Parakram Pyakurel, Sarah Peers, Bertie Knight and James Newby write about how NMITE's approach to maths teaching help widen access to engineering education.
Introduction
Enabling more people to participate in engineering and technology is not just a nice-to-have, but a necessity, especially if we are aiming to create “new engineers” (Goldberg, Somerville, & Whitney, 2014). Removing barriers to engineering and technology education without compromising the quality of engineering graduates is an imperative if we are to meet the demands for the engineering workforce, and tackle the global problems facing us. Likewise, there exists a major gender gap in engineering and technology sectors with significantly fewer women choosing STEM (Science, Technology, Engineering and Maths) education. It has long been recognised that different and innovative approaches are needed to reduce gender disparity in engineering education, and in turn these approaches can also support wider diversity.
We could start by noting that school mathematics and physics can be barriers to engineering education. In the UK, the Institute of Physics have long identified some of the educational and societal issues that lead to too few young women in the UK taking up physics at A-Levels, which start in early years education. AS/A-level courses in mathematics and further mathematics have gender imbalances. The lack of mathematics and science teachers in the UK leads to many secondary schools in disadvantaged areas having non-mathematicians and scientists teaching GCSE level mathematics and science, arguably delivering a low-quality experience to school children at Key Stages 2 and 3. This learning experience impacts negatively on children’s “science capital” (Louise Archer, IOE) and their identity as possible future engineers and technologists.
Even students with vocational technical backgrounds (e.g. engineering and technology T-levels, BTEC etc., from the UK’s UTCs programmes, where practical skills are prioritised over theoretical knowledge) can also suffer from difficulties in the transition into professional engineering programmes. In the UK (and in the US), there is a long history, pre-dating the introduction of GCSEs, BTECs, and even “modern maths”, of complaints by engineering academics about the levels of maths skills in their students. It is about time that we look closely at not only entry requirements but also approaches to delivery.
An obvious way to reduce barriers is to remove the standard requirement for Level 3 (e.g. A-Levels in the UK) mathematics and physics to enrol in engineering programmes, and to reassess assumptions of expected knowledge of maths and physics, at least in the early stages of engineering curricula. At NMITE we deliberately chose to remove the normal A Level maths entry requirement as a challenge to the assumption that capability in maths must be credentialed at the point of admission. Our experience at NMITE shows that there are many young people who have a passion for engineering but do not meet the entry requirements of maths and physics to enrol in engineering programmes at conventional HEIs, so these entry requirements are acting as a filter of talent, not an enabler, and misrepresenting the true potential of applicants. Industry has been advocating for some time opening up engineering programmes to those who have not studied maths and physics; for example see the views of the Head of Talent at Jaguar Landrover in a Tata report from over 8 years ago (Tata, 2017). We argue that maths and physics should be embedded in engineering programmes in such a way that the usual entry requirements of maths and physics can be removed.
Maths approach
Approaches such as “just-in-time” maths delivery, dedicated maths and basic science support centres for personalised learning, and effective personal tutoring systems can be capitalised to help students who do not meet maths and physics entry requirements at conventional HEIs join and complete engineering degree programmes. Personalisation of teaching and learning in general would also support students with cognitive or neuro diversities.
Broader discussions may be needed to revisit mathematics contents and levels of skills (Kent & Noss, 2002) in engineering related curricula, and the required or anticipated mathematical skills for engineers. Anecdotally, many practicing engineers report that they do not encounter most of the maths they learn at the university in their workplaces. On the other hand, there is an argument that often professional engineers may not always recognise when they are applying mathematical thinking.
Identifying the “basic” mathematical prerequisites needed to progress through education and training should be aligned to requirements for practicing engineers. Engineering students with greater mathematical interests and abilities can and should be supported to pursue higher levels of competencies, i.e. a wider range of topics and a greater ability to mathematise. This personalised maths approach would recognise that while minimum threshold of mathematical knowledge is anticipated for every engineer, there can be wide variation in how practising engineers might employ mathematics. It may be helpful to differentiate between different types of “maths for engineers”. One way is to consider topics and levels of difficulty of techniques and processes, for example being able to work with calculus, from easier: knowing how to write velocity as a rate of change, to harder: to being able to solve complex differential equations. Another is to identify different maths thinking skills such as being able to read mathematics, apply procedures, connecting ideas, and translating real problems into mathematical models or mathematising (De Lange in Goold & Devitt, 2012). Recognition by engineering academics of the need to allow for this variety of mathematical competence among engineers and technologists may be a good starting point to enable richer and more fruitful discussions.
Not only can we argue (and at NMITE we do!) that there is a need to revisit what mathematical content is taught in engineering curricula, but we also argue for an approach to teaching and learning that is more meaningful and accessible for students and relevant to engineering practice. Namely, in a way that departs from teaching mathematics that has been described before as ‘narrow’ in which students are often shown how to reproduce step-by-step methods for solving abstract problems, in order to garner ‘the single correct answer’, and which can leave worrying gaps in technical understanding (Jo Boaler; David Tall). Instead, we could adopt a constructivist approach to learning, where key underpinnings to its delivery include (Knight, Pyakurel, & Souppez, 2024):
Open-ended – Emphasis on students demonstrating how they rationalise and solve problems in their own unique way, for which several solutions and approaches are valid, and peer-to-peer collaboration is encouraged
Concept-led – Emphasis on students learning mathematics in its qualitative/physical interpretation, over being able to reproduce abstract steps/techniques
Engineering-led – Mathematics not typically being taught in its abstract form, but instead being taught in context with engineering concepts and applications
Or in other words, we should focus on authentic mathematics for engineering and technology.
While factors such as longstanding societal norms contribute to the existing gender imbalance in engineering across the world, lack of awareness among prospective students regarding the diverse engineering roles and perceptions of engineering further aggravates the imbalance. The image of engineering being purely about engines, spanners and greasy rags is particularly noticeable in the UK and impacts on more than the gender of students who aspire to engineering. The roles that engineering play in addressing global and local societal challenges such as pollution control, enhancing access to clean energy, deployment of technological solutions to improve quality of life and so on, are generally not promoted sufficiently enough to attract students of different interests. There are examples of programmes that have made these roles much more visible from the outset and successfully disrupted expectations of who takes up engineering (Dartmouth College, 2016). Embedding liberal studies in engineering could improve the understanding of how engineering interacts with society and attract wider pools of students, including women and men who do not identify as “techies”. We also need to address the sexism, classicism, and stereotyping that can occur in engineering programmes, influencing progression and success, as evidenced by work in the US and in the UK (Seron, Silbey, & Rubineau, 2015; Archer, 2023).
If, as we so often say we do, we want more engineers and a new type of engineer, we need not only a wider pool to fish for engineering talent, but we also need to rethink the pre-requisites for budding engineers and technologists. Those who worry that not demanding maths at entry will water down the quality of engineering graduates, would do well to note that for many years it has been known that there is little to no correlation between good maths A-Levels and final year degree classification. A final little icing on the cake: preliminary data analysis indicates there is little disparity in attainment between students at NMITE with and without an A-level in mathematics by year 2 of our programme. We believe that this is evidence to counter the view that selectivity always equates to quality. A Level maths may not be a reliable predictor of future success in engineering education and to continue to require it at pint of admission simply prioritises previous opportunity over future potential. Engineering education must adapt and change to deliver authentic engineering skills and knowledge.
References
Archer, L. D. (2023). ASPIRES3: Main Report. UCL. Retrieved from https://www.ucl.ac.uk/.
Dartmouth College. (2016, Jun 16). Dartmouth Makes History by Graduating a Majority-Female Engineering Class. Retrieved from Dartmouth Engineering News: https://engineering.dartmouth.edu/news/dartmouth-makes-history-by-graduating-a-majority-female-engineering-class
Goldberg, D. E., Somerville, M., & Whitney, C. (2014). A Whole New Engineer: The Coming Revolution in Engineering Education. Threejoy Associates.
Goold, E., & Devitt, F. (2012). The role of mathematics In engineering practice and in the formation of engineers. Proceedings of the 40th SEFI Annual Conference 2012 - Engineering Education 2020: Meet the Future. Thessaloniki: SEFI. Retrieved from https://www.researchgate.net/
Kent, P., & Noss, R. (2002). The mathematical components of engineering expertise: the relationship between doing and understanding mathematics. Engineering Education 2002: Professional Engineering Scenarios (Ref. No. 2002/056), IEE Volume: 2. doi:DOI: 10.1049/ic:20020120
Seron, C., Silbey, S., & Rubineau, B. (2015). Persistence Is Cultural: Professional Socialization and the Reproduction of Sex Segregation. Work and Occupations, 43(2), 178-214. doi:https://doi.org/10.1177/0730888415618728
Tata. (2017). Building the right skills.