Monthly Archives: February 2012

Invitation: Mathematics Group Work and Asperger Syndrome

The following announcement about a meeting of our working group on ‘Group work’ on 13th March in Bath is being circulated. Please pass this message along to colleagues who may be interested.

Subject: Invitation to working group meeting, 13th March: Mathematics Group Work and Asperger Syndrome

Dear All,

This project is looking at the advantages and disadvantages of group
work used in Mathematics degree programmes especially in relation to
students with Asperger’s Syndrome.

Our aim is to build a community of academics that use group work for
assessment and developing graduates’ skills. We realise that students
with Asperger’s Syndrome may have difficulties participating in group
work thus hindering them from accessing the benefits particularly in
terms of graduate / employability skills development.

Our first meeting will be held at the University of Bath on Tuesday 13th
March from 11am – 3.30pm approx. There will an opportunity for all
involved to share their thoughts and current practices. Speakers will
include Barrie Cooper (University of Exeter) on group work in
mathematics and Daniel Aherne (National Autistic Society).

Please contact Noel-Ann Bradshaw ( and Emma Cliffe
( if you would like to attend the meeting at Bath
on 13th March, are interested in attending a subsequent meeting at
Birmingham or contributing to this work in any other way.

Please pass this message along to colleagues who may be interested.

Kind regards,

Emma Cliffe and Noel-Ann Bradshaw

Interim report: ‘Problem Solving 2’

Sue Pope has submitted the following interim report for the project “PSUM: problem-solving in undergraduate mathematics” (referred to as “Problem Solving 2“).

To date one interactive starting point has been developed and there is a questionnaire available for users to report their experiences:

Picture This!‘ is an interactive problem solving application, to explore the application further, follow the link below.

A short anonymous questionnaire is available here (ethical clearance was obtained via Liverpool Hope University).

There are three other starting points in development: exploring graphs and networks, linear programming and ‘filling shapes’. All will be trialled at Liverpool Hope University and University of Cambridge as a minimum. Hopefully, focus groups will be held with some questionnaire respondents. The problem-solving starting points have been developed using open-source software and will be hosted by NRICH. This means that the longevity and sustainability of the approach is ensured.

Good links have been established with the HE STEM problem-solving project based at Coventry University and we have agreed to work collaboratively on the production of guidance. We will contribute cases studies on the use of the interactive problem-solving starting points. On 3 March we are presenting a joint paper at the BSRLM day conference in Manchester.

The progress against the proposed timeline is included in the Appendix. Progress has been slower than originally planned due to the project lead changing institutions and delays in getting information about some of the interactive starting points for problem-solving to the programmer.

However, we are confident that we will deliver four interactive starting points for problem-solving and contributions to guidance and case studies.


Key Activity Planned Date Actual Date Commentary
Notify mathematics community about the project through all existing networks August 2011 September 2011 MSOR and HE STEM conferences
Appoint technical expert to begin work on virtual problem solving environment August 2011 October 2011 Jason Davis appointed
Seminar for interested parties October 2011 Not held, meeting with other contractor November 2011
HE STEM workshop 26/10/2011 26/10/2011 Attended
Trialling and Evaluation of problems, generation of case studies November 2011 – January 2012 December 2011 – One problem is available for evaluation, three others are in development
Collation of material for problem solving guide November 2011 – February 2012 January 2012 – Working in collaboration with the other contractor who is leading on the development of the guide
Focus groups with students February 2012 Not held. Hope to have at least one focus group before the end of April 2012
Further refinement of problems February – March 2012 March 2012
Draft of problem solving guide and case studies sent for critical review by interested parties/stakeholder representatives March 2012 March-April 2012 In collaboration with other contractor
Independent testing of the virtual problem solving environment March 2012 March-April 2012
Preparation of dissemination materials April 2012
Case studies on problem solving complete 30/4/2012
Problem solving guide complete 30/4/2012
Virtual problem solving environment launched 30/4/2012 This will be a small number of starting points
Report completed 31/05/2012 31/05/2012
HE STEM dissemination event July 2012 July 2012

Course availability

The University and College Union (UCU) have issued a report Course cuts: How choice has declined in higher education. The UCU press release give the headline figure as:

The number of full-time undergraduate courses on offer at UK universities has fallen by more than a quarter (27%) since 2006… Despite an increase in student numbers.

The press release gives as a key finding that “Single subject STEM courses down 15% and arts and humanities down 14%”.  (Given that, it is a little strange to see Times Higher Education putting the emphasis solely on arts and humanities courses.)

The focus from UCU is on choice, with general secretary Sally Hunt quoted saying:

This report shows that, while government rhetoric is all about students as consumers, the curriculum has actually narrowed significantly.
If we want to compete globally, we simply cannot have areas of the country where students do not have access to a broad range of courses.

This focus on geographical differences puts me in mind of the Steele report, “Keeping HE Maths where it Counts” (2007), which took an interest in the regional availability of courses with a broad range of entry requirements and had a finding about “mathematical deserts”, areas where students tended to stay local for university where mathematics is not available as an option.

Key findings aside, I was struck by the per subject data for course availability. I am not as aware of cross-subject comparisons as I should be. I am used to hearing a complaint that the professional and learned bodies in mathematics (IMA & LMS) only have about 7 thousand members, compared to forty or fifty thousand each for IOP and RSC, despite mathematics graduating nearly as many students per year as physics and chemistry combined (and what this says about how mathematics undergraduates view themselves as part of a wider mathematical community). This gives me the idea that mathematics is a widely available subject compared to others. This, it seems, may be a fallacy.

The table below is a reduced version of this table, which I compiled from data given in the Course cuts report. The totals refer to degree course provision in the UK. I have taken the liberty of combining a few lines from the original report. There were some subdivided disciplines with relatively few courses. I may, in my ignorance, be committing a sin as terrible as combining biology and computer science as the same, but I have combined three courses on history, two on law, three modern languages and two classics into single lines. These combinations are indicated in the table. I hope these are reasonable.

Subject 2012 total decline since 2006 decline as percentage of 2006 total Proportion of G100 Mathematics
I100 Computer Science 169 38 18.36% 2.49
N100 Business studies 151 11 6.79% 2.22
Q300 English studies 116 -4 -3.57% 1.71
Law: M100 Law by area & M200 Law by topic 145 6 3.97% 2.13
History: V100 History by period, V200 History by area & V300 History by topic 143 17 10.63% 2.1
L300 Sociology 92 14 13.21% 1.35
C100 Biology 88 11 11.11% 1.29
L200 Politics 79 2 2.47% 1.16
H200 Civil engineering 73 -2 -2.82% 1.07
L100 Economics 71 9 11.25% 1.04
G100 Mathematics 68 7 9.33% 1
F800 Physical geographical sciences 65 21 24.42% 0.96
F100 Chemistry 59 3 4.84% 0.87
L700 Human & social geography 50 13 20.63% 0.74
F300 Physics 47 -3 -6.82% 0.69
V500 Philosophy 45 3 6.25% 0.66
Modern languages: R100 French studies, R200 German studies & T100 Chinese studies 77 15 16.30% 1.13
Classics: Q600 Latin studies & Q700 Classical Greek studies 16 1 5.88% 0.24

In case you are interested, the numbers for the subjects the report claims the decline is most particularly in are:

For STEM: biology (down 11 to 88 courses, an 11% reduction of 2006 numbers), physical geographical sciences (down 21 to 65, a 24% reduction) and computer science (down 38 to 169, an 18% reduction);
For social sciences: human and social geography (down 13 to 50, a 21% reduction) and sociology (down 14 to 92, a 13% reduction);
For arts and humanities: French studies (down 10 to 26, a 21% reduction), German studies (down 6 to 21, a 17% reduction) and history by topic (down 13 to 34, a 27% reduction).

What I am most struck by is the number of courses still available for some subjects. Having thought mathematics was relatively available, based on a comparison with physics and chemistry,of the subjects included in the report I see only physical geographical sciences, chemistry, human and social geography, physics, philosophy and classics are less available. (I wondered about combining physical and human & social geography, which would take geography above mathematics, but decided against it because the report classified one as STEM and the other as Social sciences.)

There are more degree courses available to study in each of computer science, business, law, history, English, sociology, biology, politics, modern languages, civil engineering and economics than in mathematics.

Perhaps this isn’t unreasonable. Of course, there is always going to be variation and the availability will be demand-led, but when I see that an applicant wanting to study computer science, business, law or history has more than twice as many options as those wishing to study mathematics, and that mathematics is the twelfth most available subject out of eighteen in both 2012 and 2006, I can’t help feeling a little sad for my discipline. (Of course, the picture is even worse for other subjects; those I have listed as twice as available as mathematics have more than three times the number of physics courses available.)

Interim report: ‘MU-MAP: Mapping University Mathematics Assessment Practices’

Paola Iannone, University of East Anglia, and Adrian Simpson, Durham University, have submitted the following interim report for their project ‘MU-MAP: Mapping University Mathematics Assessment Practices‘.

Start date: 9th November 2011 – initial preparation between 01.10.11.and 09.11.11

Initial preparation:

The RA to the MU MAP Project was appointed in August 2011 and started work at UEA on the 9th of November 2011. Some initial preparation for the project was carried out by the PI and Co-Applicant before the project started. These include:

  1. Creation of a one-page website for the project at This website will be populated as the projects progresses. A team of web developer familiar with the UEA web design package has been commissioned to develop this website. This will house the materials and outcomes of the MU MAP project and will be maintained by UEA for the next 5 years.
  2. A dissemination workshop (two 2-hours sessions) at the forthcoming British Mathematical Colloquium (BMC -16-19 April 2012, University of Kent) has been organised with the conference organisers. The title of the workshop is “How we assess mathematics students: a survey and case studies. Findings from the MU MAP Project”

First MU MAP Meeting – Loughborough University – 17.11.11

The First MU MAP meeting with mathematics lecturers was held on the 17.11.11 at Loughborough University. During this meeting we presented preliminary findings from the survey of assessment practices and we launched the call for Mini Projects, part of Phase 4 of MU MAP.

Phase 1: Comprehensive Review of the Literature

The review of the literature (as detailed in Phase 1 of MU MAP) is well under way. We have collected papers relevant to

  1. Existing empirical research in university assessment practices, particularly focussed on STEM.
  2. Existing empirical research in mathematics university assessment practice.
  3. Existing pedagogical scholarship in mathematics university assessment practice.

Currently we are writing summaries of the papers included in the literature review. These summaries will form part of the searchable database on the MU MAP website. A summary of findings from this literature review will form the first part of the MU MAP Good Practice Book and will be posted on the MU MAP website.

Phase 2: Surveying Existing Practice

The web-based survey (as detailed in Phase 2 of MU MAP) has been completed and the results are collected in our database. The interviews with the Head of Schools of mathematics departments are under way – so far we have interviewed 27 Head of Schools.

Phase 3: Identification of Good Practice

As part of the interviews with the Head of Schools we have asked them to nominate staff in their department who assess their modules with innovative, interesting assessment practices (as detailed in Phase 3 of MU MAP). We have interviewed 17 lecturers about their assessment practices. These will constitute the anonymised short case studies of good assessment practice which will be posted on the website and will be included in the MU MAP Good Practice book.

Phase 4: Costs and Effects of Change

(As detailed in Phase 4 of MU MAP) After the call of mini projects at the Loughborough meeting we received 8 applications. We were able to fund 7 mini projects. The list of the mini-projects funded with lead applicants, institutions and brief summary of the projects is included below. The successful applicants have been notified and work is underway to start the mini-projects. Project leaders will disseminate their findings at the forthcoming BMC, as described above.

Mini projects funded by MU MAP

Audience Response devices for formative and summative assessment
Paul Hewson and David Graham
School of Computing and Mathematics, Plymouth University

Audience response devices have received tremendous attention in the learning community. Kay and Sage (2009) “Examining the benefits and challenges of using audience response systems: A review of the literature” Computers & Education 53:819-827 present a review of these devices in class use. There are many advantages, and one notable potential pitfall – that students may not appreciate being constantly assessed. However, our experience is that students do like constant assessment if it is accompanied by rapid feedback. Also, surprisingly, we have had students suggest they would prefer to take in-class tests (that is, summative assessment) using these devices. The aim of this project is to determine the suitability of audience response clickers for this kind of assessment. The literature isn’t clear on the problems – there is a lot of emphasis on “fun” and “engagement”.
We also note that we use clickers that allow for numeric as well as multiple choice input, which lets us set a wider range of questions than are possible with many systems. We also have experience in dealing with the equipment (again, the literature suggests this is the largest barrier to effective use of these devices). What we don’t know is whether it is possible or desirable to incorporate use of these clickers as part of the formal assessed work in a module. By integrating assessment more thoroughly within learning we may obtain better learning rather than a focus on preparing for tests. On the other hand, it is less easy to be flexible with the questions you use in class which can be hugely advantageous (for example Chin and Brown (2002) “Student-generated questions: A meaningful aspect of learning in science” International Journal of Science Education 24: 521-549) and more difficult to implement with clicker based learning.

Assessing proofs in pure mathematics
Timothy Hetherington
School of Science and Technology, Nottingham Trent University

Can the marking burden be reduced through innovative assessment, whilst keeping the task educationally rich and maintaining the same level of student engagement and learning from the assessment? What novel methods might be used to assess student comprehension? How can the ideas behind mathematical proof be assessed? Can an imaginative approach be developed to determine a student’s ability to identify assumptions in a mathematical argument? These are the questions that have provided the motivation for this project. So far the applicant has begun the exciting development of an interesting and innovative assessment; a multiple-choice test on mathematical proof. This project seeks to further the implementation of this novel assessment practice. It also aims to obtain detailed feedback from students to enable a comprehensive evaluation of this interesting new method of assessment of pure mathematics. Being part of the MU-MAP project will facilitate the dissemination of new ideas, the development of resources, and provide a mechanism to share good practice.

Evaluating assessment practices in a Business and Industrial Mathematics module
Edmund Chadwick
School of Computing Science and Engineering, Salford University

The Business and Industrial Mathematics module is run in the second year of the mathematics undergraduate degree at the University of Salford. The module is 100% coursework, 20 credits and spans two semesters. The module attempts to prepare and assess students for work related skills important for mathematicians in the workplace. A variety of assessment methods are used to quantify this, and this proposal aims to compare and evaluate the various assessment practices used.

Towards an efficient approach for examining employability skills
Stephen Garrett
Department of Mathematics, University of Leicester

With the recent shift in undergraduate funding, the future success or failure of a university department has been placed in the hands of student recruitment and so to league-table performance. The employability of graduates has therefore never been more important. But how best should math departments assess these skills in their students? A student’s approach to an open-ended problem, one with no necessarily right or wrong answer, is crucial for their employability and is often used on graduate assessment days. Indeed the value of a math graduate is in his/her problem solving skills. The scope for such open-ended problems in applied mathematics is great, yet traditionally these skills are not examined until final-year projects. This severely limits the number of opportunities to develop and assess these skills over an undergraduate programme. This proposed project intends to look at how best to examine a student’s approach to open-ended problems. It will compare the summative attainment of two cohorts of students, both enrolled on modules with common lectures. One group of students will be assessed with a 2hr written examination consisting of 4 compulsory questions, and an extended project over the semester. The other group will be examined by a 3hr written examination, consisting of the same 4 questions and an additional open-ended question, closely related to the extended project. Such an assessment scheme already exists within a related pair of modules at Leicester. I intend to use this as an opportunity to gauge whether open-ended exam questions are a useful addition to the assessment armoury in math departments. If open-ended exam questions can be shown to be as useful as extended projects for assessing particular skills (to be determined), their significant practical advantages mean more use should be made of them across undergraduate programmes.

Summative peer assessment of undergraduate calculus using Adaptive Comparative Judgement
Ian Jones and Lara Alcock
Mathematics Education Centre, Loughborough University

The project aims to demonstrate that sustained mathematical reasoning can be peer assessed with high reliability using Adaptive Comparative Judgement (ACJ). This will be a live trial and the outcome, checked against expert assessment, will be used as part (5%) of the summative assessment of first year undergraduates studying calculus at Loughborough University (first year modules do not contribute to overall degree credit). This innovation has important implications for assessment of mathematical skills that are traditionally seen as difficult to test, such as making judgements about the relative quality of different mathematical explanations. Therefore it needs to be evaluated rigorously and the project will allow us to undertake this evaluation.

Mathematics Lecturers’ Practice and Perception of Computer-Aided Assessment
Carol Robinson and Paul Hernandez-Martinez
Mathematics Education Centre, Loughborough University

Mathematics lecturers at Loughborough University are in the position of being able to utilise Computer Assisted Assessment (CAA) without the need for developing their own questions. Two projects, undertaken a few years ago by colleagues at Loughborough University and elsewhere have resulted in question banks containing thousands of CAA questions ready to use (see, for example, the HELM project – .) This project aims to evaluate the issues arising for lecturers who utilise existing resources and adopt this method of assessment. It would appear at first sight that the ready availability of CAA questions is an extremely efficient way of assessing hundreds of first year students and would be welcomed by all involved. Question banks are available for both practice and coursework tests and lecturers are freed from marking students’ work. The workload for lecturers is minimal, as dedicated e-learning staff are available to upload tests and the computer software provides pre-prepared feedback to the students and summary statistics for the lecturers. However all is not necessarily as straightforward as it might appear. For most large classes it is not possible to invigilate the coursework tests due to the lack of availability of computer labs for this purpose. Some lecturers and/or departments are concerned that plagiarism is an issue and in these cases paper-based versions of tests may need to be prepared and marked, thus reducing the efficiency of the system. Other lecturers are concerned about the questions which are available for use. Sometimes they do not fully cover the required syllabus. However the steep learning curve and associated time involved in developing new questions is prohibitive and so lecturers may be tempted to ‘make do’. Other concerns involve the procedural nature of many CAA questions. Clearly lecturers wish their students to be able to apply standard techniques to solving problems. But what of the students’ conceptual understanding of the mathematics? Is CAA able to test this? Does it matter to lecturers if it does not?

PAMPER: Performance Assessment in Mathematics – Preliminary Empirical Research
Adrian Simpson
School of Education, Durham University.

Closed book examinations dominate the assessment diet of undergraduate mathematics in the UK (Ianonne and Simpson, 2011) and while there this is leavened by some variety, oral examinations as a core component at this level disappeared by the 20th Century (Stray 2001). However, there is renewed interest in this form of assessment as more validly grading students’ performance of mathematics (Levesley, 2011). This mini-project aims to investigate the difficulties and advantages to introducing an oral performance component to the assessment of a pure mathematics course. Anecdotal evidence amongst staff at high ranking mathematics departments suggests that the modal assessment method (closed book examination) does not provide them with the clearest insight into students’ mathematical understanding. Those with experience of oral exams from their own mathematics education (such as those from most other European countries) note that these can provide such insight relatively quickly. However, there is concern about the fairness and resource implications of such examinations. It is not clear whether examiners might be biased (consciously or unconsciously) towards certain students; whether student nervousness might overwhelm their performance or how the standard of assessment can be assured. It is also felt that the time taken to assess each student individually and the administration of such a process could be disproportionate to the quality of the information gained.
This project will
a) explore the perceptions of staff and tutors on the course to implementing the assessment
b) detail the process of undertaking performance assessment in a core module
c) outline student attitudes to the assessment process

Interim report: ‘A Statistical Awareness Curriculum for STEM Employees’

Neville Davies and John Marriott of the Royal Statistical Society Centre for Statistical Education, University of Plymouth, have submitted the following as an interim report for their project ‘A Statistical Awareness Curriculum for STEM Employees‘.

A draft statistical audit questionnaire has been designed to circulate electronically to STEM graduates in a range of companies that include BT, Toyota, GKN Aerospace and The Met Office.

The tool has been refined in the light of feedback from a number of people including John Harris and Paul Morgan, both of SEMTA, and colleagues on the Royal Statistical Society getstats board.

In the current economic climate it has proved very difficult to get appointments to meet appropriate people in companies, although Paul O’Brien, who heads the Business Modelling & Operational Transformation unit within BT Research at British Telecom (Adastral Park) and Paul Fitzpatrick of Toyota, Derby, have been particularly helpful. The SEMTA south west colleagues named above together with Brian Fowler, have been extremely helpful in facilitating contacts with industry and progress in this regard is slow but sure.

Steve Gerry, secretary of the Plymouth Manufacturing Group, is making arrangements for us to give a short presentation about the project to a meeting of a range of manufacturers in Plymouth on 28 February. After this we plan to engage with those Plymouth companies that have expressed interest in helping us. On the 29th February we will be meeting people in the Met Office (Exeter) to discuss their contribution to the project and discussions with GKN Aerospace are currently underway.

The structure and design of the Moodle site have been completed and the draft questionnaire is now available online. Paul O’Brien’s team have agreed to pilot the questionnaire and have indicated that the Moodle site would prove useful in providing support for a training programme that is currently under development.

Interim report: ‘Industrial problems for the HE curriculum (stats)’

Neville Davies and John Marriott of the Royal Statistical Society Centre for Statistical Education, University of Plymouth, have submitted the following as an interim report for their project ‘Industrial problems for the HE curriculum (stats)‘.

Four meetings have taken place with the industrial partner, a major food producer and processor in the south west. Mary McAlinden attended one of these meetings, but was unable to attend another. Dr Shirley Coleman, Newcastle University, is advisor to the project and she will be attending the next meeting in March.

The range of industrial problems suitable for embedding in the HE curriculum is very large, with the industrial partner producing several million items of food a week. We have focussed on products that are mass produced and have discussed a range of problems that can be devised using the large amount of real data provided.

The data to be used for some of the problems involves measuring pre- and post-baking weights and dimensions of the items for a range of different products. Measurements and counts are being used to create real problems that will populate the Moodle-based management system that has been developed.

The software for generating different real data for each of the problems has been designed and successfully tested. The mechanism by means of which student will be allocated a random problem, with associated data, when they choose a problem is currently being implemented.

The system will allow free access to individualised problems and their solutions at two levels of difficulty. A third, higher level of project-related problems is being created which will involve the student contacting the company and engaging with a real industrial project.

Interim report: ‘Problem Solving 1’

Matthew Badger, Trevor Hawkes and Chris Sangwin have submitted the following as an interim report for their project ‘Problem Solving 1‘.
Problem-Solving Project – Interim Report

Principal Investigators: Trevor Hawkes and Christopher Sangwin
Project Research Assistant: Matthew Badger

Summary of Progress as of 15 February 2012

1. On 12th September Sangwin and Hawkes meet Project Advisor Imre Leader in Trinity College, Cambridge to discuss project goals and methodology.

2. Mid-September the RA Post is advertised. Five applicants out of 22 were shortlisted and the interviews were help on 13th October. Matthew Badger was appointed and began work on 2nd November.

3. On 22nd November a joint meeting with Sue Pope’s Project Team held in Sangwin’s office in Birmingham

4. To survey the current role of problem solving in English and Welsh HE mathematics departments, a questionnaire was prepared using Google spreadsheets and circulated by email to the Heads of Departments in 60 institutions. This has been followed up with phone calls and contacts with staff responsible for teaching and learning on those departments. To date we have had 30 responses, and we intend to pursue colleagues further to get a higher strike rate,

5. The structure of the Problem-Solving Guide has been agreed. It will contain two main sections (Theory and Practice) and will have appendices covering 6 case studies and a section on the role of mathematics software. The first section of the guide, covering theory, is in draft form.

6. A format for the case study interviews has been agreed and one study based on the Birmingham Moore Method module is in draft form.

7. A specification for the project website was agreed. Matthew Badger will be commissioned to build and populate the site outside his hours of work for the project (according to CU rules, his grade allows the post-holder to do overtime) and this has been approved by the Dean of the Faculty).

8. 6th February – Badger, Hawkes and Sangwin met in Coventry and agreed the following actions:

  • All three of us to meet John Mason at the Oxford Institute of Education on 9th Feb (see below)
  • Sue Pope and Matthew Badger to attend the British Society for Research into Learning Mathematics meeting in Manchester on 6th March and give a short presentation about our projects
  • To contact Mike Savage about his HE STEM Modelling Project and arrange an informal joint meeting to discuss our progress, possible overlap, and evaluation.
  • Both projects will present sessions at the CETL-MSOR conference in July and will also approach HE STEM about the possibility running a PS workshop within their September conference, perhaps in tandem with Mike Savage’s modelling project.

9. 9th February – Meeting with John Mason at the Oxford Institute of Education. Discussed plans for the project and the outline of the guide; J.M. agreed to draft an article on the meaning of Polya in the 21st Century, and gave guidance on previous attempts, world-wide, at teaching problem-solving in HE..

10. A number of institutions have been identified for the case studies but a final decision won’t be made until we have more responses to the questionnaire.