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
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
A-level subjects for female students 2012
A-level subjects for male students 2012
1
English
63838
1
Mathematics
51413
2
Psychology
41308
2
Biology
27410
3
Biology
35664
3
Physics
27148
4
Art and Design subjects
34523
4
Chemistry
25974
5
Mathematics
34301
5
English
25800
6
History
26491
6
History
25161
7
Sociology
23514
8
Chemistry
23260
14
Physical Education
11030
15
Design and Technology
9807
15
French
8593
16
Mathematics Further
9251
16
Economics
8037
17
Political Studies
8669
17
Law
7994
18
Sociology
7843
18
Physics
7361
19
Religious Studies
7298
19
Design and Technology
7298
20
ICT
6804
20
Political Studies
6591
24
Spanish
4871
24
Drama
4763
25
ICT
4284
25
Other modern languages
4020
26
Mathematics Further
3972
26
French
3918
27
Music
27
Computing
3512
3790
36
Irish
203
36
Irish
101
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
Variation in extent to which expectations around
mathematical content were met, both in terms of amount…
Further Maths: 38%; No Further Maths: 57%
Total (393)
14
Physics (180)
33
11
Engineering (183)
38
15
Computer Science (30)
10%
30%
2
45
27
20%
5 1
49
30
23
0%
47
40%
9
47
50%
60%
70%
1
3
80%
There is a great deal more mathematical content than I expected
There is somewhat more mathematical content than I expected
The degree of mathematical content meets my expectations
There is somewhat less mathematical content than I expected
There is a great deal less mathematical content than I expected
90%
100%
…and difficulty
Further Maths: 36%; No Further Maths: 56%
Total (393)
Physics (180)
9
36
4
Engineering (183)
42
14
Computer Science (30)
7
0%
42
42
32
39
30
20%
60%
It is a great deal more difficult than I expected
It is somewhat more difficult than I expected
It is at the level I expected
It is somewhat easier than I expected
It is a great deal easier than I expected
1
11
1
13
53
40%
12
2
10
80%
100%
Vast majority of academics also agreed that students
joining their course lacked fluency in Maths
Level of agreement that incoming students lack fluency in Maths
Academics (40) 2 2 5
0%
Strongly disagree
63
20%
40%
Somewhat disagree
*Base: 36 academics
28
60%
80%
Neither agree nor disagree
Somewhat agree
100%
Strongly agree
“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
Elements that academics perceived
students to find particularly challenging
Elements that students found particularly challenging
Integration
Integration
Being able to identify the…
Being able to identify the appropriate…
Vectors and scalars
Vectors and scalars
Complex numbers
Matrices
Calculus
Calculus
Algebra
Matrices
Complex numbers
Logs
Differentiation
Differentiation
Transposing equations
Exponentials
Geometry
Transposing equations
Total (393)
Physics (180)
Engineering (183)
Computer Science (30)
Exponentials
Geometry
Logs
Other
None
None
0
50
100
0
50
100
Many academics believed there could be long-term
consequences
92% academics felt a lack of mathematical fluency could be an obstacle to
achieving full potential
3
5
0%
61
10%
Strongly disagree
20%
30%
31
40%
Somewhat disagree
50%
60%
70%
Neither agree nor disagree
80%
90%
Somewhat agree
100%
Strongly agree
85% academics felt this affected their departments’ ability to deliver an
optimal programme of study
2
0%
5
8
10%
Strongly disagree
54
20%
30%
40%
Somewhat disagree
31
50%
60%
70%
Neither agree nor disagree
80%
90%
Somewhat agree
100%
Strongly agree
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
1e. Trig. F’ns in calculators
2c. Means
2d. Percentages
5d. Log graphs
3f. Solve e.g. y=k/x
5f. y = mx + c
5g. Rate of change
5h. Tangent
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.

Simplification
Identifying 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….?
peter.main@iop.org,
www.iop.org