Mathematics: the language of physics and engineering

Mathematics: the language of physics and engineering Professor Peter MainMaths 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

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

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%

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

“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 Vast majority of academics also agreed that students joining their course lacked fluency in Maths Academics (40) *Base: 36 academics

Specific areas of difficulty according to students and academics

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 85% academics felt this affected their departments’ ability to deliver an optimal programme of study

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

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

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

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

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

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

Mathematics: the language of physics and engineering