[*quote*]
1.23
Values of EDI should permeate the curriculum and every aspect of the learning
experience to ensure the diverse nature of society in all its forms is evident. MSOR providers
should reflect on their curricula and processes to ensure that no group is disadvantaged or
othered; for example, decolonising the curriculum can involve explicit reflection on the
history of MSOR knowledge generation, as well as reflecting on how delivery or admission
practices might adversely impact on certain subgroups within the student cohort. EDI
aspects of student engagement and achievement should be monitored and actions formed
to ensure equity.[*/quote*]
[*quote*]
1.26
[...]
Curriculum - the curriculum should present a multicultural and decolonised view of MSOR,
informed by the student voice. Where possible, it should present the work of a diverse group
of MSOR practitioners. Students should be made aware of problematic issues in the
development of the MSOR content they are being taught, for example some pioneers of
statistics supported eugenics, or some mathematicians had connections to the slave trade,
racism or Nazism. Students should be educated in general EDI matters and also those that
are specifically relevant to MSOR, such as the need to consider diversity in data collection
and analysis.[*/quote*]
So we can conclude that mathematics fundamentals found by a caucasian are less worth than mathematics fundamentals found by an Indian?
Mathematics in no way ever is related with ANY personal background.
The QAA assholes should go to hell.
DO NEVER AGAIN DARE TO TOUCH MATHEMATICS, YOU NAZI BASTARDS!Subject Benchmark Statement: Mathematics, Statistics and Operational Research - version for consultationPublication date: 21 Sep 2022
https://www.qaa.ac.uk/docs/qaa/quality-code/sbs-mathematics-statistics-and-operational-research-consultation-22.pdf?sfvrsn=f3b9a581_4[*quote*]
Subject Benchmark Statement
Mathematics, Statistics
and Operational Research
Fifth Edition
Version for consultation
September 2022Contents
About this Statement ............................................................................................... 1
How can I use this document? .............................................................................................. 1
Relationship to legislation ... 1
Additional sector reference points ......................................................................................... 2
1
Context and purposes of a Mathematics, Statistics and Operational
Research degree ... 3
Purposes and characteristics of an MSOR degree ................................................................ 4
Equality, diversity and inclusion ............................................................................................ 6
Accessibility ... 8
Sustainability ... 10
Enterprise and entrepreneurship education ......................................................................... 11
2
Distinctive features of MSOR courses ........................................................ 13
Design ... 13
Progression ... 14
Flexibility ... 15
Partnership ... 16
Monitoring and review ... 17
3
Content, structure and delivery .................................................................. 18
Content ... 18
Subject-specific knowledge and understanding ................................................................... 18
Teaching and learning ... 22
Assessment ... 25
4
Benchmark standards .................................................................................. 27
Introduction ... 27
Academic standards ... 27
Professional standards ... 28
5 List of references and further resources .................................................... 30
6 Membership of the Advisory Group............................................................ 32About this Statement
This document is a QAA Subject Benchmark Statement for Mathematics, Statistics and
Operational Research that defines what can be expected of a graduate in the subject, in
terms of what they might know, do and understand at the end of their studies. Subject
Benchmark Statements also describe the nature and characteristics of awards in a particular
subject or area. Subject Benchmark Statements are published in QAA's capacity as a
membership organisation on behalf of the higher education sector. A summary of the
Statement is also available on the QAA website.
Key changes from the previous Subject Benchmark Statement include:
•
•
a revised structure for the Statement, which includes the introduction of cross-
cutting themes of:
- equality, diversity, accessibility and inclusion
- education for sustainable development
- employability, entrepreneurship and enterprise education
a comprehensive review updating the context and purposes of Mathematics,
Statistics and Operational Research (MSOR) including course design and content
in order to inform and underpin the revised benchmark standards.
How can I use this document?
Subject Benchmark Statements are often used by higher education providers in the design
and development of new courses in the relevant subject, as they provide a framework for
specifying intended learning outcomes in an academic or vocational discipline. They are also
used as a reference point when reviewing or revalidating degree courses. They may be used
by external examiners in considering whether the design of a course and the threshold
standards of achievement are comparable with other higher education providers. They also
provide professional, statutory and regulatory bodies (PSRBs) with the academic standards
expected of students.
Subject Benchmark Statements provide general guidance for understanding the learning
outcomes associated with a course but are not intended to represent a national curriculum in
a subject or to prescribe set approaches to teaching, learning or assessment. Instead, they
allow for flexibility and innovation in course design within a framework agreed by the subject
community.
You may want to read this document if you are:
•
•
•
involved in the design, delivery and review of courses in Mathematics, Statistics and
Operational Research
a prospective student thinking about undertaking a course in Mathematics,
Statistics and Operational Research
an employer, to find out about the knowledge and skills generally expected of
Mathematics, Statistics and Operational Research graduates.
Relationship to legislation
The responsibility for academic standards lies with the higher education provider which
awards the degree. Higher education providers are responsible for meeting the requirements
of legislation and any other regulatory requirements placed upon them by their relevant
funding and regulatory bodies. This Statement does not interpret legislation, nor does it
incorporate statutory or regulatory requirements.
1The regulatory status of the Statement will differ with regard to the educational jurisdictions
of the UK. In England, Subject Benchmark Statements are not sector-recognised standards
as set out under the Office for Students' regulatory framework. However, they are specified
as a key reference point, as appropriate, for academic standards in Wales under Quality
Assessment Framework for Wales and in Scotland as part of the Quality Enhancement
Framework. Subject Benchmark Statements are part of the current quality requirements in
Northern Ireland. Because the Statement describes outcomes and attributes expected at the
threshold standard of achievement in a UK-wide context, many higher education providers
will use them as an enhancement tool for course design and approval, and for subsequent
monitoring and review, in addition to helping demonstrate the security of academic
standards.
Additional sector reference points
Higher education providers are likely to consider other reference points in addition to this
Statement in designing, delivering and reviewing courses. These may include requirements
set out by PSRBs and industry or employer expectations. QAA has also published
Advice and Guidance to support the Quality Code which will be helpful when using this
Statement, for example, in course design, learning and teaching, external expertise and
monitoring and evaluation.
Explanations of unfamiliar terms used in this Subject Benchmark Statement can be found in
QAA's Glossary. Sources of information about other requirements and examples of guidance
and good practice are signposted within the Statement where appropriate.
21
Context and purposes of a Mathematics, Statistics
and Operational Research degree
1.1
For the purposes of this document, the term 'MSOR' (Mathematics, Statistics and
Operational Research) should be understood to be more than the disjoint union of its three
named elements and instead be understood to encompass a wide variety of combinations of
the various fields. There is considerable overlap between mathematics, statistics and
operational research, and the modern practitioner of any of the individually named fields is
likely to be familiar with elements of the others. Indeed, many MSOR courses and modules,
such as those in interdisciplinary programmes in data science, exploit this commonality to
assemble a coherent educational provision that draws together elements of mathematics,
statistics, operational research and other disciplines in order to address particular problems.
1.2
Although, for the purposes of this Subject Benchmark Statement, we refer to MSOR
as a coherent corpus of knowledge and skills in its own right, it is perhaps useful to briefly
describe each of the named subfields.
1.3
Mathematics is a major intellectual subject in its own right, with a history that
extends back through various cultures, both ancient and recent. It has its roots in the
systematic development of methods to solve practical problems in areas such as surveying,
mechanical construction and commerce. The subject evolved with the realisation that such
methods, when stripped of the details of the particular situation, had a wide range of
applications and highlighted the essential common characteristics of many different
problems. Therefore, generalisation and abstraction became important features of the
subject. This abstraction allows mathematicians to find deeper relationships within the
patterns than could otherwise have been found from observation or unaided reasoning. This
then enables common solutions to be found to problems that would otherwise have seemed
unrelated.
1.4
Today, mathematics is a subject in which strict logical deductions are used to draw
conclusions that follow with certainty from a given set of assumptions. These assumptions
may be abstractions of fundamental concepts such as number, shape or symmetry, or they
may be simplified models of real-world systems. While the mathematics of earlier times still
remains relevant, it is now only a small part of an ever-expanding and dynamic subject.
1.5
Statistics is the scientific discipline of collecting, analysing, interpreting and
presenting data, particularly in situations where there is random variation in the data caused
by, for example, sampling variation or observational errors. At its heart is probability theory,
a branch of mathematics which formalises concepts such as probability distributions and
stochastic processes based on an axiomatic system. The modern field of probability and
statistics primarily began in seventeenth century Europe through the study of games of
chance but some concepts were explored much earlier; for example, Arab mathematicians
wrote about combinatorics in the eighth century and the Roman Empire routinely compiled
official statistics from census data.
1.6
Today, statistical models are built to represent relationships within the data in order
to test hypotheses, describe associations or forecast/predict unobserved values, while
probability modelling is at the heart of areas such as epidemiological modelling and machine
learning. Statistical techniques are also a key part of the rapidly growing interdisciplinary
field of data science where they are used to gain insights from the large amounts of data
generated in this digital age, including non-numerical forms of data such as images and text.
While statistics and probability are a mathematical science because of the rigorous theory
that underpins them, the subjects are routinely applied in a wide range of contexts, such as
analysing data from scientific experiments or supporting decision making in business
3management and government. Consequently, a key aspect of applied statistics is
communicating conclusions to non-experts.
1.7
Operational research is a more recent subject, beginning during the twentieth
century. Many of its origins are to be found in the organisation of activities during the Second
World War. The subject ranges from complex optimisation procedures with significant
mathematical underpinning to non-mathematical but academically rigorous problem-
structuring methods and techniques for informing decision making and strategy
development. It finds important applications throughout industry, business and commerce, in
government, health and social services and the armed forces.
1.8
The subject area of analytics has become increasingly associated with operational
research in recent years and operational research has become one of the key quantitative
management approaches of modern times. Although the name 'operational research' is
generally well understood, a number of providers use other titles for courses in this area,
such as 'management science'. Titles of this sort often indicate very application-focused
courses, perhaps with relatively little mathematical content. Such courses, by virtue of their
design, might not fall entirely within this Subject Benchmark Statement.
1.9
The influence of MSOR continues to grow significantly, within and outside traditional
science, technology, engineering and mathematics (STEM) disciplines, and both in research
and in taught courses. MSOR is also distinctive in the extent to which the subject is taught
by subject experts to non-specialists as service courses. Some programmes of study in
other disciplines, or individual courses within those programmes, are sufficiently dependent
on MSOR that this Subject Benchmark Statement is directly relevant, such as Mathematics
for Engineering.
1.10
MSOR course curricula form a broad spectrum of styles. To meet students’ needs
courses may combine or focus more on one of these styles. At one end of the spectrum are
‘theory-based courses’ that are concerned with the way in which theory establishes general
propositions leading to methods and techniques which can then be applied to a range of
problems. At the other end are ‘practice-based courses’ that cover the understanding and
application of results, methods and techniques to a variety of situations in different contexts.
The discipline’s interdisciplinary nature means courses may apply theory and practice to
areas both within and outside the subject. Providers should take steps to ensure that all
MSOR graduates, whatever the nature of the course they have studied, are able to fully
identify as professional MSOR practitioners.
Purposes and characteristics of an MSOR degree
1.11
The study of MSOR develops analytical creativity and explores relationships among
abstract concepts without necessarily considering potential real-world counterparts. Many
years later even solely academic research can have ground-breaking impact in new and
developing fields. Equally, MSOR can focus on solving problems with immediate practical
applications. The distinction between theoretical and applied approaches can be blurred with
shared techniques that examine patterns and relationships, with differences only emerging
through purpose.
1.12
As a result of the breadth of MSOR as a discipline, each higher education provider
awarding qualifications in MSOR defines the content, nature and organisation of its courses
and modules. Consequently, MSOR courses offered by individual providers will have their
own particular characteristics.
41.13
MSOR courses include a wide variety of configurations, including foundation years,
apprenticeships, single honours, joint honours, integrated master’s and postgraduate taught
master’s degrees. Many providers find each plays an important and distinctive role.
•
•
•
•
Integrated master's courses generally include aspects of MSOR in greater depth
and/or breadth than bachelor's courses and better prepare students for
postgraduate research studies or employment. They typically include a substantial
project. Some MSOR-led integrated master’s courses have a focus in particular
areas of application.
Postgraduate taught master’s courses have a range of distinct purposes. Some are
conversion courses, allowing graduates from a broad range of other disciplines to
retrain in MSOR. Others allow students to further extend the depth of specialised
study, particularly as preparation for postgraduate research.
Foundation years enable applicants to develop their foundational knowledge before
progressing onto an honours degree course, either on standalone programmes or
via direct progression.
Some providers offer courses where learners spend a year, or shorter periods, in a
supervised professional placement in industry, business or commerce.
1.14
MSOR courses are an intellectual pursuit that develops wide-ranging academic and
transferable skills, open up a range of further study opportunities, and provide an excellent
route to employment. MSOR graduates have a wide choice of careers available to them.
1.15
MSOR has important general characteristics which pervade the culture of the
discipline, including an underpinning in abstract and logical reasoning and a need for
accuracy in numerical work and symbolic manipulation. As these occur throughout the
discipline, time is needed to consolidate learning when developing and practising discipline
skills.
1.16
It is an inherent characteristic of the subject that an individual student's performance
may vary greatly over different modules. This non-uniform profile of attainment is a
characteristic feature of MSOR. See also paragraph 3.52 on Assessment in section 3.
1.17
An important characteristic of the discipline is the cumulative nature of the subject;
modules often require essential background knowledge and have strict formal prerequisites.
It follows that it is quite normal, and often necessary, to teach very similar subject matters in
different years. For example, identical material taught to single honours students in year one
might be taught to joint-honours students in later years. Students on a conversion master’s
course might well need to learn material encountered much earlier by specialists. While
greater general academic maturity might be expected from learners in subsequent years of a
course there are no shortcuts to prerequisites. See also paragraph 2.12 on
Design/Progression.
1.18
MSOR graduates are well prepared to undertake further study in various subject
areas, including but not limited to MSOR, and are highly employable. Employment
opportunities may draw on explicit MSOR skills or utilise the skills developed in areas less
directly related to their subject domain. An extensive source of information is available to
students and graduates of MSOR courses from the Maths Careers website.
1.19
As described in both the 2012 report Measuring the Economic Benefits of
Mathematical Science Research in the UK and the 2018 report The Era of Mathematics
reviewing knowledge exchange in the mathematical sciences, MSOR and mathematical
sciences more broadly make a vast, quantifiable contribution to the UK economy and
society. For example, the gross value added by mathematical sciences research in 2010
5was over 40% of the UK total. MSOR degrees are key to establishing a workforce to
maintain and drive forward these societal and economic benefits.
1.20
As of 2022, the following societies offer professional recognition schemes based on
the nature of the degree programme, an individual's education, an individual's work
experience or a combination of these.
•
•
•
•
The Institute of Mathematics and its Applications (IMA) accredits courses where
they meet its requirements for graduates to attain its Chartered Mathematician
status.
The Royal Statistical Society (RSS) accredits courses where they meet its
requirements for graduates to attain its Graduate Statistician status. The RSS also
accredit individual modules that teach statistical literacy, awarding them the RSS
Quality Mark.
The IMA, RSS and Operational Research Society (ORS) all operate individual
professional recognition schemes based on either the nature of the individual's
education, engagement with continued professional development, their work
experience or a combination of these.
The Institute and Faculty of Actuaries (IFoA) accredits courses and modules, with
accreditation providing students with exemption from certain IFoA examinations.
Equality, diversity and inclusion
1.21
Equality, diversity and inclusion (EDI) is essential for the health of MSOR, and it is
important that the discipline encourages inclusivity and access to ensure learners are
attracted from diverse backgrounds, that the curriculum and environment enable them to
succeed in their studies, and that the subject is enriched by input from diverse practitioners.
1.22
Students come to MSOR courses with different backgrounds, aspirations,
expectations and academic experiences. As such, all students benefit from developing their
knowledge and understanding within an inclusive learning environment providing rich
opportunities for academic, pastoral and well-being support which recognises this diversity.
This would include the provision of suitable support for students with different needs and
varying pre-university experience, as outlined in more detail below.
1.23
Values of EDI should permeate the curriculum and every aspect of the learning
experience to ensure the diverse nature of society in all its forms is evident. MSOR providers
should reflect on their curricula and processes to ensure that no group is disadvantaged or
othered; for example, decolonising the curriculum can involve explicit reflection on the
history of MSOR knowledge generation, as well as reflecting on how delivery or admission
practices might adversely impact on certain subgroups within the student cohort. EDI
aspects of student engagement and achievement should be monitored and actions formed
to ensure equity.1.24
MSOR providers throughout the UK are committed to championing EDI, with
several possessing Athena SWAN awards and/or providing publicly available information
describing their commitment to EDI and initiatives in this domain. The London Mathematical
Society (LMS) runs a Good Practice Scheme supporting women’s careers in MSOR in
higher education and many providers work to these standards.
1.25
It is imperative that students encounter a wide range of role models within higher
education. This is particularly important given the well-known gender imbalance in the
subject (the 2015 Council for Mathematical Sciences report on The Mathematical Sciences
People Pipeline contains data on the demographic imbalances), retention and attainment
gaps, and the strong focus of curricula on the historical work of white Western males. There
6is a need for inclusive language and scenarios in all publicity and teaching material, and for
courses to be informed by the student voice and taught in a way which makes the resources
meaningful to all students and with topics and examples which have relevance to a wide
range of people.
1.26
EDI has implications for all aspects of provision. For example, good practice might
include the following:
Environment - providers should make efforts to present visible diverse role models, attract
diverse staff in all roles, and ensure a suitable working and study environment for all, for
example having an understanding of caring responsibilities for staff, which considers the
timing of meetings, and other practical arrangements. There should be a suitable study
environment for all with accessible facilities and equal access to specialist software and
other technology. Providers should be responsive to the student voice and should actively
solicit suggestions to enhance their provision.
Recruitment - admissions decisions should acknowledge the variety of qualifications
applicants might have, and consider the provision of opportunities for those without A Level
Mathematics or equivalent (for example, via foundation years) or Further Mathematics.
Providers should recruit from a variety of schools and colleges, promoting diverse role
models and advertising the support they offer.
Delivery - the timetable should consider the needs of students with commitments such as
childcare and other caring responsibilities, religious beliefs and work, and should ensure that
suitable teaching spaces appropriate for all are allocated. Materials should be accessible,
written in inclusive language, with examples and scenarios which are appealing to all and
relevant beyond the UK, recommending textbooks and other resources which conform to
modern expectations regarding EDI. A variety of teaching methods should be in use to
support learners with differing needs. The use of tools like recording and electronic provision
of resources should support those who may not be able to attend all lectures, or who may
use these to learn more effectively (see also paragraph 1.38). Care should be taken over, for
example, the assignment of students for groupwork. Teaching staff should be available to
support students and there may also be university-wide mathematics and statistics support
provision.
Curriculum - the curriculum should present a multicultural and decolonised view of MSOR,
informed by the student voice. Where possible, it should present the work of a diverse group
of MSOR practitioners. Students should be made aware of problematic issues in the
development of the MSOR content they are being taught, for example some pioneers of
statistics supported eugenics, or some mathematicians had connections to the slave trade,
racism or Nazism. Students should be educated in general EDI matters and also those that
are specifically relevant to MSOR, such as the need to consider diversity in data collection
and analysis.Employment skills - the curriculum should deliver career skills, balancing the needs of
students who plan to go into graduate careers on completion of their degree and those
aspiring to further study. Strategies should be embedded to make teamwork inclusive,
addressing issues such as norms regarding decision making, attitudes to authority,
positioning within a team, past experiences of task designation, reaching group decisions,
and geopolitical issues.
Assessment - a variety of assessment methods should be available, and assessment
should acknowledge the difficulties that students from different academic, social or cultural
backgrounds may face with some forms of assessment. Data on attainment should be
monitored and there should be actions to address the issues identified. Reasonable
7adjustments should be made where appropriate (see paragraph 1.30). The design of
assessments and assessment schedules should consider students' mental well-being, and
care should be taken to minimise the stress these cause to students.
Support - support should be available for all students, including disabled students and those
from diverse backgrounds or different cultures. There should be an inclusive culture across
the institution, including internal workshops and training sessions to raise the awareness of
MSOR teaching staff of issues relating to EDI.
Accessibility
1.27
In order to ensure an accessible course experience, providers need to anticipate
their learners’ needs and proactively ensure that these are met.
1.28
Providers should consider the challenges and barriers that need to be overcome to
successfully empower their students to be full participants in their own education and
academic communities. The diverse nature of MSOR courses and individual modules within
courses means these challenges and barriers should be considered both at course level and
within modules to create a coherent and consistent approach to accessibility.
1.29
In addition, it is imperative that providers anticipate the discipline-specific digital,
physical and pedagogical accessibility needs of disabled students, embedding accessibility
in a manner that minimises or eliminates the need for reasonable adjustments.
1.30
Reasonable adjustments respond to both the individual and the discipline, and
provide authentic participation in all course activities. Where reasonable adjustments are
necessary for individual students then providers may need to work with internal or external
specialist disability advisory services to provide them.
1.31
Embedded accessibility has benefits for all students. In addition, it typically further
benefits particular groups of students, such as those with caring responsibilities, those
working part-time, those with a temporary impairment due to short-term illness or injury, and
those experiencing acute mental distress.
1.32
Providers should seek to ensure that their courses are well curated. Well-curated
courses benefit all students by promoting good mental health and well-being and reduce the
administrative burden and cognitive load on disabled students. Well-curated courses include
clearly communicated learning opportunities, assessments that are appropriately spaced
and provide particular support when concepts and skills are initially introduced.
1.33 Distinctive discipline characteristics that may require specific attention include:
• the use of a wide range of special symbolism which is essential to understanding
the subject matter, and special notation used by all MSOR specialists to
communicate effectively and unambiguously
traditional practices in teaching MSOR, for example, presenting a technical
argument carefully at a board, which have evolved and are retained for very sound
reasons: the highly compressed nature of the concepts and relationships encoded
in mathematical notation needs to be discussed very carefully, sometimes symbol
by symbol, with extended arguments presented
discussion of mathematical arguments is often highly non-linear for example,
regularly referring backwards to previous statements in precise ways
the essential role played by diagrams and pictures in MSOR.
•
•
•
81.34
Specialist technology for MSOR is developing rapidly and continues to remove
barriers to access. There have been significant positive advances for digital accessibility
throughout this century. Technological changes can be expected for the foreseeable future;
for example, developing mathematical arguments by writing on a tablet can offer advantages
over boards in terms of visibility in the lecture room, handwriting recognition, and clarity of
captured content.
1.35
A mainstream adaptive technology, for example learning management systems,
screen readers and automatic captioning software, often does not effectively support MSOR
content. To mitigate this deficiency:
•
•
•
providers should acknowledge the special needs of MSOR and the deficiencies in
many adaptive features of mainstream technology by providing additional resources
which may not be needed by subjects where the medium is primarily language
based
academic staff will require specialist technical support to solve particular digital
accessibility challenges
staff and students are likely to need special hardware and software to better access
MSOR content.
1.36
Consequently, creativity may be required to addresses challenges which, at the
time of writing, remain.
1.37
Including elements of online, hybrid, or blended learning across courses can
significantly increase access for students, as can, where appropriate, the provision of
captured content from in-person sessions. Associated enabling technology is required to
capture the live display of extended written material and ensure accurate captions. Within a
physical venue, consideration of the visibility of boards and other display equipment is
essential.
1.38
Those in support roles, including scribes, note takers, readers and communication
support workers, need to have an understanding of MSOR terminology and symbolism since
even minor symbolic differences can radically change the intended meaning.
1.39
Some teaching and learning activities are found relatively infrequently in MSOR
courses. In such instances providers may take advice from other disciplines. This includes
experimental mathematics and fieldwork which, where it exists, is typically such that
students can benefit from local opportunities.
1.40
A flexible course pedagogy provides students with a variety of learning
opportunities, alternative ways to acquire knowledge and time to consolidate material. For
instance, where material is delivered by a traditional lecture, the advanced provision of
accessible lecture notes complemented by in-person delivery of the material which is
recorded may provide such variety.
1.41
Implicit MSOR course requirements, social and culture behaviours assumed without
direct instruction are context dependent, where a specific task or situation can change
expectations, and these can be additional barriers for disabled students. Examples may
include appropriate computational accuracy, study expectations, organising independent
study and teamwork skills. All students will benefit from, and disabled students may require,
explicit instructions on these traditionally implied course norms.
1.42
Assessment design should anticipate and remove potentially irrelevant, or context-
dependent, barriers that are irrelevant to knowledge, skills or abilities measured by the
assessment. For example, consideration should be given to whether a student will spend
9disproportionate time and effort interpreting material; be exposed to distracting and needless
imagery; be unfamiliar with the assumed context, customs or colloquialism of a task.
1.43
The MSOR community supports providers’ accessible course development through
a variety of resources, for example, the LMS website Mathematics and Accessibility.
Sustainability
1.44
MSOR has a vital role to play in achieving the UN’s Sustainable Development
Goals, underpinning many technological, scientific and digital developments which have
potential to improve health, drive economic growth, transform societies and enhance our
environment. For example, mathematical models inform forecasts of climate change,
analysis of health data informs public health provision and algorithms help users optimally
navigate transport networks. Policies which encourage sustainable development and reduce
inequalities can be developed and analysed based on mathematical models and data
analysis. MSOR degrees are themselves a driver of social mobility with many graduates
from a range of socio-economic backgrounds earning high incomes.
1.45
MSOR is such a versatile subject that many of the 17 UN Sustainable Development
Goals could be discussed in the context of MSOR degrees. As noted elsewhere in this
Subject Benchmark Statement, MSOR is often taught using real-world examples or in the
context of applications in other disciplines. Through these examples and applications
graduates can appreciate how MSOR can help society to achieve the UN’s sustainable
development goals. Further, the skills developed through MSOR degrees such as critical
thinking and problem-solving are useful in understanding, analysing and resolving issues in
complex systems such as ecosystems, societies and networks which are impacted by
unsustainable development.
1.46
The Education for Sustainable Development Guidance produced by QAA and
Advance HE outlines pedagogic approaches for implementation in UK higher education
institutions. In the context of MSOR degrees these might include the following.
•
•
•
•
•
•
Projects or dissertations where the focus is on modelling or analysing a problem
connected to sustainability. The project or dissertation may be interdisciplinary in
nature and involve working with students or supervisors in other fields. Topics could
include, for example, modelling energy needs or measuring ecological biodiversity.
Specific modules which focus directly on the use of MSOR in addressing a specific
sustainability issue. For example, mathematical medicine or environmental
modelling could be the basis of a module.
Case studies which illustrate the applicability of a MSOR method or technique to a
sustainability issue; or case studies which have motivated new MSOR research.
MSOR problems where the motivation or context of the question is a sustainability
issue.
Discussion of inequalities, perhaps in the context of professional ethics, protected
characteristics and/or equality, diversity and inclusion.
Consideration of ethical issues and unintended consequences of MSOR, such as
the environmental impact of high-performance computing or the use of pure areas
such as graph theory in controversial social media practices.
1.47
The following are examples of how MSOR methods may be linked to sustainability
issues.
•
Pollution levels connected with transport could be reduced by applying fluid
dynamics to improve aerodynamic efficiency or optimisation algorithms to reduce
delays in networks.
10•
•
•
•
•
Population dynamics can be modelled using ordinary differential equations in the
context of species growth and decline, using SIR (susceptible, infected, removed)
models in the context of epidemics or using network theory applied to ecosystems.
Automated diagnosis based on medical images may be achieved using
classification algorithms and low rank approximations of images using matrix
factorisation.
There are various mathematical models for climate forecasting, such as those
based on Navier-Stokes equations, and extreme value theory to estimate the risks
of weather events.
Machine learning, artificial intelligence and data science have many applications in
sustainability in the contexts of, for example, energy, resource management,
biodiversity, crop yields and climate.
Applications of pure mathematics in cryptography and blockchain techniques which
have significant environmental consequences.
1.48
Sustainable development may be revisited multiple times in the curriculum to
reinforce the connections between different areas of MSOR and economic, social and
environmental issues. Education for sustainable development is an emerging field within
MSOR and providers are encouraged to innovate and evaluate pedagogical developments in
this area.
Enterprise and entrepreneurship education
1.49
In general, as articulated in QAA’s guidance, enterprise and entrepreneurship
education supports behaviours, attributes and competencies that are likely to have a
significant impact on the individual student in terms of successful careers. It prepares
students for changing environments and provides enhanced impact through placements and
activities that build links between academic institutions and external organisations.
1.50
Preparing students of MSOR to move successfully from education into employment
is an essential part of a degree course. While there are other departments within institutions
that will support students in taking the next steps in their career together with a personal
responsibility for the student themselves to take ownership, the development of employability
skills should be embedded into MSOR courses, including through enterprise and
entrepreneurship education.
1.51
Enterprise is defined here as the generation and application of ideas, which are set
within practical situations during a project or undertaking. This is a generic concept involving
creativity and problem-solving that can be situated in a MSOR context and applies across all
areas of professional life. MSOR courses are particularly well suited to developing this, with
a generalised focus that will prepare students for a range of possible future careers.
1.52
Entrepreneurship is defined as the application of enterprise behaviours, attributes
and competencies into the creation of cultural, social or economic value. This can, but does
not exclusively, lead to venture creation.
1.53
Enterprise and entrepreneurship education is defined here as the process of
developing students in a manner that provides them with an enhanced capacity to generate
and evaluate ideas, and to broaden their behaviours, attributes and competencies to
implement them.
1.54
A key part of any MSOR degree is its focus on problem-solving which is one of the
core competencies associated with enterprise and entrepreneurship education along with
problem identification, creativity and strategic thinking. Other relevant behaviours, attributes
11and competencies developed through many MSOR modules are adaptability, curiosity,
determination and resilience.
1.55
Modules such as a final dissertation or project can foster a student’s ability to
reflect, take responsibility and take risks in a supervised environment. Modules enabling
students to work in groups can provide opportunities for developing and improving skills in
influencing, leadership, negotiation and communication. In advance of any group work,
students should be supported in developing an appreciation of the differences between
working individually and working with others, group management and general good group
work behaviours. An ability to work with and interrogate large data sets is key to successful
entrepreneurship and enterprise and a module that provides this opportunity will enable
students to develop many of the competencies mentioned above.
1.56
A problem-based learning approach in taught modules can help students to
appreciate the complex nature of real-world problems. This approach can also help students
to develop resilience and encourage them to be adaptable in their approach to problem-
solving. These skills are sought after by employers.
1.57
Project work for simulated or real clients can be especially effective in embedding
entrepreneurship and enterprise skills in the curriculum and can be a satisfying alternative to
placements which provides students with opportunities to develop similar skills. When
possible, collaborating with employers on the design of student projects can be a mutually
beneficial endeavour which helps to ensure that academic institutions are setting projects
which are current, relevant and authentic. Consulting with employers on suitable outputs can
lead to a range of possible authentic assessment strategies, with posters, executive
summaries and client reports being just some of the possible assessed outputs.
1.58
As graduates can find rewarding employment in many different areas, it is useful for
academic institutions to organise regular, targeted events for students where they can hear
from and network with employers and alumni.
1.59
During their course, students may have the opportunity to apply for a wide variety of
placement opportunities. Students reap many benefits from placements, especially in terms
of skills development. Placement opportunities can also help students to develop
entrepreneurial skills such as an awareness and appreciation of business, cultural or societal
considerations and priorities. By undertaking placements, students are able to see how
MSOR work can make a significant contribution to understanding and tackling complex
problems in an organisation.
1.60
In order for graduates to build on these skills in their future career or further studies
they need to be able to reflect, understand and articulate that their degree has given them
the opportunities to develop many areas of entrepreneurship and enterprise as well as
general employability skills.
122
Distinctive features of MSOR courses
Design
2.1
Some courses are concerned more with the underlying theory of the subject and the
way in which this establishes general propositions leading to methods and techniques, which
can then be applied elsewhere. Other courses are more concerned with understanding
MSOR results, methods and techniques and their application in MSOR and beyond. For
convenience, these different 'styles' will be referred to, respectively, as 'theory-based
courses' and 'practice-based courses' (see paragraph 1.10).
2.2
While there are a few courses that are entirely theory or practice-based, most have
elements of both approaches and there is a complete spectrum of courses covering the
range between the two extremes. It is possible for courses with the same title to have very
different emphases; it is the curriculum of a course, rather than its title, that makes clear its
position within the spectrum. These different emphases are all equally valuable.
2.3
Possible paths to undergraduate degree study include academic routes,
apprenticeships and vocational routes, with some providers offering routes for students with
relevant access qualifications. The majority of undergraduate MSOR courses require an A
Level or equivalent in a relevant MSOR subject area, for example A Level Mathematics.
Some also require A Level Further Mathematics or have other admissions requirements,
such as STEP (Sixth Term Examination Paper). Some courses offer foundation years which
are designed to provide preparatory work for Level 4 study in the subject. Equally, some
applicants may undertake international foundation year courses allied with MSOR degree
providers. Such foundation courses can be studied as standalone courses or may be
integrated into the degree to enable direct progression to Level 4 of the degree.
2.4
Possible routes to postgraduate taught degrees also vary depending on the nature
of provision. The broad discipline area of MSOR encompasses several types of master’s
degrees, ranging from conversion master’s provision, often in the areas of data science and
statistics, where students may come from a variety of backgrounds with varying levels of
MSOR content, to other more specialist master’s degrees in areas such as pure
mathematics, where students need the mathematical rigour obtained from an appropriate
undergraduate qualification.
2.5
Undergraduates in MSOR may choose to study a standard bachelor’s degree with
honours (FHEQ Level 6; FQHEIS Level 10) or an integrated master’s degree with honours
(FHEQ Level 7; FQHEIS Level 11). These each have distinct learning outcomes to reflect
the level of the award. Bachelor’s degrees should provide students with the subject-specific
knowledge, understanding and skills, as well as the wider transferable skills and attributes
that prepare graduates for a wide range of careers in many sectors.
2.6
Integrated master's degree with honours courses, for example MMath, encompass
both bachelor's degrees with honours and master's degree outcomes. An integrated
master's degree is awarded after an extended course which allows students to study an
MSOR subject to a greater breadth and/or depth than is possible on a bachelor's course,
and to extend the opportunities to develop specialist knowledge, advanced skills and
undertake more extensive project work. These master's degrees thus provide a coherent,
integrated opportunity to develop a deeper and/or wider level of knowledge, understanding
and experience, sufficient to prepare students for a professional career in MSOR.
Standalone master's degrees in MSOR, for example MSc and MRes, are self-contained
courses, normally involving the equivalent of one or two years of full-time postgraduate study
in a specialist area.
132.7
In addition to single honours courses in MSOR subjects, many joint honours
courses studying MSOR in combination with another distinct discipline are available. In joint
honours courses, undergraduates will achieve core elements of the specific and generic
skills for each subject, and will add others according to the modules on offer within the
degree. Additionally, students may explore the overlap between their two subject areas,
creating opportunities for interdisciplinary study. In interdisciplinary degrees, such as data
science, students will study a set of core knowledge across the subject areas while
potentially specialising in one or more of the component disciplines.
2.8
Some MSOR courses will enable students to learn outside the formal academic
environment, for example through placements or internships in industry or educational
settings, for example, within schools or colleges through initiatives such as undergraduate
ambassador schemes, or to study at an international university. Such placements may last
for a few weeks, a term, a semester or an entire year and can also be arranged on a part-
time basis. They typically take place after completion of the equivalent of at least two full
years of study.
2.9
Both bachelor's and integrated master’s degrees may include such periods of study,
and this may or may not extend the period of the degree, depending on the expected
learning undertaken during the year. Credit awarded during such study also varies according
to the learning and assessment workload during the experience. Credit-bearing placements
(see paragraph 2.28 in the Partnership section) should, however, be integrated within the
programme of study, so that students can relate their experience to, and use the skills that
they have developed in, their academic study. Many providers also offer or facilitate non-
credit-bearing industrial and research placement experiences during vacations to enhance
student experience and development.
2.10
Where a provider offers several MSOR courses, these may be based around a
common core of shared compulsory modules, especially in the early years, with options in
later years that allow students to specialise. This approach enables both flexibility and
efficiency of delivery and may even allow students to defer selection of the award title until
later years, by retaining the option to transfer between cognate courses (see paragraph 2.16
on Flexibility).
2.11
The academic component of integrated degree apprenticeships in MSOR should
follow the guidelines in this Subject Benchmark Statement. Degree apprenticeships in higher
education are covered explicitly in the Characteristics Statement for Higher Education in
Apprenticeships which describes the general characteristics and distinctive features of
apprenticeships in the UK.
Progression
2.12
Over the course of a bachelor’s degree with honours (FHEQ Level 6; FQHEIS Level
10) or an integrated master’s degree (FHEQ Level 7; FQHEIS Level 11), an MSOR student
will progress from one level of study to the next, in line with the regulations and processes
for each institution. However, it is expected that each level would see the attainment of
knowledge, expertise and experience that build towards the final achievement of meeting at
least the threshold-level subject-specific and generic skills listed in this Statement. This
would include successful completion and the award of credit for the full range of learning and
assessment. Upon graduation from an undergraduate degree, it would be expected that a
student who has achieved a second-class degree or higher would be capable of, and
equipped for, undertaking postgraduate study in MSOR or an associated discipline. Entry
requirements to postgraduate courses are, however, determined by individual providers and
may require specified levels of achievement at undergraduate level.
142.13
Undergraduates studying a combined, joint or major-minor route will achieve core
elements of the specific and generic skills for each subject, and will add others according to
the modules on offer within the degree. Additionally, students may explore the overlap
between their two subject areas, creating opportunities for interdisciplinary study.
2.14
Integrated master’s degrees (FHEQ Level 7; FQHEIS Level 11) typically require the
equivalent of an additional full-time year of study when compared to a bachelor’s degree.
2.15
In undergraduate honours degree courses, students may exit earlier and be eligible
for a Certificate of Higher Education, a Diploma of Higher Education, or a pass or ordinary
degree depending upon the levels of study and credit completed to a satisfactory standard.
In Scotland, bachelor’s degrees with honours are typically designed to include four years of
study, which relates to the structure of Scottish primary and secondary education. For
students following part-time routes, their study time would be the equivalent of the three or
four-year degree.
Flexibility
2.16
The progressive acquisition of knowledge and skills within the subject area also
enables flexibility between courses, both within and between institutions.
2.17
As has been set out in paragraph 2.10 in the Design section, MSOR courses
designed around a common core of shared compulsory modules in the early years, followed
by specialisation in later years, facilitate both flexibility and efficiency of delivery. They can
also enable students to defer selection of their award title until later years and can make the
transfer between cognate courses more straightforward.
2.18
MSOR students should also have flexibility to select some optional modules in
alignment with their interests, and therefore appropriate guidance on option choices should
be made available to the students.
2.19
The cumulative nature of the subject limits the flexibility that can be designed into
some MSOR courses that require certain prerequisites for certain modules. This will also
limit the flexibility of the credit transfer process as, in such cases, students will require a
sufficient number of specific credits that cover the prerequisites in order to transfer onto
some MSOR courses.
2.20
In England, some higher education providers use a flexible approach to the staging
of modules in order to offer courses where learners spend part of their final year in a school
in order to gain Qualified Teacher Status (QTS) and a full honours MSOR degree without
extending the duration of the degree course.
2.21
Flexible educational approaches enable learners to adapt their education to their
situational and contextual individual needs and constraints, and may also play a key role in
increasing access into further and higher education and social mobility. For example, such
approaches could provide scope for learners to select educational opportunities that are
better suited to their current level of proficiency and interests (see paragraphs 1.22 and
1.40).
2.22 To this end, it is beneficial for higher education providers to have:
• flexible approaches to assessment tasks that enable learners to demonstrate
different competencies
flexible approaches to awarding and transferring credits, for example the integration
of alternative recognition of learning (such as prior experiential learning and micro-
credentials) with traditional modular credits.
•
15• flexible approaches to recruitment processes that recognise prior learning and/or
work experience in the field of MSOR.
2.23 In addition, across the sector, it is beneficial to have:
• flexible delivery modes, including but not limited to campus-based, distance
learning, block release and hybrid (campus-based and distance learning).
flexible study patterns in terms of intensity of study and start dates.
•
2.24
MSOR courses should be sufficiently flexible to be able to respond to and anticipate
change, in the advancement of the subject and its interface with other disciplines, as well as
in the needs of its graduates and their employers. They should also take account of learners’
needs and make appropriate reasonable adjustments, as required.
Partnership
2.25
Partnerships may be academic, as a collaboration with other educational
organisations, or may be professional, as a collaboration between providers and industry.
2.26
An academic partnership may be between providers and other UK or international
educational institutions. These may include partnership programmes that give advanced
standing to students with prior study abroad, for admission into year two or three of existing
UK degree courses.
2.27
Partnerships between providers and industry can involve employers or professional
organisations and may include, but are not limited to, placements and work-related projects.
These can be offered, organised and advertised by external organisations, but can also be
developed as a collaborative effort between higher education providers and employers. They
may be part of the formal curriculum, be awarded credit and the employer might contribute to
assessing the students’ work.
2.28
Placements may include working for an employer for a short time each week over
the length of a module or in a block in or outside term time. Employers include private and
public sector organisations as well as charities and other voluntary groups. Organisations
such as schools and colleges can provide placements for MSOR students analysing and
presenting student data or applying MSOR in areas such as timetabling. Work can be
focused on a specific project or include a variety of tasks as directed by the employer.
2.29
Many employers are keen to take on MSOR students for a year-long sandwich
placement between years of study. MSOR students are in demand especially due to their
potential skills around handling data and programming as well as their knowledge of specific
MSOR techniques.
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