. IOP Curriculum Committee l Instead of defining physics by content, defining physics by universal themes and competencies l Mathematics includes making estimates and modelling physical situations l Defining the types of assessment, e.g. multiple step

29. Some of the universal themes l Reductionism The properties of a system can be understood in terms of the “next level down” l Universality of physical laws l Unification of laws l Conservation laws l Fields l Synthesis Problems can be approached from many different directions l Mathematical formulation Physical laws can be represented in a mathematical form

30. Some of the competencies l Approximation, taking limiting cases etc. l Simplification Identifying the core elements of a problem l Modelling Developing models of physical systems l Using experiments to test ideas

31. Overview l Background l Mind the Gap l SCORE analysis of maths in the sciences l Examples of assessment l IOP Curriculum Committee l Some suggestions for the future

32. Suggestions l Need coherence between A-levels to allow physics to use maths beyond GCSE l 30,000 students take M and P together: why not have a paired qualification? l It is essential that the assessment of physics A-level is prescribed in terms of mathematical requirements… l …and monitored (by professional bodies?)

33. Thank you Questions, comments, disagreements….? peter.main@iop.org, www.iop.org