Mathematical Sciences People Pipeline Project - Full Report

Mathematical Sciences People Pipeline Project Qualitative Information Study Final Report

Table of Contents 1

Executive Summary ............................................................................................... 1 Study Methodology ............................................................................................................. 1 Key Findings ........................................................................................................................ 1 Pre-PhD ...................................................................................................................................... 2 During PhD ................................................................................................................................. 2 Post-PhD ..................................................................................................................................... 2 Discussion............................................................................................................................ 3 Conclusions ......................................................................................................................... 3

2

Background ........................................................................................................... 4 Why Mathematics Research and the People Pipeline are Important ...................................... 4 Engineering and Physical Sciences Research Council................................................................. 4 Mathematical Sciences People Pipeline Project .................................................................... 5 Qualitative Information Study.................................................................................................... 5

3

Study Methodology ............................................................................................... 7 Establishing Respondent Sample Size ................................................................................... 7 Mathematical Sciences Postgraduate Research Students by Sub-Discipline............................. 7 Phase 1: Survey.................................................................................................................... 8 Survey Design ............................................................................................................................. 8 Sample Representation .............................................................................................................. 9 Phase 2: Consultations ....................................................................................................... 12 PhD and ECR Focus Groups ...................................................................................................... 12 Employer Consultations ........................................................................................................... 13

4

Key Findings .........................................................................................................15 Pre-PhD ............................................................................................................................. 15 The Decision to Study a Mathematical Sciences PhD .............................................................. 15 Reputation and Deciding where to Study ................................................................................ 15 Moving Locations for PhD Study (and Work) ........................................................................... 16 During PhD ........................................................................................................................ 17 Perceptions about what undertaking a PhD would be like ...................................................... 17 Quality of Training during PhD ................................................................................................. 18 Competitiveness of the UK PhD ............................................................................................... 19 Perceptions of Competitiveness .............................................................................................. 19 Preferred PhD Models .............................................................................................................. 21

EPSRC Mathematical Sciences Qualitative Information Study – Final Report

Post-PhD ........................................................................................................................... 21 Why Employers Hire Mathematical Sciences PhD Graduates ................................................. 21

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Discussion ............................................................................................................24 Pre-PhD ............................................................................................................................. 24 The Decision to Study a Mathematical Sciences PhD .............................................................. 24 During PhD ........................................................................................................................ 27 Mathematics Sub-Disciplines ................................................................................................... 27 Skills Developed During a PhD ................................................................................................. 30 UK and non-UK Mathematical Sciences Education .................................................................. 35 Post-PhD ........................................................................................................................... 43 Transition from Study into Work.............................................................................................. 43 Continuing Professional Development..................................................................................... 46

6

Conclusions ..........................................................................................................50 Mathematical Sciences People Pipeline .............................................................................. 50 Pre-PhD .................................................................................................................................... 50 During PhD ............................................................................................................................... 51 Post-PhD ................................................................................................................................... 52 Emergent Themes .............................................................................................................. 53

The following report has been written and prepared by Timothy Dixon (tdixon@ers.org.uk) and Kate Vittle (kvittle@ers.org.uk) of ERS (www.ers.org.uk) for EPSRC. We would like to thank the EPSRC project team and the working group for their continued help and support. We would also like to thank all the PhD and ECR participants, the academic employers for help in distributing and completing surveys, all those who aided the team with focus groups, and the various academic, industry and government consultees. ŠERS Ltd. 2014

EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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EXECUTIVE SUMMARY

1.1

In July 2013, ERS was commissioned by the Engineering and Physical Sciences Research Council (EPSRC) to undertake a Qualitative Information Study as part of the ongoing Mathematical Sciences People Pipeline Project.

1.2

Building on the 2010 International Review of Mathematical Sciences, EPSRC established the People Pipeline Project to address some of the concerns raised around mathematical sciences PhDs. A number of areas of concern were highlighted, including: funding models, lack of transferrable skills training for PhD students, and accessible career paths for Early Career Researchers (ECRs).

1.3

The Project seeks to identify actions to improve how mathematical knowledge and skills are used to sustain and grow UK economic and social well-being. Specifically, the project aims to identify actions and recommendations to: generate sufficient high quality internationally competitive postgraduate research students to support the UK both in academia and industry, as well as retain the best young researchers and attract the best academic researchers to the UK.

1.4

This Qualitative Information Study is an integral part of the wider Project and investigated people’s perspectives on mathematical sciences along the career pathway, including PhD students and ECRs, as well as academic, industry and government employers. More specifically the key aims of the Study are to investigate: perceptions of the competitiveness of PhD training; motivations for undertaking a PhD; perceptions of carrying out a PhD in the UK; and expectations of obtaining a PhD.

Study Methodology 1.5

The Study used a two Phase approach: Phase 1 utilised broad surveys of mathematical sciences PhD students, ECRs, and their employers (both academic and non-academic), whilst the second Phase utilised more in-depth focus groups and one-to-one consultations in order to explore the issues uncovered in Phase 1.

1.6

In total, five surveys were designed and distributed in Phase 1; PhD student, ECR and academic employer surveys were issued electronically, whilst industry and government employer surveys were carried out via telephone.

1.7

Six focus groups took place in Phase 2 at academic institutions across Britain, with a combination of PhD students and ECRs from different sub-disciplines and institutions sought for each focus group. In addition, 34 employers were consulted with one-to-one or in small groups (maximum of three people), mostly face-to-face with 11 consultations via telephone.

Key Findings 1.8

The key findings relate to the four main objectives for the Study: the motivations, perceptions, understanding of competitiveness and future expectations of carrying out a mathematical sciences PhD in the UK. These can be seen as falling along specific points of the pipeline, with motivations arising prior to commencing a PhD, perceptions and competitiveness relating to during the PhD and expectations more focused on post-PhD. EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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Pre-PhD 1.9

It was found that there were a variety of intrinsic and extrinsic motivations for studying mathematical sciences, with three key factors being:   

An underlying interest or passions for solving mathematical problems; A keenness to use mathematical tools to solve real world problems; and A route to a particular career.

1.10

Reputation in various forms was an underlying motivator for many people in dictating where they chose to study; this included reputation of the supervisor, department or university, research area within an institution. Other factors included a desire to be near to or move away from home and funding availability.

1.11

There was found to be significant value attached to moving location between undergraduate (or master’s) degree and PhD, with this further enhanced if the individual moved country as well.

During PhD

1.12

It was found that people’s perceptions of what a PhD would entail varied a great deal, with some expecting more structure and others less. There was some difference found in how well people who has studied for their undergraduate degree outside the UK rated their course as having prepared them more adequately for their PhD than those who had come through the UK undergraduate system.

1.13

The issue of training quality during the UK PhD was discussed in some detail within focus groups as well as with employers. In particular, three types of training were identified relating to technical (mathematics) skills, research skills, and personal skills.

1.14

There was a general agreement that communication and team working skills of some form were very useful if not essential for competitive PhD students to have, although training in these skills should come as part of an authentic (uncontrived) process integrated into times that the student actually needs to use the skills.

1.15

Various models of PhD programme were contrasted with one another in order to establish which elements of each might be more competitive. It was found that the basic UK system of a three year undergraduate directly followed by a three year PhD rarely happened anymore and was regarded as being highly uncompetitive. In contrast, longer periods in academic training (i.e. more than four years) were seen as beneficial for those intending to move into academia, whilst shorter (three or four years) were thought be more competitive for those aiming for non-academic roles, particularly when combined with industry experience. The importance of a master’s course was agreed universally in consultations.

Post-PhD

1.16

For employers, there were found to be two main reasons for taking on those who have PhDs in mathematical sciences: either as a fundamental part of the work that is undertaken or due to searching for individuals with broader numerate skillsets.

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1.17

PhD student and ECR career expectations were explored in some detail, with particular emphasis on progression through academic or non-academic pathways. Other issues considered included availability and appropriateness of careers advice, access to Continuing Professional Development (CPD) and the attributes of a successful academic.

1.18

It was found that there was a broad consensus accepting the need to work on short-term post-doctoral research contracts for around four to six years post-PhD before expecting to gain a permanent position. This was agreed on by most PhD students and ECRs, regardless of where they had undertaken their first degree or PhD (inside or outside the UK).

1.19

Focus group consultations reported a lack of academic positions at all levels in the UK. This was agreed upon and even seen as self-evident by many of those consulted with. The shared view was that there is a particular lack of permanent roles, whilst ECRs also noted the low availability of fellowships.

Discussion 1.20

The discussion draws together the evidence from Phases 1 and 2 in relation to progress and other experiences along the mathematical sciences people pipeline, commencing with pre-PhD experiences, giving a detailed analysis of the PhD offering in the UK and elsewhere, and finally developing the themes of the post-PhD situation in the UK.

1.21

This section provides more in-depth analysis of the key topics raised in the findings section, providing further evidence for the findings in the form of data and statements from PhD students, ECRs and employers, providing a rich tapestry of the qualitative experiences of those in the mathematical sciences pipeline in the UK.

Conclusions 1.22

Finally, conclusions on the survey, and the focus group and employer consultations are drawn, considering how the information presented should be considered by the Project Working Group and wider mathematics community. Where relevant, suggestions have been provided for additional work that would enhance the current Study findings.

1.23

In addition, there were found to be several emergent themes that became apparent during undertaking the Study. These include:      

The purpose of the PhD; Industry engagement; Understanding of the recent changes in UK HE delivery; Terminology; PhD experience compared with ECR experience; and Individual variations.

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2

BACKGROUND

2.1

This chapter provides a brief overview of the background to the Mathematical Sciences People Pipeline Project.

Why Mathematics Research and the People Pipeline are Important 2.2

Mathematics is a vital science in its own right as well as in the role it plays in the advancement of all areas of science, engineering and technology. As noted by the Institute of Mathematics and its Applications (IMA) the contribution of mathematics is frequently overlooked to a surprising extent 1.

2.3

A 2012 report by Deloitte showed that the quantified contribution of mathematics to the UK economy in 2010 was £208 billion in terms of GVA (or 16 per cent of total UK GVA) 2.

This found that the top five employment sectors for mathematical sciences graduates (at all academic levels) were: computer science; public administration and defence; architectural activities and technical consulting; construction; and education.

2.4

The International Review of Mathematical Sciences (IRMS) 2010 3 put forward the actions required to safeguard the UK’s international standing in mathematics research. The report recognised the progress made since an earlier 2004 International Review of UK Research in Mathematics 4, notably regarding organisational structures, but highlighted the key concern that UK mathematics PhDs are not internationally competitive. Whilst UK academic positions remain attractive internationally, very few Early Career Researchers (ECRs) actually received their PhD education in the UK.

2.5

More positively, the 2010 review found that mathematical sciences research in the UK is of an excellent standard by international comparison. Mathematical scientists were found to interact productively with one another, with other disciplines and with industry to help to solve major problems in science, engineering and medicine. The Review concluded that mathematics researchers contribute creativity, inspiration and solutions to some of society’s most complex challenges; however this important role was invisible or disguised. It was therefore suggested that more can be done to highlight where successful contributions and promote the role of mathematics within multi-disciplinary teams and projects.

Engineering and Physical Sciences Research Council

2.6

The Engineering and Physical Sciences Research Council (EPSRC) aims to sustain and build on mathematical sciences research capability. The EPSRC Mathematical Sciences Strategy 5 sets out the need to:  

Secure the pipeline of future talent by addressing concerns about the quality and international competitiveness of UK PhD provision; Safeguard research capability through career development, focusing on current and potential future research leaders;

1

Institute of Mathematics and its Applications, 2013, “Mathematics Matters” Deloitte, 2012, “Measuring the Economic Benefits of Mathematical Science Research in the UK” 3 International Review of Mathematical Sciences, 2010 4 An International Review of UK Research in Mathematics, 2004 5 EPSRC, 2011, Mathematical Sciences Strategy 2

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



2.7

Promote connectivity within and across disciplines and further reflect the needs of industry. Integrating mathematical science in multi-disciplinary research will enhance its significance, relevance and recognition; and Focus on advanced and novel mathematical sciences which contribute to the RCUK societal challenge themes of: energy, digital economy, living with environmental change and global uncertainties.

EPSRC has highlighted in its mathematical sciences strategy that: “[s]ecuring the pipeline of future talent through PhD training and targeted support for individuals remain a high priority and [EPSRC] will work with universities to improve the quality and competitiveness of doctoral training and career development in mathematics.”

Mathematical Sciences People Pipeline Project 2.8

Building on the 2004 and 2010 International Reviews of Mathematical Sciences, as well as the recommendations made by a House of Lords report on Higher Education in Science Technology Engineering and Mathematics (STEM) Subjects6, the EPSRC established the People Pipeline Project. The Project seeks to identify actions to improve how the mathematical knowledge and skills are used to sustain and grow UK economic and social well-being. Specifically the objectives of the Project are to: 



Investigate how to generate sufficient high quality internationally competitive postgraduate research students to support the UK in both academia and industry, given the changing UK and global landscape; and Investigate how to retain the best young researchers and attract the best academic researchers to the UK, and what support they require.

Qualitative Information Study 2.9

This Qualitative Information Study (hereafter, the Study) is complementary to the quantitative analysis of wider People Pipeline Project and forms an integral part of the overall Project. In order to obtain credible and robust information, EPSRC commissioned a dedicated team from ERS to carry out the Study.

2.10

The Study seeks to complement the quantitative data gathered by investigating perceptions, motivations and expectations that are not recorded within metrics. Within the specific field of mathematical sciences this Study is looking for robust evidence covering:    

Perceptions of the competitiveness of PhD training; Motivations for undertaking PhD in mathematical sciences; Perceptions of carrying out a PhD in mathematical sciences; and Expectations of obtaining a PhD in mathematical sciences and whether those expectations have been met.

6

House of Lords Select Committee on Science and Technology, 2012, Higher Education in Science, Technology, Engineering and Mathematics (STEM) subjects

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2.11

The Study gathered views throughout the PhD career pathway from first year PhD students through to ECRs (those working within academia and within 10 years of obtaining their PhDs, excluding time spent working outside academia). In addition, the views of academic, industry/private sector and government/public sector employers were collected.

2.12

As the name suggests, the emphasis of the Study is on qualitative data utilising a variety of sources and methodologies. It is not seeking enumerate the totality of the UK mathematical sciences, it is instead focused on understanding the views and experiences of individuals and groups within UK mathematical sciences. The overall aim to establish reliable evidenced narratives that can be posited as being issues for consideration by the mathematics community.

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3

STUDY METHODOLOGY

3.1

The Qualitative Information Study utilised a two Phase design, with the first Phase focused upon a broader survey of mathematical sciences PhD students, ECRs and their employers, whist Phase 2 explored more in-depth the issues across the UK mathematical sciences landscape through targeted Focus Groups and one-to-one/two consultations.

Establishing Respondent Sample Size 3.2

To develop and scope the survey, an understanding of the current mathematical sciences academic landscape was needed. To do this, data was analysed from: the Higher Education Information Database for Institutions (HEIDI), the Higher Education Statistics Authority (HESA 7, via EPSRC) and EPSRC records regarding overall numbers of students and postdoctoral researchers they fund.

3.3

This data identified:  





Which universities have mathematical sciences researchers and thus institutions to contact in Phases 1 and 2; Total numbers of postgraduate researchers in mathematical sciences sub-disciplines in order to give estimates for the UK postgraduate student population to assist in planning survey sample size; Trends in postgraduate learners domicile in recent years to understand the demographics of the postgraduate student population across time to assist in planning survey and focus group composition; and Numbers of PhDs funded by EPSRC to assist in the planning survey and focus group composition.

Mathematical Sciences Postgraduate Research Students by Sub-Discipline 3.4

HESA data revealed that in the 2011/12 academic year 8 there were a total 2,565 mathematical sciences postgraduate research students studying at 61 separate HE institutions across the UK, in any year of their degree programme. Table 3.1 overleaf details the number of research students in their first year of study and first years as a percentage of all years.

3.5

The data also showed that, as a percentage of the total, the number of first years is approaching one third (31 per cent) as might be expected across three years of study, with first years studying mathematics and statistics similarly around this point (as shown in Table 3.1).

3.6

The 61 universities that were identified as having any mathematical sciences postgraduate research students in the past three years formed the basis of the sample for the PhD, ECR and academic employer surveys in Phase 1.

7

It should be noted that HESA uses only broad category names for MS sub-disciplines, some of which do not clearly map onto other more detailed categorisations such as the IRMS 2010. Further, it is possible to search only for ‘research postgraduate’ within the HESA data, not specifically for ‘PhD student’, meaning that this group would likely include those studying for a research masters and other postgraduate research degrees as well as those studying for a PhD. 8 Latest year data were available during Phase 1 of the Study.

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Table 3.1: HESA Sub-Discipline Data for Academic Year 2011/12 HESA Sub-discipline

All Years

Mathematics

First years as % of all years

First Years

1,870

590

32%

Statistics

475

165

35%

Operational Research

195

35

18%

25

0

0%

5

0

0%

2,570

790

31%

Others in Mathematical Sciences Broadly-based Programmes in Mathematical Sciences Total

Mathematical Sciences Postgraduate Research Students by Domicile and Year 3.7

HESA data of the number of UK mathematical sciences research postgraduates in the five most recent academic years identified whether they are domiciled in the UK, the EU or outside the EU. As shown in Table 3.2, the figures show a slight drop in the overall number of students between 2007-08 and 2008-09, followed by an increase in students through to 2011-12.

Table 3.2: HESA Data Mathematical Sciences Postgraduate Researchers by Domicile and Year 2007-2008 2008-2009 2009-2010 2010-2011 2011-2012 Domicile (%) (%) (%) (%) (%) UK

1145 (51%)

1105 (51%)

1130 (51%)

1255 (52%)

1340 (52%)

EU

405 (18%)

360 (17%)

350 (17%)

420 (17%)

445 (17%)

Non-EU

700 (31%)

690 (32%)

715 (32%)

745 (31%)

785 (31%)

2250

2155

2195

2420

2570

Total

3.8

Further analysis revealed the percentage of students from each domicile for each year varied very little from 2007 to 2012, with UK-domiciled postgraduates ranging from 51 per cent to 52 per cent across the five years, EU students from 31 per cent to 33 per cent and non-EU from 16 per cent to 18 per cent.

Phase 1: Survey Survey Design 3.9

The ERS Study Team designed five separate surveys, for:     

3.10

Mathematical sciences PhD students; Mathematical sciences ECRs; Private sector (industry) employers; Public sector (government) employers; and Academic employers.

The final survey questions can be made available upon request.

Survey Terminology: ‘Theoretical’ and ‘Applicable’ Mathematical Sciences

3.11

The consultations on survey design specifically identified that the terms ‘theoretical’ and ‘applicable’ mathematics should be used when asking PhD students to categorise their area of work as opposed to ‘pure’ and ‘applied’. It was suggested that much work carried EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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out in mathematical sciences, for example in traditional pure sub-disciplines, was now applicable to other areas of science and real world problems. Therefore the terms ‘theoretical’ and ‘applicable’ were used over the course of the Study in place of ‘pure’ and ‘applied’.

Sample Representation 3.12 For PhD students, the Study brief required representation from: first year, final year and those who had recently left; EPSRC-funded and non-EPSRC-funded; as well as national and international students. For ECRs, the respondents needed to reflect those with fixedterm and permanent contracts, as well as those who were now working in the same institution that they undertook their PhD at, and those that had moved. The employers were split between academic (i.e. Heads of Department [HoDs] and senior staff), Industry/private sector, and government/public sector.

3.13 The Study Team attempted to survey all HoDs at the 61 institutions forming the PhD survey population. Survey scoping identified that many mathematical scientists might be missed if only mathematical sciences departments were targeted. Therefore, it was decided to also contact all HoDs of Computer Science (CS) and Biological Science (BS) departments in the same 61 universities.

3.14 To determine which industry employers to approach, data on destination sectors was considered. Research by Deloitte in 2012 estimated there to be over 2.8 million mathematical sciences occupational jobs in the UK. The key sectors with over 50,000 mathematical sciences jobs are shown in Figure 3.1 below 9

Figure 3.1: Number of Mathematical Sciences Jobs in Key Sectors (Source: Deloitte, 2012)

3.15 A list of employers was compiled after liaising with the Industrial Mathematics Knowledge Transfer Network, who signposted the projects section of their website for industrial project partners. In most instances this gave a named contact at the company who could then be called. The list covered 52 different organisations (including three government 9

Measuring the Economic Benefits of Mathematical Science Research in the UK, Deloitte, 2012

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agencies) across 10 sectors. This was supplemented with a second list of companies from the ‘Maths Careers: who employs mathematicians?’ webpage 10 which was used to fill any gaps in terms of sector coverage.

3.16

In relation to public sector employers of mathematical sciences PhD graduates, it was acknowledged that whilst there were obvious candidates (e.g. GCHQ, ONS, GORS, GSS, GES, DSTL, Met Office, PHE, HEFCE) there were also less obvious places where a mathematical sciences graduate might work (e.g. Forestry Commission, English Institute of Sport). It was therefore decided to consult across all departments, agencies and public bodies listed online 11, with particular focus on those organisations likely to have mathematical sciences PhD graduates.

Sample Size Targets

3.17

The number of responses required to obtain a reliable sample was calculated from the HESA data available for PhD students, with 334 12 responses necessary. An accurate measure for ECRs was however much harder to establish. A lack of definitive data on academic mathematical sciences researchers in their first 10 years of work after PhD completion meant that estimates had to be calculated based on proxy data available, including the number of PDRAs funded by EPSRC, the number of academics of any level reported by HEFCE 13, ONS population estimates and research by the Institute of Physics 14.

Through analysis of these proxy data it was estimated that 309 responses were necessary for the ECR group 15.

3.18

To estimate how many employers to contact, the Study team were guided by previous experience of running similar types of studies, as well as using a power calculation 16.

Through this process it was found that 49 responses would be necessary in each employer group for differences in means to be statistically reliable (147 in total).

Sample Achieved

3.19

Table 3.3 overleaf summarises the target and achieved sample sizes for each survey group. It should be noted that, for example of the 370 that began the PhD survey, 250 went on to complete it. Questions therefore had a declining response rate throughout the survey.

3.20

Table 3.4 overleaf details the headline PhD respondent profiles. Also included is the number of respondents in each survey that said they were happy to be contacted again about taking part in a Focus Group in Phase 2 of the Study, indicating good engagement with the issues covered by the Study.

3.21

Table 3.5 overleaf gives the headline ECR respondent profiles. Of the 171 respondents that began the survey, 150 went on to complete it. Forty-two percent of ECRs agreed to be contacted for Phase 2 again suggesting good engagement with the issues covered by the Study.

10

http://www.mathscareers.org.uk/viewItem.cfm?cit_id=383039 https://www.gov.uk/government/organisations 12 Based on three year population of 2,570; 95% confidence level; ±5 confidence interval.

13 HEFCE (2012) “Staff employed at HEFCE-funded HEIs: Trends and profiles 1995-96 to 2010-11” 14 Institute of Physics Research; Nb. figures are for permanent academic staff only, but act as a rough guide.

15 Based on population estimate of 1,580; 95% confidence level; ±5 confidence interval.

16 A power calculation is a way of identifying sample sizes when testing hypotheses that compare survey responses of different groups.

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Table 3.3: Phase One Survey Target and Achieved Sample Size Target Survey Group PhD Students

Early Career Researchers

Employers

Profile 1st Year Final Year 1st Destination Leaver Movers/fixed-term Movers/permanent Stayers/fixed-term Stayers/permanent Academic Industry Government

Phase 1 Actions

Sample Size: Sample Size: Achieved Target (completed)

Confidence Interval 17 (completed)

e-survey

334

370 (250)

4.7 (5.9)

e-survey

309

171 (150)

7.1 (7.6) 18

147

56 (35) 28 13

Telephone/ e-survey

Table 3.4: PhD Student Headline Respondent Profiles Profile Measure Frequency Percentage of Total Year of Study 0-1 113 31% 1-2 79 21% 2-3 68 18% 3+ 73 20% First Year Leaver 37 10% Location of UK 243 66% Undergraduate Degree EU 69 18% Non-EU 58 16% Funding EPSRC 133 49% Non-EPSRC 127 47% Don’t know 10 4% Agree to Phase 2 94 38%

Table 3.5: ECR Headline Respondent Profiles Profile Measure Frequency Percentage of Total Contract Type Fixed-term 98 57% Permanent 73 43% Current Location Same 34 20% Compared with PhD Different 137 80% Location of PhD UK 96 59% EU 38 23% Non-EU 28 17% Location of UK 68 42% Undergraduate Degree EU 61 38% Non-EU 33 20% Agree to Phase 2 61 42% 17

The procedure for calculating confidence intervals is given in the Section: Survey Samples. In general, with a confidence level of 95%, a confidence interval 95% and a confidence interval between 4 and 8 is deemed acceptable.

18 This calculation uses proxies for the population, as outlined in the Section: Survey Samples.

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3.22

Table 3.6 below shows the headline employer respondent profiles for the three types of employer. In the academic survey 56 respondents began answering the survey questions and 35 went on to complete it, with 43 filling out enough of the survey to be usable to some degree. The industry and government surveys were mostly carried out via telephone, so completion rates were less of an issue as people were more willing to finish the survey once they had begun completing it via telephone.

3.23

Twenty-eight industry employer contacts were consulted across 23 organisations and 13 government/public sector contacts responded from 11 organisations.

Table 3.6: Employer Headline Respondent Profiles (Completed) Employer Type Frequency Percentage of Total 19 Academic Computer Science 3 9% Economics (with Maths and Stats.)

1 3% Management Science 2 6% Mathematical Sciences (incl. Stats.)

22 63% Maths and Physics 4 11% Maths and Computer Science 2 6% Zoology 1 3% Industry Agriculture, Forestry and Fishing 1 3% Electricity, gas, steam 2 7% Financial and Insurance Services 3 10% Information and communication 2 7% Manufacturing 6 21% Professional, scientific & technical 8 31% Public admin. and defence 4 14% Water supply, sewerage 1 3% Wholesale and retail trade 1 3% Government Agriculture, Forestry and Fishing 3 23% Arts, entertainment & recreation 2 15% Education 1 8% Human health and social work 2 15% Professional, scientific & technical 3 23% Public admin. and defence 2 15%

Phase 2: Consultations PhD and ECR Focus Groups 3.24

The planned approach for Phase 2 was to hold six focus groups at three locations around the UK; three focus groups with PhD Students and three with ECRs. Attendance was incentivised with individual prize draws (ÂŁ50 vouchers), one for each focus group and were organised with the assistance of mathematical sciences departments, who were, in some cases, able to encourage attendance amongst their students and staff. Despite this recruitment to the focus groups was challenging with travel cited as being the biggest

19

Including one broader science and engineering school.

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barrier to attendance. Focus groups were therefore hosted in 6 locations and comprised a combination of ECRs and PhDs 20. The 6 locations were as follows:  Bristol University;

 London School of Economics and Political Science;

 Cambridge University;

 Warwick University; and

 Glasgow University;

 York University.

3.25

In addition, several people who could not attend at the specified data and time said that they were still keen to assist if possible. These people were given the option of completing the same questions as discussed in the focus groups and returning them via email. These are indicated as email respondents in Table 3.7.

3.26

Table 3.7 shows the numbers of PhD students and ECRs that took part in consultations, either in person or via email. As can be seen, the numbers were somewhat lower than the 60 or more person attendance range that had been anticipated given the interest in Phase 1. However, there was wide range of sub-disciplines, study locations, experience in PhD/academia exhibited amongst those who attended. Given the detailed discussions that were carried out, it is considered that these focus groups provided robust feedback for understanding the issues presented in this report.

Table 3.7: Focus Group Attendance Profiles Location Cambridge Glasgow London York Warwick Bristol Email Totals

PhDs 4 3 3 1 3 2 3 19

ECRs 0 2 3 5 5 3 3 21

Total 4 5 6 6 8 5 6 40

Employer Consultations 3.27

The planned and achieved numbers of Phase 2 employer consultations is shown Table 3.8, overleaf. The employers were consulted though face-to-face meetings where possible, or alternatively via telephone. They were sent a copy of the questions to be discussed prior to the interview. Academic interviews included additional questions regarding careers advice and Continuing Professional Development (CPD) in the department.

20

ECRs and PhDs were asked to sit in separate groups in order to minimise the potential influence of opinion that the more experienced ECRs might have had on PhD students. The ERS focus group facilitators used a flexible approach in order to maximise discussion and response potential. If there were too few people in a sub-group to create a meaningful discussion then all focus group attendees were asked to contribute together; this was the case at the Glasgow and York focus groups. In total, only one PhD student in attendance at these focus groups was in the same department as any ECR, minimising the risk of peer influence.

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Table 3.8: Numbers of Employers Consulted with in Phase 2 Employer Profile

Consultation Type

Count

Academic, one-to-one consultations spread geographically, including those who receive EPSRC funding and not, CDT/TCC departments and not.

Face-to-face

Industry, one-to-one consultations spread geographically, by those who receive EPSRC funding or not, size, sector

Face-to-face Telephone

3

Government, one-to-one consultations to cover each of the key public sector employers

Face-to-face

2

Telephone

4

10 5

Telephone

11

Total

35

3.28

The academic consultations took place with HoDs and other senior staff with detailed knowledge of supervising and leading projects. These came from departments of: mathematical sciences; applied mathematics; computer science; statistics; and management at 11 institutions across the UK. Industry consultees came from 12 companies spanning eight sectors. Government contacts were from five departments and public sector organisations.

3.29

As can be seen in Table 3.8 there was a high number of employer consultations, providing an excellent basis for the understanding of mathematical sciences employer experiences and issues. The consultations generally lasted around an hour, dependent on how closely aligned with mathematical sciences the company was and their knowledge of the people pipeline, showing that employers were clearly willing to engage in the issues highlighted in the Study.

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4

KEY FINDINGS

4.1

This section details key the findings of Phases 1 and 2 of the Study along the people pipeline. In accordance with the objectives of the Study evidence is specifically presented on:    

Motivations for undertaking PhD in mathematical sciences; Perceptions of carrying out a PhD in mathematical sciences; Perceptions of the competitiveness of PhD training; and Expectations of obtaining a PhD in mathematical sciences.

Pre-PhD The Decision to Study a Mathematical Sciences PhD 4.2

In Phases 1 and 2 of the Study there was revealed to be an authentic sense of intrinsic motivation stemming from interest in, excitement about and passion for mathematical sciences. This was true for mathematicians researching both theoretical and applicable topics. Others were motivated by a desire to use mathematical tools to solve real world problems. A third, smaller group found motivation in mathematics as a means towards recruitment and a secure future career.

“It will be a ‘big data’ world in the future, statistics will play an important role in it” “[My chosen sub-discipline] is a growing field that has the potential to benefit society. It is theoretically interesting. It provides valuable experience for a future career.”

4.3

Survey responses revealed that a majority of PhD students (57 per cent) had planned to do a PhD since around the time of their undergraduate degree, with over three quarters (77 per cent) saying that their undergraduate course had a positive influence on whether to do a PhD. In PhDs and ECRs focus groups, there was a clear motivational theme discussed about the influence of undergraduate or master’s degree tutors in encouraging individuals and guiding the decision to undertake a PhD. The interactions with undergraduate and master’s degree students should therefore not be underestimated in terms of its significance in the decision to study for a PhD in mathematical sciences.

4.4

Other notable factors included funding availability, continuing own research interests, reputation of university, developing skills for future academic work and reputation of supervisor. Further motivations mentioned were often more opportune e.g. having studied an area previously.

Reputation and Deciding where to Study

4.5

Common motivators for those who had studied abroad for their undergraduate degree to choose the UK for their PhD 21 included: reputation of the university or department, reputation of a supervisor, reputation of their chosen research area at that university, as well as the desire to travel to a different country to study. Current UK PhD students who had previously studied abroad were also more likely to be motivated by reputation at a country level when deciding where to study.

21

34% of all PhD students; 20% of all ECRs

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4.6

Where people had stayed in the UK from undergraduate to postgraduate study there was more commonly an emphasis on the reputation of universities or departments and whether they were good for their chosen research area, as opposed to their individual supervisors. Those who had studied abroad, at any stage of their higher education, tended to be somewhat more conscientious regarding their supervisor, checking up beforehand or early on in the PhD course to ensure this person was of high calibre.

Potentially reflecting the personal drive and ambition of those who travel to study.

4.7

The Study findings suggest that there are qualitatively different motivations amongst UK first degree graduates when choosing where to study dependant on whether they ultimately stay at the same institution or change location for their PhD. The apparent importance or influence placed on the supervisor was usually confined to those who continued from undergraduate or master’s in the same institution to study their PhD. The supervisors’ reputation was a less relevant issue at application stage for those ECRs who had undertaken their PhD in the US as they did not choose their supervisor until after commencing their second year.

4.8

4.9

The factors that motivated the decisions of particular groups can be summarised as: 







Those who stayed at the same institute as pre-PhD: usually more awareness of supervisors particularly if already worked with him/her as well as the institution; some attention to reputation of the department and research at institution.

Those who moved to a different institution as pre-PhD, staying in the UK: focus on reputation of the institution in general; often through comparative searches, particularly the intended area of research; moderate-to-little awareness of supervisors.

Those who moved to the UK from overseas: motivation is often based around the institution’s reputation, less often the department (except very top maths departments); supervisor is also an important factor here.

Those who moved overseas from the UK: reputation of the country becomes a major factor; sometimes awareness of institution’s reputation, but not driving force; little known about supervisor at this stage or reputation of research at the location.

Moving Locations for PhD Study (and Work) 4.10

Nearly all those consulted, academic and non-academic alike, recognised the considerable added value of changing locations for different stages of study and work. Moving location was seen as a way to:      

Develop personal skills through broadening one’s contacts, meeting new people, living in a new culture, learning a new language; Learn new approaches to mathematics, broadening academic culture understanding; Acquire new research tools and methods from people who might already use them; Meet new collaborators/networks/peer groups with whom to work/to enable finding future work; Explore different academic/institutional models, consider how these might relate and be imported to one’s future destinations; and Gaining the experience necessary to continue in academia in the UK.

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4.11

Nearly a third of PhD students who responded to the Phase 1 survey (30 per cent) chose to stay in the same location between undergraduate and PhD courses. It is curious that this is likely to be one of the least problematic times for a person to move locations as there are less likely to be familial ties or extraneous factors to accommodate. When exploring this with PhD students they mentioned an ‘easiness’ to stay-put, or lack of perceived urgency in moving, particularly if studying at a well-regarded department or institution. For others, there was a lack of preparedness in terms of life experience or drive to make such a step at that point in their career.

4.12

For those who did move, different factors provided the catalyst to move at different points in the academic lifecycle. Few UK nationals mentioned any consideration of moving to another country for undergraduate study, whereas those who came to the UK at that stage mentioned a desire to improve language and ‘broaden horizons’ in a general sense. Moving to study for a PhD was often predicated on a desire to improve technical and research skills, whilst movement post-PhD was more focused on career-progression, through expanding one’s research network, experiencing alternative educational systems and gaining the experience necessary to gain a permanent position (often in the UK).

During PhD Perceptions about what undertaking a PhD would be like 4.13

Many PhD students revealed that they had not really known what to expect prior to commencing their PhD, leading to level of stress and uncertainty, even when staying on in the same department. The core themes included the extent the programme would be more or less structured or loose, the focus and depth of study and the level of collaboration and input from their supervisor.

“I expected it would be more collaborative with supervisor than it was; it was selfmanaged work, with the expectation of: 'here's the problem, get on with it'. It's not the best way of doing research, especially as I’m doing multi-disciplinary area of study.”

(Post-PhD Student) “Found it to be very focused – I expected it to be broad, working around problems, taking time to explore new things. But in reality only had three years so had to solve the problems that I was presented with.” (ECR)

4.14

From a perspective of well-being, a number of respondents did not feel prepared for the stress stemming from perceived slow progress tacking a large problem.

“I wasn’t prepared for how bad the bad bits would be - it can be that things don't go right for months and months… Everyone had told me this would happen so I should have been prepared; it’s perhaps a process that you HAVE to go through to get through to the other side stronger.” (PhD student – 3rd year)

4.15

When surveyed, current PhD students who studied for their undergraduate degree in the EU rated their undergraduate degree as having prepared them more adequately for their PhD course content than those who studied in the UK or the non-EU countries. UK undergraduates felt less well prepared by their undergraduate course in terms of their ability to communicate complex ideas. Furthermore they felt that their undergraduate degree had not influenced their post-PhD career choices as much as EU and non-EU undergraduates.

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Quality of Training during PhD 4.16

PhD students were asked to rate on a five-point scale from very good (2) to very poor (-2) their prior expectations of PhD training and how the training had been in practice. This showed that expectations were higher than the reality of training experienced (see Table 4.1). The mean scores for all areas were within the positive range between ‘good’ (1) and ‘average’ (0).

Table 4.1: PhD Student Training Expectations vs. Current Opinions 22 EPSRC Funded Non-EPSRC Funded Training Issue Before PhD Current Before PhD Current 0.86 0.71 0.86 0.79 Range of topics/specialisation available 0.92 0.76 0.96 0.77 Quality of training provided Delivery methods (e.g. one-to-one 0.78 0.66 0.75 0.56 tutorials, online tutorials, seminars etc.)

4.17

There were small differences in experiences of those funded by EPSRC or not: those funded by EPSRC gave higher ratings for training delivery methods than non-EPSRC, whilst the latter group rated the range of topics that were available as slightly higher than EPSRC-funded respondents.

4.18

When preferred training methods were discussed, there was often mention of working one-to-one (e.g. with supervisor) or in small groups on bespoke forms of training.

Generic courses were disliked, sometimes strongly, by students particularly if they were given at a university-wide level.

Skills Developed during PhD

4.19

Employers were asked how well prepared PhD graduates were for working in the employer’s organisation in terms of technical, research and personal skills. The overriding consensus was that additional training was needed in personal or soft skills, with communications skills and team working the most desirable of these across all employer types. It is significant and was highlighted by research participants that developing these skills could be seen as at odds with the central output of a PhD (i.e. thesis of an individual’s original research). The fundamental need for good communications was repeated in all consultations held, with this also seen as one area that could dictate successful career progression.

4.20

As Table 4.2 indicates, there is a trend amongst academic employers to regard those recruits who undertook their PhD in EU and non-EU institutions as requiring less technical and research training compared with those from UK universities. The same trend is not apparent within the responses from industry or government.

Table 4.2: Additional Training Required for PhD Graduates when Recruited 23 Academic Industry Government Skillset UK EU Non-EU UK EU Non-EU UK EU Non-EU Technical 1.38 1.13 1.18 1.48 1.43 1.54 1.11 1.40 1.40 Research 1.28 1.07 1.07 0.89 1.00 0.70 1.25 1.40 1.67 Personal 1.77 1.84 1.93 2.14 2.08 2.45 2.00 1.80 2.00 22

Table gives weighted mean of 5-point Likert scale responses: ‘Very good’=2; ‘Good’=1; ‘Average’=0; ‘Poor’= -1; ‘Very poor’= -2.

23 Table gives weighted mean of 5-point Likert scale responses: ‘none’=0; ‘a little’=1; ‘some’=2; ‘a lot’=3; ‘extensive’=4.

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4.21

There was a clear difference in how the employer types viewed the need for more technical (mathematical) training. Academia saw the need for somewhere between ‘a little’ and ‘some’ more training, with industry perceiving a greater need for training and government not needing as much. It is likely, given the nature of academia, to always expect a new candidate to be learning more, whilst in industry it was made clear in discussions that there would be a requirement to somewhat ‘retrain’ or at least reposition the graduate’s previously built knowledge to fit the organisational requirements.

4.22

Government employers in general had less stated need for such high level mathematical skills training so were less likely to rate the need for additional technical training highly.

This might suggest that the PhD programme may not be the most appropriate training for quantitative roles required by many government agencies; a master’s degree appearing sufficient in many (although clearly not all) cases.

Competitiveness of the UK PhD

4.23

In discussions regarding the competitiveness of UK PhD training there was a split between people suggesting the UK retains an edge, particularly in certain areas of specialism that are globally recognised, and those that said there was a serious need to make changes to what has become a dated and uncompetitive model of HE training. Whilst the latter group were in the minority within the academic employers consulted, they did hold stronger views in their comments.

4.24

Those PhD students who were aware of any concerns were generally guided by discussion with international researchers they met at conferences. Two PhD students mentioned discussions with US academics who “don’t even look at UK applications [for postdoc positions]” due to lack of substantial teaching experience, and others exhibiting more “mathematical maturity…time to mull problems over” due to longer courses.

4.25

Industry and government employers were generally quite satisfied with the calibre of the PhD graduates that came through the UK HE system. Graduate recruits were viewed as good, filling the requirements of most organisations, but at times there were not enough coming through the pipeline to fill demand.

Perceptions of Competitiveness

4.26

Employers were asked to consider why there might be similarities or differences between PhD graduate recruits from different locations. Many academic employers commented that EU as well as US candidates had more experience, while particular countries such as Germany and France had specific areas of mathematical where they have developed a competitive advantage. Many said there was no difference between employing people who had studied for their PhD in the UK or abroad (beyond interrelated issues such as visas, language, or nationality issues of working in particular government departments).

Some pointed out it was more relevant to consider which university the person had studied in, regardless of which country that might be in.

4.27

Some 41 per cent of PhD students surveyed had also thought about studying outside the UK whilst deciding where to study. The breakdown of where people considered studying is shown in Table 4.3, overleaf. Whilst approximately half of those who studied for their undergraduate degrees in EU or non-EU countries contemplated studying in the same region, three quarters of UK-based undergraduates only considered studying in the UK. EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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Table 4.3: Consideration of Studying Outside the UK for PhD Did you Consider Study Outside the UK? Location of Undergraduate Degree Yes: EU Yes: Non-EU No UK 7.6% 18% 75% EU 51% 27% 22% Non-EU 17% 49% 34%

4.28

This finding might suggest that graduates from other countries feel that they are better prepared or able to operate internationally, even before the PhD. Locations considered

by UK undergraduates included USA, Germany, Canada, France and Switzerland.

4.29

It was raised that there might not be an issue with PhD training, but rather a result of prePhD training in the UK. Reasoning included the lack of a two year master’s course before PhD (as in Europe) or at the start of the PhD (as in the US), combined with an undergraduate teaching approach referred to by one consultee as the “theory of past papers 24.” However, others did comment that UK first degree graduates would usually be more advanced than US graduates at the same stage.

4.30

Overall, 39 per cent of employers surveyed said that they considered the country a PhD graduate had carried out their PhD in when recruiting whilst 61 per cent said they did not; academic employers considered this more than public and private sector employers. It should be noted that in several government agencies contacted there is a requirement either to have UK nationality, to have lived in the UK for a specific amount of time, or other such restrictions. Academic and industry employers reported that Germany was the most common country for PhD graduates to come from outside the UK, with USA and France also frequently mentioned by Heads of Department. China, USA, EU and India were frequently mentioned by the private sector and public sector employers mentioned USA, France, Australia, China and Italy amongst others.

4.31

A consultee at one academic institution explained that: “Certain countries have longer PhD periods, the level of supervision is different, there is a difference in the amount of teaching done. This all means that for certain countries we would consider hiring somebody directly after a PhD, while for other countries we would not”

4.32

Many employers however stated that the country of PhD training was not an issue and that each individual would be considered on their own merit. It was a matter of being reassured that “the quality of the PhD training is adequate”.

4.33

There was an implication that worries about the competitiveness of the UK PhD were somewhat based on the assumption that the UK PhD graduate will have done a maximum of seven years study; the reality given by most academic consultees is that this is now the minimum. In many cases such as those who are studying via CDT, students will graduate with something like four years of undergraduate (either in the form of an MMath degree or three year undergrad with a year master’s) and then have a 1+3 PhD course after that.

These recent forms of training do not seem to have been fully accounted for in previous discussion of competitiveness and should certainly be considered in future work considering UK PhD competitiveness.

24

The suggestion being that undergraduates only learn to pass exams, via past papers, not learn the true theory of mathematics itself and how to creatively apply this.

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Preferred PhD Models 4.34

The preferred PhD model for each group surveyed is shown in Table 4.4. Of the models offered, the enhanced UK was preferred, with the European model also well regarded.

Some consultees commented that they saw little difference between these models in real terms. Suggestions regarding best or worst structures included a more ideal model involving four years of undergraduate followed by four years of PhD, as well as various other combinations of course length.

Table 4.4: Responses for Five Surveys regarding Preferred PhD Model (including % of response)

Model 25 Basic UK (3+3) Enhanced UK (3+1+3) European (4/5+3) US (3/4+5)

PhD 26 ECR35 Academic 27 Industry36 Government36 3rd (1.9) 4th (1.5) 4th (2.9%) 3rd (0%) 4th (12.5%) 1st (3.3) 2nd (2.8) 1st (43%) 1st (50%) 2nd (25%) 2nd (3.1) 1st (3.3) 3rd (14%) 2nd (30%) 1st (37.5%) th rd nd th 4 (1.8) 3 (2.5) 2 (40%) 4 (20%) 2nd (25%)

4.35

At focus groups there was unanimous agreement that the presence of the master’s course within the UK model was important if not essential for those continuing in academia. This was seen as particularly important for the benefit of providing additional broader mathematical training experience, ideally with a research project involved as well. Combined four year undergraduate degrees were generally also well perceived, although there was some discussion amongst a small number of employers and ECRs that they might act more like an extended bachelor’s course rather than a master’s.

4.36

Another key element of PhD structure particularly highlighted by industrial employers was the overriding benefit of doing some form of internship or on the job learning. This was explored in detail by several employers, who saw major benefits in the recruits they took that had undertaken some form of work experience. An interesting idea explored in consultations was that placements would also be useful for those wishing to remain in academia, with an ‘internship’ involving time at another university during the PhD, enabling the researcher to gain some of the benefits of moving locations.

Post-PhD Why Employers Hire Mathematical Sciences PhD Graduates 4.37

Non-academic employer motivations for hiring people with mathematical sciences PhDs highlighted the ability of PhD graduates to ‘hit the ground running’ with having attained more experience and expertise during their studies. This enables them to “think outside the box” when compared to independently come up with a solution to complex analytical questions.

25

A simplified version of different models was used: ‘Basic UK’: three years undergraduate course followed by three years PhD; ‘Enhanced UK’: three yeas undergraduate followed by some form of master’s degree (either integrated into undergraduate or separate) followed by three years PhD; ‘European’: four (to five) years undergraduate including two years master’s equivalent followed by three (or more) years of more flexible PhD; and ‘US’: four years of undergraduate degree followed by four to five years of PhD including two years of taught courses.

26 Based on a weighted average: Rank 1=4; Rank 2=3; Rank 3=2; Rank 4=1 27 Percentage of employers that selected each model as the one that would generate the ideal MS PhD graduate candidate for their organisation.

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4.38

The importance of mathematical sciences to the economy was stressed by industry employers. This was concisely expressed by one who said that: “Our business will sink or swim on the availability of maths PhDs.” Expectations for the Future

4.39

Of the 29 per cent of PhD students surveyed that had received some form of careers advice, 61 per cent felt that the advice was adequate to make an informed decision about future plans. When asked whether they had an idea of their next step following their PhD, 82 per cent of this group said that they did compared with 63 per cent of those that had not received any careers advice at that stage. The main source of advice had been supervisors (33 per cent of all advice given), with a careers advice service also used by a quarter of respondents (26 per cent).

4.40

When surveyed, ECRs were also asked about whether they felt that their PhD course had prepared them for their current role. The areas that they felt most prepared were:   

My PhD improved my ability to work on my own; My PhD improved my ability to communicate complex ideas; and My PhD prepared me in terms of research techniques necessary for my current research.

4.41

When the issue of careers advice was raised in focus group discussion it was stressed a number of times that there was inadequate provision for maths-specific advice. This was seen as necessary, with many PhD students and a number of ECRs unsure of the wide variety of jobs that are available outside the academic routes. One university had specific events that catered for mathematical sciences postgraduates, but it was acknowledged that these are resource-intensive and unlikely to work if there are insufficient numbers of PhD students within a cohort to attend them.

4.42

The overriding consensus in focus groups was that there are simply not enough postdoctoral positions given the numbers of applicants (from both inside the UK and abroad). PhD students said that this meant they were likely to have to move away from the UK; although they did understand that this would also be beneficial for their CV and potential career advancement.

4.43

Another clear expectation of gaining a PhD was that the graduate would have to work approximately four to six years before there was any real chance of getting a permanent position; this was a view shared by PhDs and ECR. This was not regarded as necessarily a bad thing and was not discussed in a context that suggested other people who had graduated through alternative PhD models would advance quicker or slower. 28 There was agreement from all that this was a normal length of time to wait for a permanent position, with several (e.g. graduates from US universities) who had already been through this process and were now lecturers.

4.44

The five year cut-off was also found in the Phase 1 surveys, as shown in Figure 4.1 overleaf. This presents data from ECRs on what role they expected to have in the next one, two, five and ten years (only including academic responses). A large increase can be

28

ECR focus group consultees had a diverse mixture of backgrounds, having graduated from UK, EU and non-EU (particularly US, although also other) universities.

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seen in the proportion of those who see predict they will be in a permanent role after five years rather than two years.

Which of the following roles do you see yourself in in the coming years?

0%

20%

Percentage of Total 40% 60%

80%

One year Two years Five years Ten years

100% PDRA

Fellowship

Lectureship

Reader/Professorship

Figure 4.1: Projected Timeline of ECR Planned Future Roles

4.45

This indicates that whilst there have been suggestions that the UK mathematical sciences PhD is less competitive than other programmes, the expected career progression for the five years post-PhD is fairly similar for those who have graduated from various different areas of the world. The difference might be in the kinds of steps that are necessary in order to get to the permanent position; for example, moving to another country or developing more multi-disciplinary or collaborative networks. This suggests a variety of avenues of further research, including a comparison data of how long people take to obtain a permanent position when coming from different PhD models, and whether there are differences in the types of activities people must carry out in order to develop the relevant experience for a permanent position.

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5

DISCUSSION

5.1

This section discusses the findings from across Phases 1 and 2 in relation to the stages of the mathematical sciences people pipeline, from pre-PhD, through to post-PhD, with particular focus on various facets of PhD training and composition.

Pre-PhD 5.2

The scope of this Study did not include the pre-PhD pipeline in terms of education and training. It does however consider the motivations for studying a mathematical sciences PhD. The Decision to Study a Mathematical Sciences PhD

5.3

Reasons why people chose to study mathematical sciences in general, and for a PhD in particular, fell into two main categories: intrinsic and extrinsic motivations. There was a sense amongst PhD students and ECRs that doing the PhD had been the ‘natural’ thing to do (intrinsic motivation), or that they had known for a long time, for example even before their undergraduate degree that they would continue to study into a PhD. In contrast, a lower number stated extrinsic motivations such as that they chose to do a PhD as they were seeking better job prospects or “didn’t have anything else to do”.

Motivations to Study a Particular Sub-Discipline

5.4

PhD students who defined their PhD sub-discipline topic as ‘theoretical’ gave reasons related to ‘interest’, ‘excitement’ or ‘passion’ when asked why they chose the topic they were studying for their PhD, which are clearly intrinsic motivations. Those who described themselves as theoretical mathematicians particularly highlighted the enjoyment of topics at master’s level as key to choosing sub-disciplines. Whilst many who were studying ‘applicable’ topics also cited similar reasons, there was a much greater diversity of reasons in the latter group, including reasons associated with a desire to apply mathematics to the real world and future career prospects which could be considered to be extrinsic factors. Also mentioned were reasons of happenstance or opportunity such as having studied the area at master’s or undergraduate level (19 per cent of all reasons given).

Motivations for Studying in Particular Locations

5.5

A variety of aspirational and practical reasons arose when PhD students and ECRs considered the reasons why they chose the particular location for their PhD. A key factor raised at nearly all PhD and ECR focus group consultations was access to funding dictating the location they were studying or had studied at.

5.6

Some others chose their location on a basis of ease, it happening to be the place where they had been studying prior to the PhD and funding being available there. This was the case for individuals at the focus groups who had applied to multiple locations but had only been offered unfunded places at institutions other than where they were studying.

5.7

Other reasons mentioned for choosing a location were that there were particular specialisms or facilities at certain institutions that made these places especially appealing, or indeed were unique to that place in the UK an example given was the fluids laboratory at Cambridge.

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Why Study in the UK? 5.8

For PhD students in Phase 1 who had undertaken their undergraduate degree in another country decided to study for their PhD in the UK:  

5.9

‘Reputation of university or department’ was the top reason those (24% of all responses given to the question), followed by ‘Reputation of supervisor’ (19% of all responses).

For PhD students that had considered studying overseas but eventually decided to study in the UK, the top reasons were:  

‘Reputation of chosen research area at university’ (21% of responses) and ‘Reputation of university or department’ (19%).

5.10

When specifically asked whether the UK had a reputation that attracted people to study in the country, some non-UK nationals felt there was indeed an amount of kudos in studying for a PhD in the UK as it is generally perceived as a high quality country in which to study or work. Those from outside the UK also highlighted that a country-level reputation can be based on ability to obtain funding and that the UK might be well regarded in this respect both in terms of PhD funding and for longer term or permanent contracts.

5.11

The views of those from within the UK system were less certain in terms of the international reputation for the UK. Those who had some experience of studying abroad felt that perhaps there was no real reputation for the UK as a whole and that internationally people had heard of Oxbridge but other excellent universities could go unknown. This perspective was corroborated by an ECR who had come to the UK as a PDRA at a ‘top-five’ mathematics department but admitted they had not known anything about the institution prior to this. The individual did however perceive that impressive progress had been made to its international reputation since this time, although this of course may be a due to their increased knowledge about the global mathematical community.

5.12

When exploring why people chose a particular country to study, the time it takes to study for a PhD was raised as a factor. For example, one focus group ECR said they decided to study for their PhD in the UK quite simply because: “you can get a PhD faster in the UK than in the US or Europe”.

Why Study Outside the UK?

5.13

The decision to choose particular mathematical sciences sub-disciplines necessitates an understanding of what that area of research involves, what typifies it and what separates it from other areas. For those who are looking to undertake a PhD but are uncertain about the exactly what they want to study, the US model of an initial stage of taught courses was considered a good option. The benefits are described as having time in the first two years to explore areas of interest and then select a topics and supervisor for PhD study. For one consultee who had been clear they were going to pursue a PhD after graduating from their first degree, but wanted to avoid doing a masters, this was a particularly attractive option.

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Moving Locations for Study and Work 5.14

The value of changing locations (both to study and after completing a PhD) was well known amongst the focus group attendees, particularly for PhD students later in their study and ECRs. ECRs noted the need to move, including for those who had learnt from their own experience of staying at the same university for undergraduate and PhD. This was not restricted to the UK; a clear ‘unwritten rule’ in Australian universities was mentioned that researchers should move institution after completing their PhD, particularly if the PhD and undergraduate locations were the same.

5.15

The value of changing location is thought to persist throughout the career pipeline, key benefits being expanding networks and learning about different academic cultures or methods. This is thought to result in higher quality research via a deeper understanding of mathematics, as well as develop a broad knowledge of other academic models and approaches. It was also commented that a lack of movement between universities and departments can lead to stagnation of novel thought.

5.16

Moving location, particularly moving country, can have a significant impact on the individual’s development in terms of personal skills. Several people recommended moving due to their experience of developing these skills. It is also for this reason that employers of all types saw a benefit of moving location, even when they did not perceive any specific technical or research benefits.

Applying to Study for a PhD

5.17

A PhD student who had made both UK and US applications found that US offers were generally higher in monetary terms and were immediately available. In the UK however they needed to forge a link with a department or institution, agree an area of research and then seek funding. An EU example suggested increased flexibility as grants can be attached to the student rather than the university or department (although are easier to obtain if sponsored by a potential supervisor). Further, these are flexible to be used with collaborative partners as established by the student. This model also has the added benefit in terms of learning to think about the project and organise, manage time and so forth whilst giving more freedom and highlighting that internationally there can be very different application processes that potential applicants need to understand to navigate.

Finding a Supervisor

5.18

In the focus groups, some people mentioned that they had taken guidance on who to work with from a previous (e.g. master’s or undergrad) supervisor, or had already heard of the supervisor that they worked with. However, more often than not, both PhDs and ECRs said that they did not have a clear idea of the true international reputation of their supervisor when they had applied for the PhD position. It was felt that this knowledge is developed during the PhD as students attend conferences and get introduced to collaborators.

An ECR recommended that a good way to assess the potential of a supervisor (or Principal Investigator) is by looking at their publication record and analysing the number of publications they have with PhD students/PDRAs. This would suggest that the person is open and amenable to working together and sharing the kudos from the research.

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During PhD Mathematics Sub-Disciplines Defining Pure and Applied, and Theoretical and Applicable 5.19

Consultees were inconsistent in terms of whether they viewed the mathematical sciences sub-disciplines as categories which could be very clearly defined as ‘pure’ and ‘applied’, or whether they were in fact a much more nebulous mixture of traditionally pure and applied subjects. Overall it was considered that many of them could be approached from either a theoretical or applicable stance.

5.20

The evidence gathered indicates that the PhD students themselves differentiated between ‘pure’ and ‘applied’ the most and were the greatest users of this terminology.

This was particularly the case in institutions where there is a clear scholarly (and sometimes physical) divide between pure and applied departments or groups.

5.21

Many industry employers and some ECR and academic employers (who naturally had more career experience in maths) felt that there was or indeed should be an applicable element to all mathematical research. An industry employer went as far as to say: “…pure and applied is an outdated distinction” Status of Mathematics Sub-Disciplines

5.22

There was a tendency for those earlier in the pipeline (i.e. students) to attach a greater level of intellectual kudos to more theoretical sub-disciplines. This perception was mentioned by PhD students involved in both applicable and theoretical projects, although was more prevalent in applicable-subject students. They felt that theoretical subdisciplines are intellectually more challenging than applicable ones, despite in one case studying applicable maths at one of the highest-ranked departments in the UK.

5.23

There was a sense that this admiration of more pure/theoretical sub-disciplines stemmed from undergraduate or earlier study. Amongst ECRs and academic employers there was an agreement that any suitably well carried out rigorous mathematical research could, and should, be of equal merit and standing.

5.24

The fact that people early and those later in the pipeline seem to have a different view towards theoretical sub-disciplines could have implications for whether or not individuals feel such topics are accessible. If it is felt that theoretical topics are more challenging and ‘not for me’ there may be a need to demystify this in order to encourage participation.

Employers views on Theoretical and Applicable Mathematics

5.25

Employers did not express fundamental distinctions regarding the intellectual pursuit of theoretical versus applicable mathematics. They did however acknowledge the desirability of newer and more exploitable mathematical sciences areas. In the Phase 1 survey whilst there was a wide range of sub-discipline studied by new recruits across employer types, all had recently taken on more people with applicable PhD subdisciplines than theoretical 29. Industry more frequently mentioned computational science and engineering, whilst academic employers also noted algebra as an area studied by those recently taken on.

29

Statistics and mathematical physics were the most frequently cited sub-disciplines.

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5.26

In Phase 2, there was a clear and strong preference for applicable sub-disciplines from consultees at seven of the 12 private sector organisations interviewed. Another industry contact suggested that there was an equal status for pure and applied researchers, and thought that whilst neither would necessarily be able to deal with real-world problems he had a personal preference for theoretical physicists in the roles he supervised. A financial sector contact suggested that a good pure mathematics PhD graduate could provide a decent building block for their employees.

5.27

Amongst the public sector employers there was much greater emphasis on broader ‘numerical skills’ without any need to distinguish between theoretical and applicable mathematical sciences. There was less need for a PhD in mathematical sciences and often an individual with a numerate master’s or first degree would be adequately skilled for the roles required. In many roles the hiring of those with PhDs was therefore more often due to happenstance rather than necessity. One explanation for this focus was that there were more roles that involved using mathematics as a tool rather than developing new mathematics.

5.28

A fairly common industry view was that the more theoretical PhD graduates would find it harder to integrate into a work environment due to i) a lack of real-world problem solving experience and ii) a perceived tendency for pure mathematicians to be more solitary and immersed in mathematics. In most cases this view was based on personal experience, such as the consultee having studied a theoretical sub-discipline themselves. The underlying suggestion was that some of the most theoretically-inclined mathematicians may be less suited to a team working role.

5.29

A crucial, but less often heard perspective is that theoretical mathematics provides a vital role furthering many areas of science and technology and this must not be lost due to a focus on more short term goals. Overall, it appears there is a trend away from the traditional concepts of sub-disciplines, and a growing understanding that applications can, and will, be found for any mathematics; albeit in some cases many years in the future. The people pipeline therefore needs to reflect the needs of industry now, whilst safeguarding longer term mathematical innovation.

Multi-Disciplinarity 30 PhD Student and ECR Views on Multi-disciplinarity

5.30

5.31

In Phase 1, PhD students and ECRS reported that:   

Nearly a third of PhD students (32%) were researching ‘multi-disciplinary’ projects; Of the PhD students whose work was theoretical, 11% was multi-disciplinary; Of those PhDs working on applicable projects, 64% were multi-disciplinary;

 

In contrast, around half of ECRs (51%) stated their work was multi-disciplinary; and Of those ECRs working on a multi-disciplinary project, 87% said that they would recommend working on such projects.

Focus group discussions revealed a plausible reason why less PhD students were working on such projects. As an ECR in a theoretical discipline put it: “[It is] hard enough becoming master of one thing in 3 years, let alone 2 things.”

30

Indicating that work is between two separate departments, schools; interdisciplinary.

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5.32

With such a demand on time in the PhD course, students felt it is too hard to expect that the sufficient level of knowledge needed for a multi-disciplinary project will be achieved.

Students also suggested that working on such projects would not allow for adequate time in either discipline and expressed concerns about whether they would be accepted by either community as a true expert.

5.33

PhD students from more theoretical backgrounds were not in favour of this kind of work for the reason that: “Within relevant areas multi-disciplinary research would be very interesting; within pure maths much less so.”

5.34

Some PhD students acknowledged that there could be advantages to multi-disciplinary projects, including increasing communications skills through dialogue with nonmathematicians, increased interest through application to real-world problems and the work creating more visibility in the field.

5.35

There does appear to be a fairly large difference in perceptions about multi-disciplinary work between PhD level and the at ECR level. ECRs were generally more tolerant or enthusiastic about the prospect of multi-disciplinary work. At one focus group PhD students felt that multi-disciplinary work “doesn’t fit with pure maths” but an ECR present confirmed he was aware of theoretical maths opportunities within multi-disciplinary projects. A lack of awareness of such opportunities amongst PhD students therefore appeared to be an issue.

5.36

A key issue for ECRs and some academic employers was that there should not be a transition towards primarily funding multi-disciplinary projects. Whilst some noted that “research nowadays basically is multi-disciplinary” it was felt that in order to remain beneficial it should not be compulsory.

Employers views on Multi-Disciplinarity

5.37

The academic employers were generally supportive of the concept of multi-disciplinarity for providing useful skills such as team working and communications in people they employed, but did not see it as necessary for PhD projects 31. First and foremost they saw strong academic ability as more important than multi-disciplinary working. Employers at seven of the 11 academic institutions consulted gave clear support for multi-disciplinary work for at least some members of their department. This often focussed on applied mathematics and statistics groups or departments, with statistics being described as: “the ultimate multi-disciplinary branch of science, the route of whose work is in other disciplines”.

5.38

Seven of the 15 industry consultees were very positive towards the multi-disciplinary work experience of some of their mathematical sciences recruits. Other industry employers were fairly neutral on the subject. Those who were more sceptical placed more emphasis on the workplace skills the approach would need to develop. For example it was considered more important to have a strong mathematician who can work with other people (such as engineers), rather than a person who has worked across both disciplines.

31

An exception was Aston University, who highlighted that every PhD student there has a second supervisor working in a slightly different area, with many working with people from other departments and private organisations on projects that are directly implementable to industry.

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5.39

It was similarly felt that this kind of working did not necessarily develop more skills in realworld problem solving, which is actually what is needed. Although it was acknowledged that multi-disciplinary working did show an interest in applying mathematical skills to the real world.

Funding and Multi-Disciplinarity

5.40

In conversations with academia regarding the application of mathematics in the context of multi-disciplinary working, there was an understanding shared by most consultees that the more applicable subjects were easier to evidence the impact of (e.g. for in the Research Excellence Framework) and therefore easier to get funded. Whilst this distinction was often not realised by PhD students themselves, post-PhD academics were well aware that there were specific advantages to ‘multi-disciplinary’ work in terms of funding.

5.41

There was an understanding that academics were becoming used to ‘using the right language’ when talking about multi-disciplinary work. The more cynical perspective was that many, if not all projects could be described as multi-disciplinary if that was what was required by funders. This was not seen as a desirable position to be in as it was felt that there should be better ways to ensure funding was fairly distributed. This was particularly highlighted by theoretical researchers.

5.42

Funders within the mathematics people pipeline should therefore be aware of their ‘true’ ability to influence research programmes through criteria such as multi-disciplinarity.

They should also recognise the longer term effect these factors could have on the theoretical mathematics knowledge base.

Skills Developed During a PhD

5.43

The Study investigated skills development in terms of the types of training people received and how this compared with their perceptions prior to commencing. In addition, employers provided a great deal of insight regarding the skill levels of recruits and the skills required in the workplace.

Overview of Skills Needs

5.44

The Study looked at skills developed throughout mathematical sciences PhD courses, namely: technical mathematical skills 32, generic research skills, and personal or soft skills 33. The Phase 1 survey found that all employers thought a PhD graduate who had been recruited would need more personal skills training than either technical or research skills training. Academic employers identified that UK PhD graduates would require more training than non-UK graduates for technical and research skills training, but slightly less than others for soft skills training.

5.45

When consulting further with employers in Phase 2, academics felt that there should not be an expectation that a PhD graduate is a ‘finished article’. It was suggested that a young researcher still has much to learn and that this might be why academic employers 32

In discussion with two academic employers it was suggested that this term might confuse some researchers, who would regard ‘technical’ training as being in, for example, computer programming, i.e. conflated with ‘technological’. Under the current definition, these would fall into the ‘research skills’ category. Care was taken in Phases 1 and 2 to describe the intended meaning of the term in surveys and discussions.

33 Including team working, multi-disciplinary working, leadership, project management and communication.

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did not expect such high levels of skills as the non-academic employers in the Phase 1 survey findings. Equally, it could be argued that a non-academic employer may see a PhD graduate as already having had advanced level training so the employer has greater expectations from this individual.

Technical Skills 5.46

It was noted by both academic and non-academic employers that there is a shortage of individuals with technical skills in some specific sub-disciplines. This shortage was thought to be related to the skills demands in the private sector, both in terms of driving PhD choices and providing and attractive alternative to academia. Several departments reported having difficulties in recruiting in areas such as statistics and financial mathematics or actuarial skills. It was also noted by some non-academic employers that their impression was that the best candidates were being spotted after completing their undergraduate degree and heading to London to work in finance.

Programming Skills

5.47

Several PhD students mentioned that there were particular skills such as programming that were beneficial to learn and were also understood to improve employability. PhD students said that they would have liked to spend more time on learning how to programme, but felt that other aspects of their PhD would have suffered if they had done so. An ECR agreed that it is a useful skill, but demonstrated the proactive approach of those further on in their career: “there is a tacit assumption that you would go find out e.g. how to programme yourself, with the support of those in the department who already know how to do it.”

Recruitment and the Level of Mathematics Ability

5.48

Many of the non-academic employers felt that they were able to find appropriately skilled candidates either quite quickly or within an appropriate timeframe, some feeling able to be extremely selective and only employing the “very best” candidates. A small number mentioned having some periods in the past when there had been a high demand for specific mathematical sciences skills and having short-term issues with recruitment. This was not widespread.

5.49

Many larger organisations were in a more similar position to academic institutions, with an international array of PhD graduate candidates to select from. Again a minority still found they struggled to fill positions, attributing this to the general downward trend in people studying STEM. It was noted that this is not confined just to the UK.

5.50

The public sector described a slightly different trend to that described by industry. Whilst overall numbers of applicants had fallen in recent years, the quality had remained high, if not increased as more candidates were getting through the initial technical tests. As with academia, GSS, ONS and GORS experienced specific problems with attracting highly skilled applicants as they found private organisations could offer greater financial remuneration than in the public sector. It was noted that private consultancies have recently started undertaking Operational Research work which, combined with the increasing fees for master’s courses, had led to an acute issue for GORS in terms of recruitment.

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Research Skills 5.51

Overall there was seen to be little concern about the level of research skills developed as part of a mathematical sciences PhD relative to the technical and, in particular, soft skills.

One area that did arise from discussion with academic employers was the consideration of what the true purpose of undertaking a PhD should be. For example, an academic employer felt that: “a PhD involves researching a significant problem across significant period of time – something which is itself a useful skill in other areas of life as well”

5.52

This theme that was raised and explored in several areas the Study, ultimately culminating in the core issue of whether: a PhD should be focused on creating a worldclass mathematics researcher or creating someone suited to particular employment options therefore developing a range of soft skills as well? An academic employer felt that a decent PhD programme should be able to instil both sets of skills, although with the caveat that soft skills need to be: “balanced against solving hard problems; one can’t be a successful mathematical sciences researcher simply by having good soft skills”.

5.53

Academic employers gave a broadly consistent perspective on the hierarchy of skills required when employing permanent staff. They seek a proven track record of outstanding, world class research, usually with some teaching experience, as well as being able to contribute to the department as a ‘good citizen’.

5.54

Interestingly, PhD students, even in the later stages of their studies, did not appear to particularly value soft skills: “It is actually the very precise mathematical skills that I have got good at [from undertaking a PhD]. I would definitely say it is about mathematical skills. I didn't do a PhD to become a more effective human-being.” (3rd year PhD student)

5.55

PhD students did report being given many opportunities to undertake broader learning activities, such as through one-to-ones with their supervisors, general university-level lectures, or more tailored workshops at the university, departmental or working group level. The closer the training session was to the specific area the individual was working in, so the more bespoke it was, the more highly it was regarded. Overall, there was a sense of expectation about being provided with training in specific areas relevant to them as an individual, preferably involving relevant material that related to work they were actively researching.

5.56

In contrast, ECRs described a much more proactive approach to developing skills.

Examples included setting up their own study or reading groups or independently learning a new skill and even a foreign language in order to pursue research goals. With the ECRs there was more of a sense of self-determination and expectation that they would take the necessary actions to obtain the required skills. Two industry employers commented on the advantages of employing someone post-PhD as being that they would go and research a problem/technique themselves without having to be sent on a training course.

Problem Solving Ability

5.57

One specific skill that was raised as important for mathematical sciences researchers to develop is the ability to apply their mathematical sciences training to solve problems, in EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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the real world. Industry employers in particular noted the lack of creative real-world problem solving skills in PhD students and graduates, saying: “PhD students miss out on the ability to apply what is known to them.” Some industry employers cited applied mathematics study groups as well as problem solving days as an initial, small step in developing these skills in PhD students.

Personal Skills 5.58

The personal skills that were seen as most desirable by all employers were communication and team working skills. Academic employers thought PhD graduates to be more likely to have the desired personal skills required than the non-academic.

5.59

During consultations, there was a divide between the employers who wanted much greater focus on soft skills training to enable PhD graduate to be ready for the workplace and those who did not see this as the purpose of a PhD course, thinking that it should only provide high level mathematical research training. The latter group saw it as preferable for soft skills training to be done post-PhD once in work rather than using valuable time during a PhD trying to learn soft skills in a generic or artificial way.

5.60

The viewpoint that was shared by these two perspectives was that most effective and beneficial way to develop soft skills was through authentic and useful activities (e.g. presenting work at meetings/conferences or writing reports for a broader range of audiences than academia). It should also be noted that it was the larger corporations that were willing to invest in up-skilling graduates post-PhD, reflecting their infrastructure for staff development.

5.61

Public sector employers had a slightly different take on this issue due to the Civil Service Competencies Framework and its use in recruitment. There was a view that mathematical sciences PhD graduates often met these competencies; however, they needed to be aware of how various aspects of their PhD training provided evidence for the competencies. It might therefore be an issue of the language as well as the presence or acquisition of the skills themselves. A private sector employer also described coaching people who they knew to be technically excellent through competency based recruitment processes.

5.62

PhD students and ECRs did not exhibit as much awareness, or place as much importance on personal skills. An ECR stated that you: “get hired based on your research not your skillsets … you will pick up [soft skills] on the job”.

5.63

A number of PhD students and ECRs thought that these skills should develop naturally through close working with the supervisor and other related activities, but that this does necessitate good quality supervision. Some PhD students thought that some personal skills training early in a three year course could be beneficial, but it should be timed to coincide with work that actually utilised the skills learned. This supported the view of employers who said that training was only effective if accompanied by genuine use of the skills day-to-day.

5.64

PhD students did provide a number of anecdotes about ineffective personal skills training.

The focus of these criticisms was about the lack of flexibility in choosing and attending courses suited to their needs. For example, some experienced public speakers reported that they had been required to attend basic presentation skills training, when they would EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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have benefitted from a more advanced or different courses. This was particularly raised as an issue regarding obligatory courses for EPSRC-funded PhD students.

5.65

Early on in discussions with PhD students it became clear that they did not relate to the concepts and language often used to describe personal skills. In some cases they exhibited some irritation in the use of phases such as ‘team working’: “Team-working, leadership aren't things you get from academia (but) you can collaborate”; “In academia team working is not a skill that you require. Not so relevant.”

“This is the language Public and Private sector use. We don't respond to well to these words in academia,” “We all need these skills, it’s these buzzwords that [academics] don’t like”.

5.66

Whist this may be understandable given the considerable effort PhD students are putting in to developing their mathematical skills, employers and funders do regard transferable skills as important. The academic sphere, as role models for students, should be careful not be cultivate this attitude by considering the language it uses and esteem in which these skills are regarded. This will help ensure PhD graduates engage positively when employers (and research councils) refer to these skillsets.

Communication

5.67

It was universally agreed that it is very difficult to succeed without the ability to communicate ideas. Furthermore, it was highlighted that it is a key skill noticeable in those who have a successful career. Both written and spoken communication skills were highly valued by non-academic employers, more specifically the ability to communicate complex mathematical ideas to ‘lay’ people. This was particularly true for those in the public sector and industry that had public-facing or influencing roles. Most non-academic employers agreed that more could be done during the PhD to develop these skills, as long as it fitted within the PhD course and activities that were being undertaken.

5.68

One academic did share that they were trialling a training process in which PhD students would work with their supervisors in writing a funding application. They would have the opportunity to read previous funding applications, write content, sit a mock interview and receive feedback on the process. This would provide authentic coaching in communication skills and was well received by some PhD students.

5.69

The role of the viva in developing communication skills was drawn out by some employers. The open oral defence of the PhD in Europe, whilst considered by some as a ‘soft’ viva, meaning that the content had to be presented in such a way it suited a public audience or lay person. In contrast, it was suggested that the closed viva in the UK meant that PhD graduates had to show the ability to think and defend their thesis at a higher level than in Europe, developing their technical communication skills.

Team Working

5.70

Discussion of team working often began with the acknowledgement that there were some ways in which team working in the mathematics community made more sense than others. Sitting down to solve an equation together was unlikely to happen whilst collaborative work on a project or paper could. It was acknowledged that some people have a predisposition to particular ways of working: EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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“some people like working with others and collaborate, some prefer working on their own; I wouldn’t want to see these disadvantaged. Encourage those who want to collaborate to do so, but don’t force everyone.”

Teaching 5.71

Teaching was viewed by many academics consulted with as being an excellent way of obtaining additional personal skills and experience that would be beneficial for future employment prospects. They confirmed that they actively encourage it amongst their PhD and ECRs, with some offering teacher training for ECRs and two institutions having specific training in place for PhD students as well. Non-academic employers also saw the experience of teaching during a PhD as being beneficial for personal skills development.

5.72

However, the necessity to undertake a postgraduate certificate in teaching was not universally praised by ECRs or in the feedback that academic employers received. Several comments stated that the courses were too focused on theory and not enough on practical teaching, meaning that a long time was spent writing essays on areas that were not deemed necessary as the courses were not geared specifically towards teaching in mathematical sciences. A PhD student who had personally faced considerable anxiety when first teaching, did raise that new undergraduates should be expecting higher levels of teaching due to higher tuition fees, including from seminar tutors and lecturers.

UK and non-UK Mathematical Sciences Education

5.73

The competitiveness of UK and non-UK education was considered from undergraduate through to PhD level. Whilst the focus of both Phases 1 and 2 was on PhD and post-PhD training and experience, a number of questions and discussions developed around the current offering in the UK and abroad at pre-PhD levels. Phase 1 found that:    

66% of PhD students had studied for their undergraduate course in the UK; 18% had studied elsewhere in the EU; and 16% outside the EU; 75% had undertaken some form of master’s course as well.

   

42% of ECRs had studied in the UK, 38% in the EU and 20% in the rest of the world.

65% of ECRs surveyed had undertaken some form of master’s course.

Undergraduate Degrees 5.74

There was some discussion that the US undergraduate system was more flexible than the UK; whilst the US necessitates ‘minor’ courses and unrelated content to mathematical sciences, this is offset by being able to choose more advanced postgraduate courses in the final year of the undergraduate degree for those who are capable. This means that a particularly gifted student could already complete postgraduate courses necessary in the first two years of a US PhD before they begin postgrad study; this was seen as an advantage by two ECRs in separate focus groups who had undertaken PhDs in the US.

5.75

There was a perception that the pre-PhD training in the UK was more thorough than in the US due to being more focused, a sentiment mirrored by PhD students at two focus groups as well as ECRs at a third focus group. In terms of transitioning from country to EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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country, there was an underlying suggestion that as the UK undergraduate course was deemed more in-depth than the US, a person would be in a good position if they undertook a UK undergraduate followed by a US PhD. It might therefore be useful for a more detailed investigation into the different elements of national international offerings at undergraduate and master’s level and how these are best matched with one another.

5.76

Several of the focus group attendees had been undergraduates in EU countries, including Italy, Portugal and Austria. There was some appreciation amongst those who had undertaken a ‘Bologna Accord’ degree of the differences with the UK model, with the former allowing three years of undergraduate and two years of master’s courses as standard, which was seen as competitive. One other ECR who had studied for undergraduate and PhD in the Ukraine was also positive about the benefits of the European system, although saw the UK as also having a strong degree programme.

5.77

Another focus group PhD student had spent an Erasmus year in France as an undergraduate. This person was aware of a difference between the French teaching at undergraduate level, which was described as more consistent between universities, e.g. using the same textbooks, in comparison with In UK where “it is quite research-led teaching, that depends on what [lecturers] specialised in. This is not the case in France.”

The overall preference from that individual was for the UK system, with focused specialisms from different members of staff.

Two industry employers were somewhat more negative about current UK undergraduate teaching. One of those employers requires good UK national graduates for employment.

An academic collaborator at a Scottish university had recently found no one of sufficient calibre coming through from undergraduate level for them to sponsor on a PhD position, leading the consultee to suggest a decline in calibre at first degree level. It should be noted that this company often sought engineers or theoretical physicists as well; the perceived dearth of skilled undergraduates was broadly looking for highly numerate real world problem solvers as opposed to mathematicians per se.

The other company was very pessimistic about the ability of UK HE institutions to create real world problem solvers. The consultee felt that there was a fundamental problem with UK education that might even be traced back to pre-university, in that students are only taught to problem solve by rote and not to creatively use a set of problem solving tools (e.g. mathematics) to overcome a range of novel problems. The consultee felt that something drastic needs to be done to support natural creative problem solvers in the education system.

5.78

Generally, academic employers consulted with did not mention any negative aspects about the UK undergraduate offering, although there was a single explication of a professor who had decided to no longer take UK undergraduates as PhD candidates due to the low calibre of students in comparison with those from elsewhere.

The Role of the Master’s

5.79

A master’s degree was widely regarded as important if not essential by most people consulted with, for individuals who have come from a UK undergraduate course and want to undertake a UK PhD. The focus groups and academic employers generally perceived a real benefit in having done either a separate master’s course (e.g. MSc, MASt etc.) or a four year undergraduate course with integrated master’s in the final year (e.g. MMath, MSci etc.) A master’s was seen as necessary by four academic employers in order for a EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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candidate even to be considered for a PhD position at their institution. In Phase 1 responses, PhD students who had carried out a master’s stated strongly that doing so had ‘prepared them for their PhD course content’, as well as enhancing other necessary skills such as ‘ability to work on own’, ‘ability to communicate complex ideas’, and ‘helping career development and understanding’. 34 5.80

One difference that did arise was in terms of the emphasis on research versus broadening of mathematical knowledge during the master’s course. It was understood that whilst some people saw the masters as a good opportunity to begin focusing on a specific research topic alongside learning some broader mathematical sciences topics, others saw it as an opportunity to learn more about various other areas, akin to the first year of a Centre for Doctoral Training (CDT) or US PhD course.

5.81

One academic employer also mentioned that some universities ask for an additional MSc masters if the candidate has an MMath, suggesting that some institutions did not value the MMath as highly as the MSc (a situation that the consultee thought was nonsensical).

The suggestion was given that in order to overcome this lack of uniform repute for differing master’s courses, it would be beneficial if universities offering a four year course were able to be more flexible in letting some students (with the intention of staying in academia) carry out “bigger projects and research training in the fourth year, as a master’s would have,” whilst the rest (leaving academia) would undertake the usual course. A PhD email respondent suggested a similar model, whilst an ECR email respondent who had previously done an MMath commented that the final year of the course “didn’t really prepare me for my PhD, as it felt like just another undergraduate year but with a small project.”

5.82

Industry and public sector employers viewed a master’s degree positively although it was noted by one consultee that based on feedback from recent graduates they considered the MMath to not be equivalent to MSc as it was “basically 4 years of BSc”. This was supported by an academic consultee, who (having previously done Part III) said that they had found graduates of an MMath course had “just learned a huge amount of data, not how to do maths,” and not prepared the student well for PhD due to lack of a research project during the course.

5.83

Ten of the non-academic employers clearly stated some form of benefits from graduates having undertaken a master’s. For some (e.g. Shell, HSBC, TotalSIM) this was important in terms of broadening knowledge, whilst at the same time some (e.g. Selex-ES, HSBC) saw it as an opportunity to undertake a substantial project pre-PhD. It was also established that masters did allow for a side-step between disciplines (e.g. two consultees at Airbus had moved from engineering undergraduate degrees to PhDs in mathematical sciences via master’s courses in mathematical sciences). However, a master’s was not regarded as necessary by consultees from four non-academic organisations if the person were staying in the same sub-discipline as their undergraduate degree.

5.84

Overall, this suggests that there might be a role for some additional signposting for undergraduate students towards the particular master’s degrees for those who wish to move into academia or industry.

34

Using a weighted average on a 5-point Likert scale: Strongly Agree=2; Agree=1; Neutral=0; Disagree=-1; Strongly Disagree=-2, ‘Preparation for course content’=1.06; ‘ability to work on own’=1.11; ‘ability to communicate complex ideas’=0.95; and ‘helping career development and understanding’=0.95.

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Transition from Pre-PhD to PhD 5.85

The master’s was regarded by some people as an important stepping stone from undergraduate degree into PhD, either from a person just completing an undergraduate degree or from someone who had worked in industry and was thinking of moving back into research. Academic employers mentioned that it was increasingly unlikely if not impossible to accept anyone onto a PhD course without a master’s of some form and none consulted with posited that scenario as a norm.

An interesting model was also highlighted in discussion with an academic consultee from the School of Mathematical Sciences at the University of Nottingham, who outlined the flexible approach taken there with regard to the master’s. This allowed for a DTA-funded PhD with either an initial six months spent undertaking taught courses that were specifically aligned with the aspiring PhD student’s needs or an initial full year with taught courses that also included a research project for those that had not already undertaken a master’s. Therefore, every PhD student would have a tailored half to one year at the start of the PhD that would ensure some broadening, some level of research skills developed, but also provide a chance to take course modules from (multidisciplinary) collaborator departments. In discussion with industry, this was seen by some as close to ideal, with the need for a focused and bespoke initial period praised here.

5.86

One other specific case where a master’s was highlighted as being beneficial in making a transition into a PhD was in statistics, with one employer at Warwick highlighting that an appropriate master’s course could provide a person with a numerate first degree from a range of fields to enter onto a statistics PhD course. It was also supported by comments from ONS and GSS in terms of people transitioning from another numerate degree into having sufficient statistical knowledge to be employable through undertaking an appropriate master’s in statistics. Given the exceptionally high demand for statisticians reported by academia and public sector employers, this would seem to be an area that could use further consideration.

Funding

5.87

Of the current PhD students surveyed in Phase 1 who had previously undertaken a master’s course, 39 per cent were funded by a university grant or scholarship, with only 3.7 per cent stating they were funded through a 1+3 PhD grant and the remainder through their own means. Concerns were shared by several academic employers that the lack of funding for master’s courses would mean fewer of the top calibre candidates from undergraduate level would be able to afford a master’s and therefore less likely to make that ‘stepping stone’ onto a PhD place, particularly with increasingly attractive/lucrative industry offers. The desire to support the four year undergraduate degree was also related to the fact that the student can then access student loan whilst undertaking their final (master’s) year of the course.

5.88

It was also noted by at least one public sector recruiter that the withdrawal of allocated master’s funding by research councils had negatively affected the numbers of adequately skilled graduate candidates. It was suggested that with costs for an OR master’s courses now costing over £20,000 at some institutions fewer people could afford such a course.

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Factors affecting PhD Quality 5.89

When asked in the focus groups to explain why particular PhD programmes were favoured, there was not a clear consensus between either PhD students or ECRs on which specific elements were most beneficial. One key factor that was agreed upon was that the ideal model for an individual depends a lot on what their post-PhD aspirations are.

For example, if they are planning to go into industry it was seen as preferable to spend a shorter amount of time doing a PhD, whilst if staying in academia it would be better to have a longer period both during a prior to the PhD. The longer period in academia was seen as necessary for several reasons, including development of broader mathematical knowledge, particularly at the early stages as it was seen as preferable to instil new maths knowledge earlier in a PhD or in the year prior to starting a PhD.

5.90

There was a lack of knowledge about the US (and to an extent the European) PhD models amongst non-academic employers. Employers generally dismissed these as deemed ‘too long’ (an attribute several focus group PhD students supposed would be the case and could understand). They needed people they could, in one industry consultee’s words, “indoctrinate” into their way of using mathematical sciences skills. As one ECR suggested, “industry probably misunderstand the US system, which is basically like the European system but…with the master’s and PhD bundled up”. What was clear is that employers were generally keen on some broader experience in the form of a +1 master’s, although most PhD students assumed that industry would prefer the shortest model.

Longer Study Period

5.91

The longer period of a US PhD or a four year CDT model was seen as useful in academia for “maximising your time” (focus group PhD student), giving more opportunity to explore varied areas of mathematics. This could be in the year(s) prior to deciding the actual PhD topic and therefore give the student a chance to broaden without the time constraints of the shorter UK and European models.

5.92

It was notable that in several focus groups people (often PhD students) were not aware of the actual make-up of the US PhD, e.g. two focus groups conflated the undergraduate and PhD courses in terms of undertaking additional unrelated courses (i.e. US undergraduates programme having ‘major’ and ‘minor’ topics). In addition, the flexibility of the US programmes (in being able to study more advanced courses than your peers) was not apparent to anyone who had not studied or worked there.

5.93

The added value of the European and particularly the US models was also highlighted in the focus groups and academic employer consultations. By having more time in the PhD to ‘explore and then specialise’, students gain valuable additional opportunities as well, including: networking time, additional time for conference attendance and most significantly, more time to publish papers during this period, all of which increase employability post-PhD beyond those who had not had these opportunities.

5.94

Two other academic employers pointed out that to compare a fresh PhD graduate from the US with a fresh PhD graduate from the UK was not comparing like with like due to the additional time spent in the US programme. Instead, if one considered that both people were the same age going into their studies and if they were likened e.g. at age 28 then they would be comparable in terms of experience and publications. This suggests that the benefits of going through the US system are short-lived and a number of PDRA positions will provide equivalent experience.

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Programme Structures 5.95

There was again little overall consensus regarding what model might provide best training, although the lengthening of funding for PhDs to 3.5 years was seen by everyone who mentioned it as beneficial to the process. It was acknowledged that PhDs do usually take longer than three years and the pressure put on people by this time constraint could cause additional (unnecessary) stress.

5.96

Employers consulted with at Warwick suggested something like a 3+2+2 model, combining the first degree in a manageable length followed by a similar two years of taught courses as the US system (or the master’s level courses of the European model) with a further two years of research PhD. It was argued that this would stop the stress of focusing on the PhD/thesis for the entire three years, which was seen as a detriment of the UK system. ECRs at one focus group also picked up on this point and felt there needed to be some non-project time integrated into the PhD model. This was seen as providing the most competitive compromise between what already exists in the UK and what other models provide.

5.97

Overall, there was found to be a lack of knowledge regarding alternative research models

by PhD students and a number of ECRs as well. Such information could be beneficial at an early stage, particularly in helping choose which of the many PhD course types might suit a person’s goals and intended career outcomes (if known). It might be that advising a shorter course for those with one destination in mind versus a longer course for another. It is also notable that the UK appears to be the only place where there is such a range of different models, suggestive of the need in the UK to adapt or explore a variety of alternatives where other models (e.g. US) provide sufficient flexibility inherently.

Taught Course Centres

5.98

The six mathematical sciences Taught Course Centres (TCCs) were established in order to provide an opportunity to gain a greater breadth of knowledge during their PhD course.

The TTCs provide a mixture of face-to-face and remote teaching in both specialised subdisciplines (i.e. statistics, operational research) as well as more general mathematics courses.

5.99

In the Study the TCCs were seen as a good idea in principle by PhD students, ECRs and employers across the board and something that could provide a competitive advantage for UK PhDs. It was seen as hard to criticise the idea of broadening one’s mathematical sciences knowledge during a PhD and as one student (via email) expressed, “it’s weird for someone to be a doctor in mathematics and not have a broad knowledge of the subject.”

5.100 Particular benefits included being able to fill holes in knowledge (e.g. a final year PhD student at one focus group who had originally graduated in economics and worked in finance for several years before commencing a PhD in mathematical biology; he had attended the London TCC). Another third year PhD student praised the TCCs, having attended well over the specified 100 hours of courses at the combined TCC during study, whilst the (first year) PhD at that focus group said the TCC was a “great experience”.

Particular praise was given to the Academy for PhD Training in Statistics (APTS).

5.101 In separate statements, two PhD students and an ECR did however raise issue with TCC courses being mandatory, with this expectation being unfeasible on top of an already heavy workload. This was exacerbated by the lack of relevant courses making them seem more like box-ticking exercises (mentioned by one PhD student via email attending the EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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LTCC and an ECR at one focus group). Likewise, those studying at Cambridge who had undertaken Part III were frustrated at having to take additional Part III courses during their PhD in order to check off the 100 hours of courses. Another PhD student (third year, theoretical research area attending the MAGIC TCC) said the courses were: “generally quite pointless. They either offer training that is not necessary for scientists, or training in skills that are extremely simple or that you would pick up ‘on the job’.” There was a sense amongst those who were less positive that they were able or motivated themselves to undertake necessary additional research.

From the ECR perspective, TCCs were generally seen as a positive thing, although it was mentioned that a more coherent strategy across all TCCs would be beneficial. ECRs at the Bristol focus group agreed that classes are somewhat ad hoc as there is not a single coordinator and so institutions choose whatever they will individually put on. Therefore, if a particular department already runs a good course in e.g. algebraic geometry (an area that was mentioned as in need of a TCC course by one PhD student at the focus group) within their department then they will not necessarily be motivated to run this again in the TCC. Thus, the places where the courses are needed less are where there are already staff who teach those courses, which then do not get shared in the TCC. 5.102 It was also suggested by one ECR that the Scottish TCC provided a good model, providing some core courses year on year to guarantee that people could receive a good level of training in those areas.

5.103 Interestingly, a comment from one HoD involved in the combined TCC suggested that whilst it was an interesting (and worthwhile) experiment, it was probably failing due to the lack of attendance at sessions that were not being hosted in a particular institution (i.e. being watched remotely). This was backed up by some frustration mentioned by a PhD student regarding technical failures when watching the sessions remotely.

Industry Involvement 5.104 Most industry consultees (seven different companies out of 11) mentioned that either the CASE or an internship of some form as being a positive way for a PhD to gain experience and start to understand the working practices inherent in an organisation. They were very supportive of this approach for providing a competitive PhD offering. Likewise, public sector consultees were not averse to such experience in PhD graduates if it helped them build a range of skills such as team working and communication.

5.105 The variety of different ways that non-academic consultees appreciated any kind of industry contact during a PhD was striking. One suggested that it would be beneficial if there was a mechanism for a PhD student to take a short break (e.g. 6 weeks) from their project and work on some different (perhaps related) blue skies research for the company. Based mostly in the academic institution, they would be supported by industry contact and then give a presentation and write a report on their findings. Interestingly, discussion with other industry and academic contacts suggested that this mechanism did already exist in the form of the KTN short placements; however, one HoD suggested that funding for such projects might be finishing.

5.106 Consultees from three companies stated that their ideal PhD graduate would have done a sandwich year, particularly for engineering firms; two consultees placed this year at undergraduate level and one during the PhD. In bigger manufacturing and heavy industry these placements were particularly favoured, with contacts at one company suggesting a EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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year placement during undergraduate as well as a chance during the PhD to take some time (e.g. six months) in industry to work on a real project as part of the course.

5.107 There were a number of industry consultees that had found a lack of coherent unified link-up between industry and academia across the UK and had therefore created their own individual links with specific institutions or on an individual basis with particular researchers at institutions. This allowed them to have collaborators for projects as well as find potential PhD candidates to sponsor, as was the case with a financial services consultee’s link with University of Oxford. This consultee strongly recommended authentic partnership between academia and industry throughout the PhD; e.g. the sponsored PhD student spend eight weeks a year in the company head office as well as numerous day trips to discuss their project.

There was an underlying sentiment from a number of academic employer consultees, particularly those on the more applicable end of the mathematical sciences spectrum, that links with industry during a PhD were beneficial on a number of levels. It was suggested by one contact at Aston University that the changing funding landscape (e.g.

CASE studentships increasingly going to large organisations and no EPSRC-funded studentships) had necessitated a new approach. As an applied mathematical sciences department with close links to industry, it was regarded as very desirable for all PhD students to have some industry contact time. With the creation of a new ‘big systems analytics institute’ with around 15-20 industry partners involved, it was likely that every new PhD student through the institute would do an internship as part of their study.

5.108 A consultee at the more theoretically focused department at LSE suggested there was potential for all PhD students (studying both theoretical and applicable topics) to do some form of internship/time outside their main study, either going into an industry placement or perhaps spending time at another academic institution.

5.109 Among PhD students, there was a lack of awareness exhibited about potential opportunities to work with industry or of the iCASE model of PhD funding/delivery. Two PhD students mentioned having been on internships with industry partners (one email respondent studying a theoretical topic was unable to attend the focus group in person as they were on an internship at the time). One ECR who was working at Oxford mentioned the study group that allows industry contacts to bring a novel problem for PhD and ECR researchers to work on. In contrast, several industry consultees had heard of these and were very favourable of the courses.

Cohort Sizes 5.110 Only one PhD consultee directly mentioned the size of the cohort they were in as having an impact on their study. Being in their third year at OU, it was mentioned that there was little chance to meet peers as the cohort was so small. In this respect the TCCs were also regarded as beneficial as they provided a cohort outside the university. PhD students at both Oxford and Cambridge (both applicable mathematical sciences researchers) mentioned they were fairly isolated in the carrying out their research, perhaps seeing one or two other people.

5.111 One of the Oxbridge individuals mentioned they could go for a day or two without seeing anyone directly related to their project as the person they had shared an office with had moved elsewhere. This had implications when these people discussed issues such as team working in academia. However, another PhD student in the same focus group had EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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a very different experience; through working in the fluids laboratory they had a network of people to speak to and sat next to their supervisor on a day-to-day basis, thus having someone literally to turn to if needed.

5.112 One focus group ECR who had also been through the CDT there mentioned that this provided a supportive system, in particular due to having two academic supervisors as well as the CDT supervisor to speak to. Another ECR mentioned the need for a supportive peer network in order to gain a good understanding of how to progress in academia.

5.113 Due to the low number of individuals funded by the various mechanisms (in particular CDT and iCASE), it was not possible to gain a clear understanding of how significantly this altered people’s experiences of carrying out a mathematical sciences PhD. Further work could be carried out in this area to fully assess the impact of particular peer networks and whether certain sub-groups might be more or less in need of such networks.

Status in Department 5.114 It was mentioned by an academic employer at LSE that in European universities PhD candidates are regarded as junior faculty members; this gives the individuals more confidence as well as providing a stronger support network of colleagues who are employed by the department. In contrast, the UK treats the PhD candidate as a student, placing ‘below’ academic staff in the departmental hierarchy.

5.115 Comments from ECRs in the first Phase supported this notion, suggesting that studying for a PhD in Germany, for example, one would be treated the same as other staff members. Likewise, a focus group ECR mentioned that the attitude in US institutions is different to the UK, with a strong support network, detailed introduction and orientation for new staff into the department and a sense that the “approach is different to aiding the person - the point of the university is to help the person there to find a job.”

Academic Role Models 5.116 It was also noted by two academic employers that there is a need to ensure that there remains a quorum of locally trained academic staff in the department in order to continue on the culture of the department and also to act as role models for undergraduates. As an academic consultee at Cambridge highlighted, if there had been no UK members of staff there was a likelihood that UK undergraduates would not see academia as something ‘for them’. Likewise, it was raised in consultation with ECRs at the Glasgow focus group that "we definitely want to have role models that people can identify with [but] there are no Scottish members of staff, we need local staff members.”

5.117 An area of further research might consider how the permanent staff composition of departments around the country affects the motivations and perceived appropriateness for individuals to continue their study there.

Post-PhD Transition from Study into Work Why Employers Hire Mathematical Sciences PhD Graduates 5.118 In Phase 1 of the Study employers were asked whether they consider the country in which a PhD was carried out in when taking on a new recruit. Across the employer types the percentage who did consider this is were as follows: EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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  

44% of academic employers; 31% of industry employers; and 36% of government-related employers.

5.119 When employers were asked to consider PhD location in more general sense during consultation, it was often commented that more significant factors were the individual calibre of the graduate and whether the PhD graduate had studied at one of the top universities in whichever country that might be.

5.120 It was however noted amongst academic employers that they were very unlikely to recruit a fresh graduate for a permanent position directly after completing a PhD at a UK institution. Some stated that this would effectively never happen anymore in their departments. In comparison, it was implied that a candidate from the US or Europe might stand an outside chance at obtaining such a position.

5.121 The majority of private sector employers stated that it was down to finding the very top tier of candidates from anywhere or that there simply was no discernable difference in terms of where a PhD had been carried out. There was also a sense that the process of bringing good quality graduates in from any country or university involved a similar level of training and induction no matter where a PhD was carried out.

5.122 One notable difference was in the – public and private – defence sector, in which it was often necessary for recruits to be UK nationals or easily achieve a high security clearance level (e.g. from a Commonwealth country). Whilst this does not necessitate studying for a PhD in the UK, it did make it significantly more likely that this would be the case due to the apparent lower mobility of UK students. Further, there can be additional requirements for candidates to have lived in the UK for the five years preceding application, in particular for government security services.

5.123 The Study also explored people’s expectations for after their PhD, including future roles and how they gained advice regarding their desired career path. In Phase 1 of the Study, results showed that the later in their course they were, the greater the number of PhDs who had an idea of what they would do next, although 31 per cent of those in their third (or greater) year of their PhD did not know at time of surveying.

Careers Advice 5.124 The Phase 1 survey, perhaps predictably, found that those later in their studies were more likely to have sought career advice. Of the students surveyed, the only year group in which more than half of those surveyed had sought advice, was in the year post-PhD completion (80 per cent)35.

5.125 PhD students mentioned awareness of careers advice and accepted that the onus was on them to find it. Academic employers indicated that supervisors in their departments would be well-placed to give academic advice, whilst private or public sector advice was better given by the careers advisory services. It was mentioned by students that specific mathematical sciences advice is more useful than generic university careers services, such as the events put on by larger mathematical sciences departments, particularly those with more connections to industry.

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For first and second years, 15% had sought careers advice; for third years and greater, 36% had.

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5.126 Many PhD consultees stated the importance of their supervisor when seeking advice on academic careers. An interesting phenomenon described by PhD students and ECRs was that the moment when their PhD supervisor asked them if they were applying for PDRA positions was when they knew for the first time that their supervisor believed they had the capabilities required to stay in academia.

Awareness of Roles 5.127 The PhD students and ECRs were pessimistic about the number of academic roles that are available in the UK. The Phase 1 survey found that both ECRs and PhD students considered there to be more industry jobs in the UK than academic jobs at any level 36. In Phase 2, every focus group discussed a lack of academic jobs in the UK at all levels, especially for permanent positions. ECRs noted a particular dearth in fellowship positions, often seen as a stepping-stone to a permanent role. This widespread perception amongst PhD students and ECRs early in their career may result in more people being pushed towards opportunities outside of UK academia.

Recruitment of PhDs 5.128 The academic employers had similar processes for taking on new staff. They described a more rigorous process for permanent positions based on key skills and academic standing, usually led by the Head of Department, and a slightly less stringent process for fixed-term positions based on skills necessary for the particular project and led by the Principal Investigator (PI).

5.129 In industry there was much more variation, given the size and approach each organisation had to hiring graduates in general, and mathematical sciences PhDs in particular.

Alongside traditional advertising for a specific role, there were two other approaches: graduate schemes not necessarily aimed at PhD-level graduates and collaborations or ties with particular institutions through which potential new recruits could be found. Public sector and large organisations had an increased focus on core competencies within recruitment processes. The recruitment process in academia was found to place a particular importance on references, especially for fixed-term positions, with some employers mentioning that they felt comfortable in the knowledge that PhD graduates with a strong reference would stand a good chance of getting a fixed-term position in the UK or abroad.

5.130 In terms of frequency and timing, different employers described a mix of annual cycles of advertising, recruitment on an ‘as-and-when’ basis as well as some cases of continuous ongoing recruitment of high calibre people. Non-academic recruitment was usually for permanent contracts, with only a few employers mentioning occasional fixed or short term contracts.

5.131 Some, usually larger, organisations with a graduate recruitment processes often did not differentiate between first degree, masters and PhD graduates, highlighting the emphasis on competency based recruitment. If successful however, these employers felt a PhD graduate could progress through the workplace quickly.

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Weighted means: What are your perceptions of job availability IN THE UK in each of the following areas?

(PRDAs; Fellowships; Lectureships’; Industry; Government) ‘Non-existent’=0; ‘Scarce’=1; ‘Adequate’=2; ‘Plenty’=3; ‘Abundant’=4. PhD responses: PRDA=1.49; Fellowship=1.32; Lectureship=1.27; Industry=2.34; Government=1.77. ECR responses: PDRA= 1.84; Fellowship=1.27; Lectureship=1.48; Industry=2.07; Government=1.47

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National and International Recruitment 5.132 The outflow of successful PhD graduates from the UK to other countries was not regarded as a problem by academic employers. They considered the mathematics community to be truly international and if a former student was offered a PDRA role at Harvard or MIT this should be celebrated and not a cause for concern. It was also noted that given the number of UK PhDs graduates from other counties a proportion of these were likely to move closer to their home country.

5.133 There was also no problem perceived in internationally trained PhD graduates or ECRs taking temporary or permanent positions in UK institutions. What was necessary was to be able to attract the UK-trained ECRs back to the UK after they had completed e.g. one or two PDRAs/fellowships and before they settled into a permanent position elsewhere.

They would then be in a similar position in terms of experience and preparation for longer term positions as those who had come through another PhD model and then moved to the UK. 5.134 For this reason it was stressed that there must be visible positions in the UK along the ECR pipeline. It was noted in the focus groups as well as in comments in the ECR survey that when asked where jobs are available many responded: “US in PDRAs, UK is good in Lectureships” (ECR).

Continuing Professional Development 5.135 There was a large variation in the academic offerings for Continuing Professional Development (CPD) at differing institutions, from non-existent to structured annual reviews for all staff. This would make it somewhat harder for prospective PhD graduates or ECRs to know what to expect when applying for positions across the country. This might be a cause of some of the uncertainty experienced by current ECRs regarding training opportunities, few of whom knew much about CPD offerings at their institutions.

Those who had were usually in more senior roles and they often had some unease with what some deemed as ‘HR’ terminology and ‘buzzwords’.

5.136 In private organisations there were more structured offerings, particularly at larger companies. In some cases this was guided by affiliations and the requirements to achieve chartership. In the public sector there was a strong recognition of CPD, particularly the link to annual appraisals with steps outlined to progress within a role.

CPD in the Initial Stages of Work Academia 5.137 Most academic departments that were consulted with had some form of CPD available for staff, either with signposting or encouragement made. There was a sense from some more traditional institutions that encouragement should not overwrite individual staff members’ personal freedoms for approaching their work life and progression. In others, particularly those with stronger private or public sector ties, there were formalised annual reviews which in some places were mandatory for all permanent and fixed-term staff. A few places also provide new staff with mentors, although there was little discussion of how much these were used.

5.138 One issue raised with academic employers was whether they took any steps to monitor the kind of support PIs and supervisors give to their staff or students, such as encouraging EPSRC Mathematical Sciences Qualitative Information Study – Final Report

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people to attend training and skills events, providing general advice and pastoral support.

No one consulted had a formalised way of being able to confirm that all PIs/supervisors were fulfilling the expectations of their role. Heads of department however felt that they could rely on staff to act in the appropriate ways. One departmental consultee went further, stating a paradox that those supervisors/PIs that most rejected the formalised and structured approaches to development (e.g. strictly enforcing students’ attendance at courses as a supervisor) were in fact the ones that achieved the best results when one considered the next stage destinations of the supervisee.

Industry 5.139 Smaller organisations were more likely to have a ‘relaxed but encouraging’ approach to CPD, suggesting staff go to conferences and undertake short training courses needed.

Leaders of small teams mentioned that the day-to-day running of their team is the equivalent to constant mentoring.

5.140 Several of the larger organisations described two routes of progression; a management route (for which it was seen as more beneficial to have personal traits such as leadership) and a research route (where time could be spent continuing in research without as many administrative duties).

5.141 Where companies offered chartership (e.g. statistician, industrial mathematics, engineering) this would give goals for annual reviews of progress. Some companies commented that as they were working on the cutting edge of research or in a novel field there were often not standardised training courses they could send new recruits on.

Instead saying: “we should be learning from them!”

Government 5.142 Public sector employers had formalised CPD when recruiting via the ‘Fast Stream’ (e.g.

GSS, GES, GORS): “There is an intense training programme for ‘fast-stream’ recruits: 100 hours CPD a year, split 50:50 between core skills and professional skills. It includes a mixture of external courses/internal workshops/training sessions/internal conferences/arts society conferences, on the job learning/coaching, reading books. Mentoring is available if people want it; some want mentoring for specific projects, others want more of a life coach for their 5yr plan.”

5.143 There was again the chance to take different progression routes, with many of the agencies ensuring that the initial two years of a graduate scheme included sufficient movement between some or all areas of work (depending on the size of the agency).

Career Progression 5.144 One striking finding that was repeated by nearly all PhD and ECR consultees was that around five years was deemed an acceptable time to work fixed-term contracts before considering or aiming for a permanent position. This was put forward in a variety of ways; some saw it as two to three PDRA positions (so between two and nine years dependent on the positions), whilst others highlighted that it was important to get one or two longer (i.e. three year) high quality positions in order to have sufficient experience.

Others suggested that if they had not gained a permanent role up to around five years post-PhD they would consider other options outside academia.

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Changing Sub-Discipline 5.145 In the Phase 1 survey it was found that 33 per cent of ECRs had changed or planned to change sub-discipline from the one in which they did their PhD. The areas that saw the greatest fall 37 were probability (down 3.2 per cent) and number theory (down 2.2 per cent), whilst the greatest increases were in computational science and engineering (up 2.6 per cent) and mathematical biology and medicine (up 2.1 per cent). The overall impression of those that had moved was that it was quite hard to do so 38. This was not viewed as surprising in consultations with ECRs/academic employers as the individual switching sub-discipline was effectively having to ‘start again’ with their research, potentially having built up a reputation in that previous sub-discipline. There would also be new terminology to learn, which could hold up progression for a time.

5.146 The fact that people were apparently moving away from theoretical to applicable subdisciplines was also not thought to be surprising. There was considered to be more funding available in such areas, whilst more recent discoveries could also have paved the way for application of previously more abstract mathematics. It was also highlighted by some ECRs that in fact someone could still be doing the same or very similar work, for example in probability, but now doing it in an area described as applicable e.g. mathematical biology. This is inked to the perception of the need to ‘sell’ one’s work in order to obtain funding.

5.147 It was widely accepted that it would be much harder to move back to a more theoretical sub-discipline once the transition away from such an area of research had been made. It was suggested that areas of theoretical mathematics can change quickly and if particular journals are not followed for say, six months to a year, much could have changed. This was considered to be more so than in applicable areas. One academic employer consulted with had studied pure mathematics then decided to move into an applicable area within industry. He stated that he knew he was making a lifetime career decision and that in making that transition he had to “draw a line at some point” and not go back.

Supervisors 5.148 A range of views were presented about best way for a supervisor to carry out their role, be that closely managing a PhD student or allowing the student to work at their own pace. Underlying these approaches was the concept that a supervisor should be able to adapt to the pace and personality of the student and be flexible to accommodate the working approaches of differing PhD students. An overriding theme was the importance of accessibility: face-to-face time with the supervisor was consistently seen as a significant benefit.

5.149 From a more strategic viewpoint, ECRs noted that it helps to have a supervisor who has many contacts and collaborators in the area the PhD student is researching. This helps the student meet more people and network, increasing the opportunities for work postPhD, but also ensures that the supervisor is aware of anyone who might be working on a similar problem to the PhD candidate for their thesis so that the supervisor can “send out smoke signals to warn [others] away”.

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Comparing overall figures for PhD sub-discipline with overall figures for current sub-discipline.

Weighted average Likert 5-point scale Q.How easy is it to make this transition? ‘Very easy’=2; ‘Easy’=1; ‘Moderate’=0; ‘Hard= -1’; ‘Very Hard’= -2: mean score = -1.

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5.150 The importance of being able to seek more informal advice from a supervisor (or PI/colleague) regarding which conferences to go to, which journals to publish in, and which contacts or collaborators to work with was also highlighted. These decisions were not only important for the early stages of PhD study but also as an aid to successful progression as an academic.

Perceptions about Achieving Success in Academia 5.151 Several focus groups commented on what they perceived to aid a successful career in academia. Many mentioned publishing papers and getting work seen or heard as fundamental to the success. It was also felt that it was crucial to be able to explain ‘why is your research useful?’ This was considered to be easier to explain in applied mathematics, but much more difficult for theoretical mathematics. In summary: “you need to be able to explain that why [your research] is important in the real world; communications are key here.”

5.152 ECRs discussed the fact that academic success is not necessarily just linked to academic ability. They considered contacts to be fundamental to successful career progression, although a more obvious link was observed between a strong network and gaining PDRA positions than for permanent positions. For those earlier in the people pipeline this was daunting prospect: “…it seems you are only competitive if you are publishing 3+ papers per year and collaborating with a number of people. That thought is quite daunting for a fresh postdoc.”

5.153 Finally, a lecturer (10 years post-PhD) who had worked and studied in various international locations put forward that success comes down to “knowledge of how the system works and what the standards are - this can be hard, for which reason it helps also to have mentors and supportive peer network.”

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6

CONCLUSIONS

6.1

This Qualitative Information Study has drawn evidence from a wide range of sources using a variety of distinct and rigorous methods. Whilst the information gathered is inherently subjective, there is scope to draw conclusions on the basis of the depth and breadth of data gathered. These conclusions provide areas for further discussion and consideration by the People Pipeline Project Working Group and the wider mathematics community.

Mathematical Sciences People Pipeline 6.2

The mathematical sciences people pipeline is shown to be in a state of change, although it has been in this state for some time due to the trialling of various models, methods and approaches to training and PhD enhancement. With the next round of CDT funding having been agreed in early 2014 there is the potential to generate continuity in funding approaches for a greater number of people.

Pre-PhD

6.3

Motivations for studying mathematical sciences often stem from intrinsic interest or passion for the subject; for others, the main aim for studying mathematical sciences lies in the application of mathematical knowledge to tangible problems. Individuals who work in sub-disciplines that are traditionally described as ‘pure’ and ‘applied’ can be found in both groups, although there is a tendency for more theoretically focused researchers to be motivated by the former factors and those more applicably focused to be motivated by the latter.

6.4

Reputation works on many levels when understanding motivations for studying in a particular location. These can vary on the basis of where the person studied for their first degree/master’s as well as whether they are planning to move or stay in the same country for their PhD, and can be summarised as follows:    

6.5

Same institute as pre-PhD, staying in the UK: usually more awareness of supervisors particularly if already worked with him/her as well as the institution.

Different institution as pre-PhD, staying in the UK: awareness of reputation of the institution in general; also some awareness of the intended area of research.

Different institution, moving away from the UK: reputation of the country becomes a major factor; sometimes awareness of institution’s reputation.

Different institution, moving into the UK: motivation is often based around the institution’s reputation; supervisor is also an important factor here.

Determining the motivation to change location is also an important factor in understanding the reasons why individuals decide to make a transition from their current location to a new one at particular stages of the pipeline. Earlier motivations often stem from a desire to expand one’s own personal and experiential boundaries, whilst the focus on academic knowledge and research skills are increasingly mentioned as reasons for moving for one’s PhD. Finally, career-based motivators arise post-PhD.

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During PhD 6.6

Perceptions of what the PhD would be like before commencing included a general lack of awareness in several cases, the assumption that it would be hard, and the idea that there would either be more or less structure, dependent upon the individual’s experiences.

6.7

The kinds of training that people received during their PhD were quite varied and dependent on the course/funding model adopted for their particular programme.

Underlying much of the discussion on training was the desire for a more flexible, bespoke model that could take into account a PhD student’s past experiences, be it in mathematical training (e.g. TCCs) or in personal skills training (e.g. CDTs). From employer consultations, the Nottingham model was noted here with regard to good practice.

6.8

The importance of personal skills, especially communication and team working skills, cannot be emphasised enough, both from an academic and non-academic standpoint.

The increasing need in academia to collaborate to show impact, as well as the rise in multi-disciplinary work, both necessitate these personal skills. Most industrial and government employers also regard these as being essential to fit into an organisation.

6.9

The UK is perceived to not compete well with many European countries (e.g. France, Germany, and Italy) at a pre-PhD level. Courses are an extra year or two longer across Bologna Accord countries, with a two year master’s-level course coming after three years of initial undergraduate teaching.

6.10

The UK is perceived to be competitive compared with the US at pre-PhD stage, with courses that allow for a UK graduate (particularly if they have studied for a master’s degree) to have a more focused understanding and higher level of technical training than a US first degree graduate. However, the flexibility in the US system allows for the more highly motivated undergraduates to study advanced courses earlier, as well as providing a broader range of skillsets from diverse course options at that early stage.

6.11

The undertaking of a master’s degree course of some type is increasingly seen as essential in the current UK mathematics educational climate in order to keep the UK mathematical sciences offering internationally competitive. It is also increasingly seen as necessary to get onto a PhD in UK institutions.

6.12

There is potentially additional work to be carried out in undertaking a more detailed investigation into the different elements of national/international offerings at undergraduate and master’s level and how these are best matched with one another.

6.13

There could also be a role for improved signposting at different stages of pre-PhD education dependent on the intentions of the undergraduate. The reasons for choosing a particular master’s course on offer may often seem obvious but some guidance might be beneficial regarding master’s degrees for those who wish to move into academia or industry. Given the interest from industry for less extended forms of HE training, the form of the PhD itself might also be considered at this stage.

6.14

The various PhD models available to potential PhD students in the UK is quite wide, notably more so than those mentioned by European and US graduates. Whilst not directly discussed in the Study, one possibility for the future offering would be for the UK to move towards a more uniform PhD offering. The alternatively, being to embrace the differing approaches with a mix-and-match model that included flexibility to choose which elements are more appropriate for the individual.

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6.15

The longer PhD models outside of the UK mean that those who studied elsewhere have had more time to gain experience and develop skills, write journal articles and present at conferences. In addition, countries that support a ‘junior faculty member’ model for PhD candidates allow the PhD to experience the genuine working life in academia, benefit from support and develop understanding of the roles involved.

6.16

The stronger links with industry through various forms of joint working are seen as a gold standard for industry and some government organisations. If there is any thought that a PhD student were considering moving into industry or public sector roles following their PhD then any recommendation should strongly favour industrial-academic working. This also applies to PhD students intending to stay in academia, perhaps offering them the opportunity for an ‘internship’ or time with another university. Within consultations, Aston University mentioned a particularly strong offering in this respect.

6.17

With the changes that have been made to the PhD models in the UK there is a current flux in the quantity and potentially the quality of peer support available to PhD students. Further work is suggested in this area to fully assess the impact of particular peer networks and whether certain sub-groups might be more or less in need of such networks.

6.18

There is a divide amongst those who are fairly confident with the UK’s current competitive edge and those who are more concerned about the mathematical sciences offering in the UK. It might be argued that those who do not see the UK mathematical sciences as in crisis are abstracted away from the realities of the UK landscape.

Alternatively, those who do perceive an urgent and impending crisis might not be accounting for the more recent diversification of training that has taken place within the UK that might still be within the early stages of generating impact.

Post-PhD

6.19

There is seen to be a good partnership at many institutions between mathematical sciences departments, with staff able to give solid and timely advice on careers in academia, and careers services that provide wider advice and support for those who might want to transition away from academia. The gap often lies in tailored (postgraduate) level advice for mathematicians wishing to find interesting and relevant work in industry or government organisations.

6.20

There is a need identified for more visibility of postdoctoral positions within the UK. Whilst it is put forward as a very positive experience to gain a PDRA position in another country, there needs to be the presence and visibility of suitable positions to entice high calibre academics back to the UK after a time in another country. There is less of a need to further draw high calibre academics from overseas into UK institutions as there is already seen to be a healthy and beneficial mix of internationally trained academics that are likely to have greater experience than an ECR of equivalent age from the UK.

6.21

There is a strong expectation that there will be around a five year work period on fixedterm contracts post-PhD before gaining a permanent position. Despite differences in training and perceived variation in competitiveness, this five year period was reported by PhD graduates from UK, European and US academic systems. It might be that after this amount of time there is little difference between those who have gone through one system or another; further research would be recommended to explore this issue.

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Emergent Themes 6.22

One significant theme that has arisen across discussions is the role of the PhD: either to create world-class independent researchers that can carry out studies using a set of tools; or to create a well-rounded individual capable of going into a variety of roles with the potential for excelling in any of them. Further, whether or not these definitions mutually exclusive.

6.23

There are clearly some differences between theoretically-minded and applicably-minded mathematical sciences researchers. The need to work within teams is perhaps less appropriate for the former group, although a younger generation of researchers now seem to be looking to make more connections between the two and not see theoretical mathematics purely as abstract cogitation in an intangible universe. Further, more similarities and agreements were found in discussions between theoretical and applicable researcher than, for example, between PhD students and ECRs.

6.24

It is also clear that with the many changes and modifications made to the UK HE system within the last 10 years there are no current indicators of the competitiveness of the latest innovations brought in. It is impossible to judge one set of systems when they are so early in development and without a relative benchmark for success. A more comprehensive assessment of the research impact of the different approaches would provide some answers in this area, as well as being more widely applicable to the engineering and physical sciences.

6.25

The use of specific terminology that does not connect well with some academics is hard to avoid when these terms have become well established in learning and development. It would however be useful to determine how much the resistance to aspects of training (possibly even to the concept of ‘training’ itself as a term) is governed by a dislike of ‘buzzwords’. Further research in turn would provide some alternative ways of presenting and delivering training to those who are unconvinced by such terminology.

6.26

Industry engagement, where it happens, is widely seen as both a useful win-win process for organisations, as well as producing added value for PhD students involved in it. The further promotion of these approaches is highly sought after by increasing numbers in both academia and industry.

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