A lesson from the Corona virus lockdown: Some advice for Engineering Students (and Educators)

Introduction

That COVID-19 has adversely impacted higher education is without doubt.  In virtually all institutions of higher education worldwide, normal lessons ended abruptly mid-way through the academic year, giving way to online delivery. Labs and other practical activities designed to equip students with hands-on skills in their disciplines stopped overnight, and the normal university bustle and activity critical for academic engagement between students and students, and between students and academics also evaporated overnight. Though online activity has replaced much of  our university life, there is a general perception that this is not quite enough – we yearn for that period of time again when we can go back to the old university life we are so much accustomed to. Yet, this disruption has opened us up to new possibilities that we could never have thought of.

Disruptions as opportunities for learning

One such possibility is this: online learning is not all bad – there are definitely some aspects of online learning that can improve learning and teaching.  The other is this: whilst face to face lectures remain the de facto signature pedagogy for universities, possibly we don’t need so much of them – there are definitely other ways to achieve the same goal, especially with blended learning approaches like flipped learning. And then there is this one: whilst we have tinkered around with the undergraduate engineering syllabus by adding more active learning components like problem/project-based and design-based learning, the engineering syllabus remains heavily oriented towards content delivery. Do we really need to be teaching all this content? Should we not move some of this content-teaching aside and focus more on higher order thinking skills such as analysis, synthesis and evaluation of knowledge?

This is precisely what I am discovering during this lockdown period. Virtually all the content that we deliver in the first and second years of university level engineering education is freely available on Internet.  Name it – it’s there – be it circuit theory and electronics, engineering dynamics and materials, physical chemistry and transport phenomena, calculus and programming or structures and fluid dynamics. This was not the case two or more decades ago, yet, save for the cosmetic changes, the undergraduate engineering syllabus remains virtually unchanged. Of course, it doesn’t mean we should stop teaching this content in universities. With so much high-quality academic material out there on the Internet, it is now the responsibility of the student to make an effort in acquiring these foundational skills. Indeed, with regard to engineering education, it is no longer a case of taking the horse to the water. The horse is already in the water, it’s now a case of the horse choosing where in the water it should take its drink.

Self-directed learning skills as the key to success

The civil engineering student may be motivated to pursue an engineering degree by a desire to design better roads, or a desire to understand bridge design; the electrical and electronics engineering student may be motivated to undertake university level studies by a desire to design and manage power system networks, or a desire to build and operate communications networks. Indeed, the Internet is awash with introductory material on all these fascinating subjects. In addition to the standard text-based lecture notes, there are also a wide variety of online videos and a plethora of interactive, simulation-based courses on all aspects of engineering. Whilst the lack of equitable digital access does indeed suggest that some students experience varying levels of digital exclusion, the current penetration and extent of ICT technologies would suggest that in developed countries almost everyone has reasonable access to the Internet.

Increasingly, students should drive their own learning, and this starts with demonstrating some preparedness to seek out information and to direct their own learning. In turn, a student who engages with their own learning has a deeper understanding of what they seek to achieve in their learning than one who waits for someone else to direct their own learning. This, in turn, will force universities to spend less time on foundational material, and to concentrate on equipping students with the higher order knowledge skills that employers are now demanding. Indeed, students who take it upon themselves to equip themselves with the requisite foundational knowledge are better able to focus on addressing the issues facing engineering today, thereby ensuring that they are better prepared for successful careers in engineering.

The student we should be welcoming into engineering

Traditionally we have demanded a certain level of academic competence in mathematics and the physical sciences for anyone contemplating doing an engineering degree. Which is a better predictor of success in engineering – a demonstration of passion and engagement in engineering, or straight A grades in A Level mathematics and physics? Surely it should be the former, but I accept, traditions take a long time to die away. This is perhaps one of the reasons why the leaky pipe phenomenon has persisted in engineering. By prioritising A grades in A Level mathematics and physics over passion and interest in engineering, we are inadvertently admitting individuals who have mastered the art of being career students, and shutting out those students whose heart is in engineering.

A call to arms

In conclusion, attainment in engineering education is no longer the responsibility of academics and institutions alone. Rather, the student now has a bigger role  to play in their own development as prospective engineers. It’s no longer about paying fees alone and attending lectures and completing the odd assignment;  it’s now more about students  demonstration a willingness and capability to drive their own learning.

The UCL-Ventura breathing aid: An insight into the emerging engineering practices of the 21st century

Introduction

The UCL-Ventura project is a project borne out of the coronavirus pandemic. Its objective was to provide a cheap, effective solution to the dire shortage of ventilator equipment in British hospitals. From conception to delivery, the project took a little over a week, drew on medical research networks spanning countries such as Italy and China, and brought together medical  and engineering expertise from multiple organisations, key amongst them being University College Hospitals,  Mercedes AMG HPP, the UCL Mechanical Engineering Department, and the UCL Institute of Health Engineering. 

What are the factors behind the success of this interdisciplinary, inter-organisational, multi-stakeholder venture? Clare Elwell, professor of Medical Engineering at UCL, has provided an inside story outlining what really transpired throughout the project. Hers is the story of human determination and endeavour; it is a story of human creativity  and innovation in the face of a cataclysmic crisis, and above all, it is a story of ordinary, passionate individuals making the most of their diversity to defeat a problem besetting all humanity. 

My objective is slightly different, though.  All over the world, reformist engineering educators have been preaching the gospel of 21st century engineering  to exasperated students and sceptical academic colleagues. The UCL-Ventura project is an embodiment of this gospel. In this blog piece, my objective is very simple. It is to highlight some of the 21st century skill sets that were deployed in this project. It is my hope that current engineering students will use this blog piece to make connections between their  studies and this project. It is one thing to talk of interdisciplinarity, collaboration and resilience, and another to actually point out and demonstrate their application in a real-life project. Increasingly we are exposing our students to short-duration, intensive, multidisciplinary projects as part of their studies. This blog piece, read in conjunction with Clare Elwell’s story will serve as a helpful case study to guide them as they prepare for these projects. For the engineering educator, my hope is that the UCL-Ventura project will serve as an excellent case study on 21st century engineering practices, and as a template for the development of realistic short duration, multidisciplinary student projects. 

What is 21st century engineering practice?

As many writers have pointed out, 21st-century engineering practice is fundamentally different from engineering practices of the past.This is because the world has become increasingly more complicated and complex. A large part of this is our increasing dependence on technology.  It is no longer possible for any one discipline to address all the problems, issues, or questions that we now face in the 21st century. Instead, problems now require interdisciplinary approaches that draw not only from engineering disciplines, but from the humanities and the physical, biological and social sciences. Not only that, the effective resolution of emerging 21st century problems now often requires a global approach that brings together knowledge and expertise from individuals and organisations drawn from different backgrounds, cultures and countries.  The current Covid-19 pandemic is a case in point. It is not just a medical problem for any one country; it is an all-embracing problem affecting all aspects of humanity, and spanning all the countries of this world. 

Essential Attributes and Skills for the 21st Century Engineer 

Most of the research on the essential graduate attributes and skills for those aspiring to become engineers in the 21st century emphasise that in addition to being technically sound, 21st century engineers should have a broad knowledge-base that goes beyond their field of specialisation, and they should also be equipped with a range of personal and interpersonal skills to enable them to carry out their roles (Abdulwahed et al, 2013). In general, such attributes and skills may include: teamwork, communication, inter/multidisciplinary knowledge, analytical thinking, ingenuity, creativity, technological innovation, business and management skills, leadership, ethics, professionalism, as well as understanding work strategies (National Academy of Engineering, 2004). 

Overview of the UCL-Ventura Project

This project required individuals from various organisations to come together  and contribute their expertise at various phases of the project. To start with, when the urgent need for ventilators became known,  Mervyn Singer, a professor of intensive care medicine at UCL Hospitals drew from his knowledge and expertise to identify an appropriate device type. In addition, he also had an awareness of someone with the engineering skills necessary to deliver the device – Tim Baker from the UCL Mechanical Engineering Department. 

Tim Baker has collaborated extensively with Andy Cowell and Ben Hodgkinson from Mercedes AMG HPP on the student Formula 1 project. As a Formula 1 company, Mercedes AMG HPP have expertise in fast track design and prototype manufacturing, and Tim was aware that this expertise was critical to the success of the project. From within Mercedes AMG HPP, Andy and Ben identified Jamie Robinson, Alex Blakesley and Ismail Ahmad as the people to lead on the fast track design and prototyping task. All three are UCL graduates.

 A team of engineers from UCL Mechanical Engineering and from the UCL Institute of Health Engineering was assembled to work alongside the  Mercedes AMG HPP team. Given the urgency of the situation, this collaborative team of UCL and Mercedes engineers were able to reverse engineer an existing product and have it ready for production within 24 hours. This required resilience and determination from everyone concerned. The fact that  Jamie Robinson, Alex Blakesley and Ismail Ahmad are UCL graduates may also have been a significant factor as the team needed to gel together and get up to speed almost from the very start.`

Before being put on clinical trials, the design had to be approved by the UK’s Medicines and Healthcare Products Regulatory Agency (MHRA). Regulatory approval is normally a very lengthy process, but the team were able to get this done within a few days. Credit for this was down to the familiarity of members of the team with the regulatory process, which led to the team’s decision to focus on reverse engineering a previously approved off-patent device, as opposed to making one from scratch. Another reason for this rapid regulatory approval may be down to the ability of the  UCL Institute of Healthcare Engineering to tap into its partnerships with organisations and colleagues within the UK health system.

Unpacking the Skills and Attributes Deployed in the UCL-Ventura Project

The design and development process of the UCL-Ventura breathing aid consisted of several sub processes, some running in tandem and some running in parallel. Examples include design, ordering of components and subsystems,  manufacturing, fabrication and assembly, testing, documentation, and clinical trials. Effective project management and coordination was therefore critical, and the UCL Institute of Healthcare Engineering drew from its experience to provide this. 

Clearly, the success of this project rested almost entirely on effective collaboration and team-working. The individuals and organisations that were brought together have worked closely, on and off,  for many years on several other projects. The assembly of the team was therefore not a random act, but was based on a clear understanding of what each partner would bring to the project. In the classroom, we are sometimes guilty of positing collaboration and team-working as one-off events. Clearly, this is not so. It takes time, money and effort to build effective collaborative partnerships within and beyond engineering, and this project succinctly demonstrates why this is a useful endeavour.

This project also demonstrates that the success of a collaborative project such as this one is dependent on access to various knowledge domains. For instance, the success of this project required knowledge of intensive care medicine, and of ventilators in particular. It also required fast track design and rapid prototyping expertise, product documentation and manufacturing knowledge. This is what we typically refer to as technical know-how.

The project could not have been successful without access to aspects of  expertise that we typically denigrate as soft skills. This includes creativity and innovation, two skills without which the idea of a ventilator could not have been brought into reality. It also includes an awareness of what is possible and what is not possible, from both a technical and regulatory viewpoint, which was important in the team deciding to go for an off-patent device as their starting point. Knowing who could do what and at what point was also important. This is network-domain knowledge that is acquired through years of developing, building and expanding professional relationships within and beyond organisations. 

Another aspect which was critical to the project was communication. This communication is both intra and inter-disciplinary , and is both within-organisation and inter-organisational.  Communication skills shared by the team enabled the transfer of knowledge from one disciplinary area to another,  and helped to facilitate a shared understanding of what needed to be done and when. The effectiveness of communication within this project team depended, in part, on the ability and willingness of team members to learn for each other, and their preparedness and ability to teach others (impart) what they knew. This falls under the umbrella of informal learning, and highlights why the ability to engage in self-directed learning is an important attribute in real-life projects.

Lessons to take forward

Can the skills exhibited in this project be taught, as Shuman et al (2005)  asked at the beginning of the 21st century? The answer is certainly yes, but how can they be taught? Certainly, these are skills for practice, and as skills for practice they are best taught through practice. This is the reason why team-based projects are now a standard staple within engineering schools. The real question, however, is how effective are current approaches to team-based projects within engineering schools? Clearly, the design and implementation of such projects is not as easy as taking a walk down the path. However, practice within engineering schools seems to indicate otherwise. Almost as a routine, academics are assigned to design and lead team-based project learning without the requisite training and support. And with regard to the assessment of such activities, how certain are we that the assessment is fit for purpose? Too many times, I have witnessed  assessors adopt a confetti approach to the awarding of project marks. What is the meaning of these marks – certainly no one knows for certain. So if anything, the UCL-Ventura project, alongside many other projects that have been rolled out during this coronavirus crisis, should force us to rethink and re-evaluate the way we do team-based projects. There is a long way to go, and these projects are a useful template to adopt and learn from. 

References

National Academy of Engineering. 2004. “4 Attributes of Engineers in 2020.” The Engineer of 2020: Visions of Engineering in the New Century. Washington, DC: The National Academies Press. doi: 10.17226/10999.

Shuman,L, Besterfield-Sacre, M. and  McGourty ,J. (2005). The ABET Professional Skills – Can They be Taught? Can They Be Assessed? The Journal of Engineering Education, Vol. 94, No. 1 

Abdulwahed, M., Balid, W., Hasna, M. O., & Pokharel, S. (2013). Skills of engineers in knowledge based economies: A comprehensive literature review, and model development. In Proceedings of 2013 IEEE International Conference on Teaching, Assessment and Learning for Engineering (TALE) (pp. 759-765). IEEE.

Interdisciplinary Engineering Education: Difficult, but not Impossible

Interdisciplinarity is now all the buzz within engineering schools. First, it was the research funding bodies demanding interdisciplinary research. Now it is industry, governments and engineering professional institutions demanding interdisciplinary education. Interdisciplinary research is hugely challenging, not least because the current university system remains clustered around individual disciplines, and mono-disciplinarity remains the modus operandi in day-to-day academic practice.  Interdisciplinary engineering education raises the challenges faced by engineering schools even further.

There are two main reasons for this state of affairs. The first reason is this: academic training and support structures designed to prepare engineering academics for 21st century higher education practices remain in short supply. The second reason is the prevailing belief that academics do not really need any pedagogic training at all.

The purpose of this blog piece is two-fold. First, it is to answer the question from the individual engineering academic: “What is interdisciplinary education, and how can I get started?” Second, it is to answer the question from directors of education: “How do we develop a truly interdisciplinary engineering curriculum?”

Why engineering education has to become interdisciplinary?

Engineers routinely deal with interdisciplinarity in their practice. For instance, the design of an everyday product like a motor vehicle requires the integration of knowledge and skills from disparate disciplines such as mechanical, electronic and computer engineering, battery technology and energy systems, environmental and sustainability engineering, and ergonomics. As Meyers and Ernst (1995) observed over thirty years ago, engineers have had to become interdisciplinary because their job requires it. Hence, for engineering, interdisciplinarity is not, and has never been an option. It is only that engineering education has so far managed to get away without incorporating interdisciplinarity for so long. However, as so many engineering education researchers have observed, this head-in-the-sand approach is no longer tenable in the 21st century.

As many writers have pointed out, 21st-century engineers have to adopt interdisciplinary approaches to deal with the critical challenges that they have to resolve. It is no longer possible for any one discipline to address all the problems, issues, or questions associated with these challenges single-handedly. Mahmud (2018) attributes the complexity of such challenges partly to the convergence of distinct technologies originating from different sectors, such as the energy, transportation, health and telecommunication sectors. According to Mahmud, this convergence has given rise to increasingly interdependent, complex socio-technical systems that demand interdisciplinary expertise.  Engineering education has to step up and impart interdisciplinary skills to its graduates.

What is interdisciplinary education?

Currently, disciplines educate and equip students with the disciplinary knowledge and skills they need to address and solve problems in their specific discipline-oriented areas of expertise. For instance, following graduation, a telecom engineering graduate  would concentrate on resolving telecom problems; a mechanical engineer on solving mechanical engineering problem, and a chemical engineer on solving chemical engineering problems. If a problem simultaneously requires the resolution of mechanical, chemical and telecom problems, a standard approach would be to bring together individuals with these skills to form a multidisciplinary team.  In this case, the chemical engineer would focus on the chemical engineering aspects of the problem; the mechanical engineer would focus on the mechanical aspects, whilst the telecom engineer would focus on issues relating to telecommunications. This is the standard multidisciplinary approach.

For complex, interdependent systems, however, the team would need to integrate their disciplinary skills, knowledge, experience and insights, and synthesise this into a shared body of knowledge that enables them to gain a more indepth understanding of the problem at hand. This process requires the individual team members to learn from each other, to shed off discipline-based misconceptions, and to develop a new understanding and awareness of the problem at hand based on a synthesis of knowledge from the individual disciplines. As  Kuldell (2007)  suggests, this process requires the whole team to fully embrace this newly synthesised body of knowledge as the basis for understanding and tackling the problem, together with all the challenges and uncertainties inherent in this new body of knowledge. This is in contrast to maintaining multidisciplinary viewpoints that persist in viewing the subject as an amalgam of their individual disciplinary knowledge. This approach is termed interdisciplinarity, and is best defined as follows:

 Interdisciplinarity is a process of answering a question, solving a problem, or addressing a topic that is too broad or complex to be dealt with adequately by a single discipline or profession… [It] draws upon disciplinary perspectives and integrates their insights through construction of a more comprehensive perspective (Newell, 1998; p.393-4).

So what then is interdisciplinary education? It is an educational process whereby learners draw from two or more disciplines to advance their understanding of a subject or a problem beyond what is achievable from any single discipline (Mahmud, 2018). In so doing, the learners integrate and develop information, concepts, methodologies and procedures from  the individual disciplines to gain new knowledge, understanding and skills so as to be able to explain or solve problems (Holley, 2017). This form of learning is necessarily active, self-directed learning.

What factors should you consider when implementing an interdisciplinary curriculum?

The first thing to remember when planning an interdisciplinary engineering curriculum is this:  University teaching is organised around the disciplines, and disciplines have different ways of disseminating, organising and thinking about the knowledge that underpins them. Because of this, individual disciplines have different approaches to teaching, and this applies to individual disciplines within engineering as well. Entwistle (2009) sums up this dilemma as follows:

There is a logic that holds together the various strands of a discipline or topic area, and there is a logical connection between the intellectual demands of the subject and how best to teach it.

The outcome of this is that academic staff engaging in interdisciplinary teaching are susceptible to reverting to their normal discipline-based teaching. Hence, if close attention is not paid to the process of designing and implementing the interdisciplinary curriculum, students on the receiving end of the curriculum will perceive their learning as a disparate, disjointed set of modules drawn from different disciplines (Foley, 2016). At a minimum, therefore, to be successful, an interdisciplinary curriculum should endeavour to create a cohesive, integrated approach that both staff and students can invest in (Kuldell, 2007).

A second consideration is that most engineering programmes are offered at undergraduate level. At this level, students mostly view themselves through the lens of their individual disciplines. They have come to university to specialise in their particular discipline, and anything other than their discipline is likely to demotivate them. Hence, the primary pursuit of students at this level is the mastery of their discipline’s approach to problem solving. How then can one can one resolve this dilemma?

Holley (2017) suggests that to be successful, an interdisciplinary curriculum should provide learning environments that allow students and academic staff from different disciplinary backgrounds to engage in scholarly conversations around issues of shared interest and importance, while also exploring connections between their majors and other sources of knowledge and experience. Within the classroom, adopting an overarching topic, theme, or problem can help to establish bridges of shared understanding between the different disciplines. With regard to pedagogy, adopting a research-based, problem solving approach may be the best approach to fostering interdisciplinarity (Kuldell, 2007).

Attention to the development of an interdisciplinary curriculum should  also focus on out-of-class activities. Lattuca et al. (2017) suggest that students should be encouraged to participate in co-curricular activities and experiences that are inherently interdisciplinary. For instance, in their study of students perceptions of interdisciplinary learning,  Lattuca et al. (2017) observed that there was a positive correlation between students perceptions of interdisciplinary learning and their participation in non-engineering clubs and activities, study abroad, and humanitarian engineering projects. This suggests that providing opportunities for students to engage in interdisciplinary activities both within and outside the classroom helps to provide a supportive environment in which students can develop their interdisciplinary skills organically.

Concluding remarks

This overview does suggest that achieving interdisciplinary education is difficult. Whilst this is true, achieving success is not beyond the realms of possibility. What this means is that implementing interdisciplinary education requires commitment and endeavour from both senior management and academic staff. To date, there is no proven cookbook approach to implementing interdisciplinary education within engineering. However, the topic is currently receiving considerable attention from engineering education researchers. This means that increasingly, we are now able to identify evidence-based approaches that can help us in our endeavours to implement interdisciplinarity within engineering education.

REFERENCES

ENTWISTLE, N. 2009. Teaching for understanding at university: Deep approaches and distinctive ways of thinking, Palgrave Macmillan.

FOLEY, G. 2016. Reflections on interdisciplinarity and teaching chemical engineering on an interdisciplinary degree programme in biotechnology. Education for Chemical Engineers, 14, 35-42.

HOLLEY, K. 2017. Interdisciplinary curriculum and learning in higher education. Oxford Research Encyclopedia of Education.

KULDELL, N. 2007. Authentic teaching and learning through synthetic biology. Journal of Biological Engineering, 1, 8.

LATTUCA, L. R., KNIGHT, D. B., RO, H. K. & NOVOSELICH, B. J. 2017. Supporting the development of Engineers’ interdisciplinary competence. Journal of Engineering Education, 106, 71-97.

MAHMUD, M. N. 2018. Interdisciplinary Learning in Engineering Practice: An Exploratory Multi-case Study of Engineering for the Life Sciences Projects. University of Cambridge.

MEYERS, C. W. & ERNST, E. W. 1995. Restructuring Engineering Education: A Focus on Change: Report of an NSF Workshop on Engineering Education, Division of Undergraduate Education, Directorate for Education and Human ….

NEWELL, W. H. 1998. Interdisciplinarity: Essays from the Literature, College Entrance Examination Board.

 

Want to get started on PBL? Some instructional resources

Although problem based learning (PBL) has been around for almost 50 years, following its introduction and development in medical education at McMaster in the late 1960s and early 1970s, it has remained relatively unknown until fairly recently. Putting this into perspective, in the period 2000 – 2010, very few engineering academics had ever heard of PBL – fast forward to today, and PBL has become almost synonymous with the term “engineering education”.

However, despite the ubiquity of PBL within the engineering academic community, it remains a challenge to come across academics who are comfortable in effectively implementing PBL in their own practice. A key reason for this may be the failure of academic development centres to keep pace with the rapid adoption of 21st century-focussed curricula within engineering education, and within higher education in general.  Another contributory factor may be the prevailing, and thoroughly misplaced, belief that academics do not really need any pedagogic training at all.

For the engineering academic needing to get up to speed with PBL-oriented pedagogic practices, it may be a challenge just to have an idea of where to turn to. In this piece, I highlight some of the online resources that an individual can access.

    1. Instructional guide on Problem based Learning: Northern Illinois University, Faculty Development and Instructional Design Center – This is a short 4 page guide that explains what PBL is, how it differs from traditional teaching, and clearly spells out the roles of both the instructors (tutors) and students within a PBL environment.
    2. Introductory Course On PBL In Higher Education – Free Online Course: Aalborg Centre for Problem Based Learning In Engineering Science And Sustainability Under The Auspices Of UNESCO (UCPBL) – A free online course that gives an overview of the PBL process as well as links to pertinent resources.
    3. The Aalborg Experiment: Project Innovation in University Education. This is an evaluation of PBL implementation at Aalborg University carried out in 1994. Although somewhat dated, it gives important insights into the practical issues that need to be addressed if PBL implementation is to be successful.
    4. Book sections on Problem and Project Based Learning: Goodhew, Peter. “Teaching engineering.” The School of Engineering’s Active Learning Lab at The University of Liverpool(2010). In this textbook, which is available for download, Peter Goodhew gives pertinent instructional advice on how one can get started on problem and project based learning. He also provides relevant engineering examples that one can try out.
    5. Problem-Based Learning:Stanford University, Speaking of Teaching Newsletter Archive. This is a short guide on PBL that provides guidance on designing problem sets, structuring PBL classes, and offers advice on assessment design.
    6. The Tutor in Problem Based Learning: A Novice’s Guide: This is a fairly comprehensive guide from McMaster University outlining how you can design and implement PBL. It also provides common problems that arise in PBL implementation and offers suggestions on resolving them.
    7. Revolutions and Re-iterations: An Intellectual History of Problem-based Learning: Virginie Servant PhD Thesis – Who were the “Founding Fathers” of PBL? What were the issues and arguments they had to grapple with? How did PBL come to be the way it is today? If you are grappling with any of these questions, this thesis is your best starting point.

Rethinking the Engineering Mathematics end-of-year Exam

It is no longer enough for higher education to focus just on the transmission of information and the retention of facts. Rather, we now expect students to come out of higher education equipped with a range of high-level skills and abilities such as:

  • critical thinking skills to enable them to handle and interpret concepts, evidence and ideas
  • the ability to think and act as experts
  • innovation and creativity to enable them to produce original insights and valuable knowledge for the benefit of society (Imperial College, 2019).

In addition to adopting learning and teaching techniques that foster the development of these high-level skills, we also need to transform higher education assessment practices as well. Within engineering mathematics, where the end of year exam still predominates, this requires careful selection and design of exam questions to ensure students are assessed for competence in both the basic and high-level mathematical skills. In this piece, I look at two taxonomies that aid the development of such exam questions. These two are the Mathematical Assessment Task Hierarchy (MATH) taxonomy (Smith et al., 1996) and  Galbraith and Haines’ Mechanical-Interpretive-Constructive taxonomy (Galbraith and Haines, 2000).

The MATH taxonomy

The MATH taxonomy groups mathematical skills into three groups, A, B, and C.

Group A skills

Smith et al defined Group A skills as the standard, routine procedures taught to students along with the factual information they have to recall. They further divided this group into three categories:

  • Factual knowledge – the ability to recall previously learned information in the way in which it was given
  • Comprehension – the ability to use standard techniques to solve a problem. This includes the ability to recognise symbols in a formula and to substitute into the formula using information learnt previously.
  • Routine procedures – the ability to use routine procedures to solve a given problem in the same way previously learnt to solve similar problems. This requires students to have worked on similar problems beforehand.

Group B skills

Group B skills focus on the ability to use mathematical information in new ways, for example, applying routine procedures to new situations. These skills fall into two categories:

  • Information transfer – includes the ability to transform mathematical information from one form to another, for example from verbal to numerical (or vice versa), or from algebraic to graphical etc. This category also includes the ability to explain the relationships between component parts of a mathematical problem, the ability to recognise whether or not a particular formula or method can be used in a new context. In addition, this category also includes the ability to explain mathematical processes, including summarising in non-technical terms for non-mathematical audiences.
  • Application in new situations – the ability to choose appropriate methods and information and apply them to new situations. This includes modelling real life situations, extrapolating new procedures to new situations, and proving previously unseen theorems and results.

Group C skills

Group C skills are the skills that enable students to apply previously learned concepts to the analysis and solution of mathematical problems for which no routine procedures have been provided. These skills fall into three categories:

  • Justifying and interpreting – the ability to justify and/or interpret a given result, or a result derived by the student. This includes proving a theorem in order to justify a result, the ability to find errors in reasoning, recognition of unstated assumptions, and recognising the limitations of a model and being able to decide on the appropriateness of a model.
  • Implications, conjectures, and comparisons – the ability to make comparisons, with justifications, in different mathematical contexts, as well as the ability to draw implications and make conjectures, with justification, when given or having found a result.
  • Evaluation – the ability to judge the value of material for a given purpose based on definite criteria. This includes the ability to make judgements, the ability to select for relevance, the ability to argue coherently on the merits, or otherwise, of an algorithm, organisational skills and the ability to rearrange information and draw previously unseen implications from it.

The Galbraith & Haines’ taxonomy

Galbraith and Haines arrived at their taxonomy independently of the Smith et al MATH taxonomy. However, after reviewing both taxonomies they suggested that their taxonomy could be interpreted as a summary of the MATH taxonomy (Galbraith and Haines, 2000).

Like the MATH taxonomy, the Galbraith & Haines taxonomy also has three levels, although they have a different terminology. The three levels are the mechanical, interpretive and constructive levels.

Mechanical skills

These skills refer to the routine use of mathematical procedures as cued by the wording of the question. They are equivalent to Group A skills in the MATH taxonomy.

Interpretive skills

These skills refer to the ability to retrieve and apply conceptual knowledge. They are equivalent to Group B skills in the MATH taxonomy.

Constructive Skills

These skills refer to the ability to arrive at a solution or conclusion using a range of mechanical and interpretive tasks without the necessary guidance for doing so. This essentially involves the construction of a solution rather than simply selecting between given alternatives. These skills are equivalent to the Group C skills on the MATH taxonomy.

Concluding remarks

Most mathematics exams only assess Group A skills, with only a few assessing Group B skills as well, and virtually none assessing Group C skills (Brown, 2010). However, Pounteny et al (2002)  suggest that we should be teaching undergraduate students up to the level of Group C as this is the skill level at which students are able to demonstrate “understanding to the point of justifying and explaining knowledge, being able to evaluate actions, and the development of new knowledge”. These, according to Pounteny et al, are the skills that we associate with being a mathematician and a problem solver. Moreover, it is clear that these are the skills expected of higher education graduates in the 21st century. Hence, to ensure that the end-of-year exam remains relevant in the 21st century,  we have to ensure that a significant proportion of the exam questions is  pitched at the Group C / Constructive level.

References

BROWN, R. G. 2010. Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested? Educational Studies in Mathematics, 73, 181-203.

GALBRAITH, P. & HAINES, C. 2000. Conceptual mis (understandings) of beginning undergraduates. International Journal of Mathematical Education in Science and Technology, 31, 651-678.

IMPERIAL COLLEGE. 2019. Project Xeper -The future of engineering teaching [Online]. Imperial College,.  [Accessed 28/07/2019 2019].

POUNTNEY, D., LEINBACH, C. & ETCHELLS, T. 2002. The issue of appropriate assessment in the presence of a CAS. International Journal of Mathematical Education in Science and Technology, 33, 15-36.

SMITH, G., WOOD, L., COUPLAND, M., STEPHENSON, B., CRAWFORD, K. & BALL, G. 1996. Constructing mathematical examinations to assess a range of knowledge and skills. International Journal of Mathematical Education in Science and Technology, 27, 65-77.

 

Adoption of Computational Modelling in Introductory Engineering Course Modules: A Case Study

Abstract for paper presented at the 8th Research in Engineering Education Symposium (REES 2019) held in Cape Town, South Africa, from 10–12 July 2019. The extended abstract can be downloaded HERE:

CONTEXT

Traditionally, mathematics and engineering principles course modules constitute the bulk of undergraduate teaching in the first and second year of the engineering curriculum. These introductory course modules play a critical role in the study of engineering by laying the foundational engineering and mathematics principles that underpin the study of more advanced engineering modules in the latter stages of the undergraduate programme. However, students often perceive these foundational modules as being disconnected from the “real” engineering that they came to study, and this often leads to heightened student dissatisfaction and disengagement from further engineering studies. To alleviate this situation, most engineering education researchers and educators have advocated the adoption of computational modelling within these foundational engineering course modules.

PURPOSE

MATLAB has been an integral part of teaching in first and second year engineering mathematics at University College London since 2013. This has improved student engagement with mathematics and raised their awareness of its relevance within their chosen engineering disciplines, and subsequently led to the adoption of MATLAB in other introductory course modules.. However, this adoption has not been uniform.  In the study that I report in this paper, I set out to establish the reasons why MATLAB adoption patterns are so variable amongst first and second year introductory engineering course modules. Specifically, I sought to establish the pedagogic and learning environment structural features that facilitate or impede the successful adoption of MATLAB as a teaching tool within the early-stage foundational engineering course modules.

APPROACH

To address these research questions, I adopted a multi-dimensional case study approach that incorporated interviews with students and lecturers in the first and second year of undergraduate engineering across five engineering departments, peer observation of teaching, evaluation of student performance and feedback, and interviews with programme leaders and directors of education. To facilitate this analysis, I framed the study as an innovation diffusion case study. This enabled me to evaluate the data and to frame the outcomes using a variety of innovation diffusion models that have been applied to the study of curriculum change in various educational establishments.

RESULTS

Whilst the study is still very much a work-in-progress, key findings that are emerging are largely consistent with emerging views of innovative learning diffusion within educational practices. Specifically, my findings point to the need for effective learning support mechanisms that incorporate both top-down and bottom-up approaches to driving innovation. The study also highlights the detrimental effects of institutional focus on disciplinary research on the adoption of innovation in learning and teaching practice. In addition, the study also highlights the need to open up the undergraduate education landscape to emerging educational practitioners such as learning technologists and education administrators.

CONCLUSIONS

The teaching and delivery of first and second year undergraduate engineering course modules can be substantially improved by incorporating computational modelling, visualisation and analysis techniques. However, this adoption process is not straightforward, and requires cultural and structural changes within engineering schools if it is to be effective. For this to happen, institutional leaders have to demonstrate a willingness to go beyond rhetoric by actively advocating and supporting the adoption of innovative practices within the undergraduate engineering curriculum.

KEYWORDS

Computational modelling and analysis, visualisation, undergraduate engineering education

Mathematical Resilience: The Holy Grail for Engineering Mathematics

Mathematics can pose significant challenges and obstacles to students who are in the early phases of their studies at university (Hernandez‐Martinez and Williams, 2013). This also includes engineering students, even though they, along with the rest of the engineering community, believe that the study of mathematics is indispensable to the study and practice of engineering (Sazhin, 1998). Students find the transition to university mathematics difficult for a number of reasons. One of these reasons is the lack of mathematical resilience, the subject of my discussion today. For this, I shall be relying on the work of Sue Johnston-Wilder and Clare Lee, who have popularized the concept of mathematical resilience within pre-university mathematics education.

Mathematical resilience

An individual is said to be resilient if they achieve “good outcomes in spite of serious threats to adaptation or development”(Masten, 2001). Previously, educators and researchers believed that resilience was an attribute that only a few people possessed. However, Masten’s studies have since debunked this notion. Instead, her studies posit that, far from being exclusive, resilience is an ordinary trait that any individual can acquire. This new understanding renders invalid prevailing deficit models of intellectual ability. Indeed, using this new understanding, Yeager and Dweck (2012) have shown that the resilience of students improves when they are redirected to see intellectual ability as “something that can be developed over time with effort, good strategies, and help from others.”

Johnston-Wilder and Lee use the construct of mathematical resilience to describe “a learner’s stance towards mathematics that enables pupils to continue learning despite finding setbacks and challenges in their mathematical learning journey” (Johnston-Wilder and Lee, 2010). Often, learning mathematics is associated with negative emotions, such as avoidance, anxiety and helplessness (Lee and Johnston-Wilder, 2017). These negative emotions can be exacerbated by poor mathematics teaching methods, enduring cultural beliefs that mathematics is only for the gifted few, and fixed mindset beliefs that if someone is not good at mathematics, then there is no way they can improve their mathematical ability, even if there is good teaching and support (Lee and Johnston-Wilder, 2017). Mathematical resilience challenges these negative notions, and seeks to engender within the minds of learners the knowledge that that they can grow their mathematical abilities (Lee and Johnston-Wilder, 2017).

Characteristics of mathematically resilient students

There are four characteristics for students with mathematical resilience. These are growth mindset, personal value of mathematics, knowing that mathematics requires struggle and knowing how to recruit support in pursuing (Lee and Johnston-Wilder, 2017).

Growth mindset (Yeager and Dweck, 2012): The notion of growth mindset suggests that the brain is malleable. Consequently, students with a growth mindset believe that their mathematical abilities improve with practice, persistence and support from others (this includes peers and academic staff).

Value: Mathematically resilient students believe that mathematics is a valuable subject and is worth studying. Such values can be fostered within engineering by making explicit the connections between mathematics and engineering theory and practice.

An understanding of how to work at mathematics: Mathematically resilient students are aware that one has to persevere if they are to make progress in learning mathematics. They are aware that everyone experiences difficulties and challenges when learning mathematics; that mistakes are part of the learning process, and that one has to persevere and learn not to succumb to the negative emotions that are a part of learning something new.

Knowing how to gain support: Mathematically resilient students are aware that learning mathematics can be challenging, and that sometimes they need to seek support in order to get ahead. They are also aware of the support structures for mathematics within and outside their university. They are also aware, and adept, at constructively working and studying with each other.

Lessons for mathematics educators

Teaching mathematics is not just about delivering subject content. It is also about developing a supportive, inclusive, collaborative learning environment that challenges and encourages students to do the best they can. Indeed, achieving this is the holy grail of learning and teaching in engineering mathematics.

References

HERNANDEZ‐MARTINEZ, P. & WILLIAMS, J. 2013. Against the odds: resilience in mathematics students in transition. British Educational Research Journal, 39, 15.

JOHNSTON-WILDER, S. & LEE, C. 2010. Mathematical Resilience. Mathematics Teaching, 218, 38-41.

LEE, C. & JOHNSTON-WILDER, S. 2017. Chapter 10 – The Construct of Mathematical Resilience. In: XOLOCOTZIN ELIGIO, U. (ed.) Understanding Emotions in Mathematical Thinking and Learning. San Diego: Academic Press.

MASTEN, A. S. 2001. Ordinary magic: Resilience processes in development. American psychologist, 56, 227.

SAZHIN, S. 1998. Teaching mathematics to engineering students. International Journal of Engineering Education, 14, 145-152.

YEAGER, D. S. & DWECK, C. S. 2012. Mindsets That Promote Resilience: When Students Believe That Personal Characteristics Can Be Developed. Educational Psychologist, 47, 302-314.