Mathematics: the language of physics and engineering

Mathematics: the language of physics and engineering

Professor Peter MainMaths in the Science CurriculumUniversity of Southampton29 July 2014

[email protected], www.iop.org

Overview

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

Overview

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

1 English 63838

2 Psychology 41308

3 Biology 35664

4 Art and Design subjects 34523

5 Mathematics 34301

6 History 26491

7 Sociology 23514

8 Chemistry 23260

15 French 8593

16 Economics 8037

17 Law 7994

18 Physics 7361

19 Design and Technology 7298

20 Political Studies 6591

24 Spanish 4871

25 ICT 4284

26 Mathematics Further 3972

27 Music 3790

36 Irish 203

1 Mathematics 51413

2 Biology 27410

3 Physics 27148

4 Chemistry 25974

5 English 25800

6 History 25161

14 Physical Education 11030

15 Design and Technology 9807

16 Mathematics Further 9251

17 Political Studies 8669

18 Sociology 7843

19 Religious Studies 7298

20 ICT 6804

24 Drama 4763

25 Other modern languages 4020

26 French 3918

27 Computing 3512

36 Irish 101

A-level subjects for female students 2012 A-level subjects for male students 2012

Source: DfE

Observations Grades are rising inexorably

Large increase in numbers that take maths and physics together (now ~86% of physicists take maths)

Essentially all students with A-level physics go to university, the vast majority to use their physics

Overview

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

Mind the Gap (2011)Rationale:

To understand the extent to which students are prepared to deal with the maths aspects of physics and engineering undergraduate courses

Transition from A-Level to degree Reactions to mathematical aspects of degree courses Most and least challenging mathematical aspects Gaps in preparation

To understand reasons for not pursuing physics to degree level

http://www.iop.org/publications/iop/2011/page_51934.html

Further Maths: 38%; No Further Maths: 57%

Variation in extent to which expectations around mathematical content were met, both in terms of amount…

Further Maths: 36%; No Further Maths: 56%

…and difficulty

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

Specific areas of difficulty according to students and academics

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

Observations Despite grades in physics and maths increasing, academics

and students do not feel students are well prepared

The lack of mathematical fluency is holding most students back

Some students reported that they they did not choose physics because they did not see it as mathematical at A-level

Overview

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

Amount of mathematics

http://www.score-education.org/publications/publications-research-policy

Type of maths and coverage

Physics

5g. Rate of change

5h. Tangent

5d. Log graphs

5f. y = mx + c3f. Solve e.g. y=k/x

1e. Trig. F’ns in calculators

2c. Means

2d. Percentages

Difficulty - steps in calculation

Observations

Substantial difference between awarding bodies

Parts of stated mathematical requirements of specifications are not examined

Very little in terms of multi-step calculations

Overview

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

Typical A-level question in 2013

An atypical A-level question 2013

→

Typical question from 1978

Comparable with harder A-level questions now – note have to set up diagram and write down equation to be solved

This was an O-level question

Typical GCSE question 2013

Not only given the formula to use but in a box and in words No physics required to answer question

Overview

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

IOP Curriculum Committee Instead of defining physics by content, defining

physics by universal themes and competencies

Mathematics includes making estimates and modelling physical situations

Defining the types of assessment, e.g. multiple step

Some of the universal themes Reductionism

The properties of a system can be understood in terms of the “next level down” Universality of physical laws Unification of laws Conservation laws Fields Synthesis

Problems can be approached from many different directions Mathematical formulation

Physical laws can be represented in a mathematical form

Some of the competencies Approximation, taking limiting cases etc.

SimplificationIdentifying the core elements of a problem

Modelling

Developing models of physical systems

Using experiments to test ideas

Overview

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

Suggestions Need coherence between A-levels to allow physics to use

maths beyond GCSE

30,000 students take M and P together: why not have a paired qualification?

It is essential that the assessment of physics A-level is prescribed in terms of mathematical requirements…

…and monitored (by professional bodies?)

Thank you

Questions, comments, disagreements….?

[email protected], www.iop.org