Introducing group projects in the teaching of engineering

MSOR Connections Vol 10 No 3 Autumn Term 2010

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Mathematics modules for engineering students are often poorly attended and results correspondingly poor. We report on two initiatives, the first with Sports Technology and the second with Materials Engineering students, that have used or will use assessed small group projects to motivate and engage students. The first of these has shown positive gains in attendance and performance. The second, which is planned for the coming academic year, will use developmental research to document outcomes and promote a developmental process. We describe the initiatives briefly and what we learn, or expect to learn from them.

Introduction

The Mathematics Education Centre at Loughborough University oversees the development and delivery of the teaching of mathematics to the majority of engineering students at Loughborough University. In 2003-4 a new initiative was introduced in the teaching of mathematics to students of Sports Technology. This included the introduction of small group projects. There was much success associated with the initiative and there has been a marked and sustained improvement in attendance, engagement and results over the intervening years. However, until very recently, and for a variety of reasons, this approach had not been used with other student groups. This paper will report on the work with Sports Technology students. It will then describe the implementation of a similar initiative with Materials Engineering students. Finally the paper will report on the research project which has commenced to research the work with Materials Engineering students.

Group projects with Sports Technology students

Description of initiative

Prior to 2003-4, there was poor attendance by Sports Technology students at mathematics classes and a high failure rate in mathematics. The reasons were varied. Some did not see the relevance of mathematics to their course and therefore were not motivated to study the mathematics module. Others found the transition from school to university mathematics difficult. During 2003-4 group projects were introduced. The ability to function as part of a team is a crucial skill for engineers and the introduction of assessed group projects allows students to learn the skill of teamwork. Moreover, group work provides the chance for students to learn from each other through discussion. MacBean et al. [1] provide an overview of the advantages and disadvantages of introducing group work in undergraduate mathematics. Moreover the group projects centre on applications of mathematics in sport. It has been noted

Acknowledgements: We are grateful to Professor Tony Croft of the Mathematics Education Centre for his contribution to the work of devising projects for the ESUM project and to the ESUM advisory

group for their input to the design of the activities and the research. We acknowledge with gratitude the funding from the HE STEM programme and the support of the RAEng for the ESUM project.

Barbara JaworskiMathematics Education CentreLoughborough [email protected]

Carol Robinson and Barbara Jaworski

Introducing group projects in the teaching of engineering mathematics

Carol RobinsonMathematics Education CentreLoughborough [email protected]


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by Yates [2] that a sufficient supply of discipline related problems is one of the factors leading to success in teaching mathematics to non-specialists.

The students undertake two group projects, one in each semester in their first year, and each is worth 10% of the 20 credit mathematics module. Typically the students work in groups of three and can choose from a selection of projects. As the mathematics entry requirement for the course is GCSE grade A, this has to be borne in mind in the setting of the projects. Typically about 40 students are registered on the module each year.

Examples of the projects include mathematical models which may be used to calculate the lane starting positions for the 200m sprint, on tracks of varying shape, models which are used to predict an approximate solution for the trajectory of a golf drive, where both lift and drag are taken into account, and a model to enable calculation of parachute sizes to ensure a safe landing. Further details are available in Robinson [3] and examples of students’ posters describing their findings are in Figs 1, 2 and 3.

Outcomes of the initiative

As stated previously, attendance had been an area of concern. In 2002-3, the average tutorial attendance was 21%, with zero attendance in six of the eleven weeks in semester 2. Since then average attendance, over the intervening years, has been 75%.

Fig 3 – Example of students’ poster for parachuting project

Fig 1 – Example of students’ poster for 200m lane stagger project

Fig 2 – Example of students’ poster for golf drive project

Introducing group projects in the teaching of engineering mathematics – Carol Robinson and Barbara Jaworski


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Pass rates have also seen significant improvement. The percentage of students passing the module, at first attempt, has increased from 55% in 2002-3 to an average of 90% in the subsequent seven years.

Finally we have noted an increase in motivation amongst the student group. It is not easy to measure directly the motivation levels of students. Attendance, standard of work and student feedback can all be used as indicators. The increased levels of attendance have been noted. It has also been found that the students work hard on the sports based projects and submit work of a high standard, as is evidenced by Figs 1, 2 and 3. Moreover, feedback obtained via the University’s standard module feedback questionnaire has given consistently high scores, indicating high levels of satisfaction with the module.

Care must be exercised when noting the very positive outcomes of the initiative as we are not directly comparing like with like. In addition to the introduction of the group work described herein, a computer algebra package, Matlab, was introduced. Moreover students in previous years had been taught alongside other engineering students in a class of about 80 students and changes were introduced in the syllabus and associated assessment. Nevertheless in a research study [4] undertaken in the first year of implementation, group projects were particularly highlighted as being useful in getting students engaged with the material – they did not wish to let down other members of the group.

Implementation considerations

For other practitioners wishing to introduce a similar initiative, there are many issues to consider. However one of the most important of these is the time required to devise projects, particularly those in the context of the students’ discipline. One way that this has been successfully addressed is to involve final year project students and summer intern students in devising projects. There is an added bonus in that these students themselves benefit from their involvement in the setting of assessment tasks for first year students. However time is still required to supervise and direct these students.

Introducing group projects to Materials Engineering students

The ESUM project

Earlier this year a decision was made to take forward and enhance the above initiative but this time with Materials Engineering students. We are aware that engineering students’ engagement with mathematics is often of a rather instrumental nature – rule following without deeper conceptual understanding. We are endeavouring to enhance participation and understanding of engineering students in mathematics, through inquiry-based group engagement with mathematical software, GeoGebra, and to study outcomes. Students in Materials Engineering have a wide

variation in prior qualifications – some are registered for B.Eng or M.Eng degrees and others for B.Sc degrees – which makes teaching much more difficult. The proposed activity in groups and with software should, for example, help

students at all levels to be motivated to engage with and understand mathematics through collaborative inquiry;

students with A-level to have a chance to learn new skills and therefore be not so easily bored;

all students to become better prepared for the workplace with group-working skills and experience of using software packages.

Learning from the previous work, this time we employed a summer intern who had recently completed a B.Sc in Mathematics. He studied first year modules in Materials Engineering and made notes of the areas in which mathematics featured. He then used this to devise projects involving, for example, curve fitting with application to oscillating strings or radioactive decay. This work has resulted in three variants on a project task for students.

Students will work in groups of four on their allocated task, which requires an inquiry approach to tackling the mathematics [5], and produce a group report for assessment. One other group will comment on the work reported and students will be expected to write a response to their peers’ comments. Members of any one group will assess each other’s contribution to the project through a Web Peer Assessment (WebPA) online system (http://webpaproject.lboro.ac.uk/) linked to the virtual learning environment used in the university. The demands of assessed collaborative inquiry are intended to engage and motivate students, but we also recognise that the organisational demands and commitment required may be especially demanding for some students. We shall be monitoring student engagement very closely as part of the proposed research into this activity.

One major difference between the Sports Technology and Materials Engineering initiatives is that of the research focus. In the earlier study a final year project student undertook evaluation of the initiative. With the Materials Engineering students, funding has been secured from the HE STEM programme, via the Royal Academy of Engineering and the MSOR Network. The project is known as ESUM - Engineering Students Understanding Mathematics: an innovative teaching approach with integrated research. The group work described is just one part of this innovation. A research officer has been appointed and will enable us to document changes arising from the initiative. Through rigorous study we aim to gain insights into processes and issues which can guide further design and promote more effective practice. The design and its interpretation will be fully documented, as will outcomes for students and issues arising.

The proposed research is developmental in that as well as charting the developmental process it is expected also to contribute to the development taking place. This means

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that we aim not only to design, engage with and report on an innovative process of teaching and assessment, but also to promote an innovative mode of thinking about developing teaching for the benefit of students that includes the teacher as a researcher working closely with more traditional researchers. We will be extending models that are well documented at pre-HE levels, but not yet widely used in HE [5, 6]

We trust that benefits to STEM will include improved engagement and motivation through group mathematical problem solving; improved progression and retention; modernisation of the engineering mathematics curriculum which will exploit emerging technology. We recognise that there will be many issues that will arise both for the participating students and those teaching the module. We will report on these as the project progresses.

References

MacBean, J., Graham, T. and Sangwin, Chris (2001) Guidelines for Introducing Group Work in Undergraduate Mathematics. Learning and Teaching in Mathematics, Statistics and Operational Research, ISSN 1476-1378. Available via: http://www.mathstore.ac.uk/?q=node/62 [Accessed 13 October 2010].

Yates, P. (2003) Teaching Mathematics to First Year Undergraduate Chemists in the Context of their

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Discipline. In Maths for Engineering and Science LTSN MathsTEAM booklet ISBN 07044 2374X. Available via: http://www.mathstore.ac.uk/?q=node/60 [Accessed 13 October 2010].

Robinson, C.L. (2007) Motivating students to learn mathematics using applications from the world of sport. Proceedings of the IMA Conference, Mathematics in Sport, 24-26 June 2007, pp 174-179. The Lowry, Salford Quays, Editors Percy, D., Scarf, P. and & Robinson, C., Institute of Mathematics and its Applications.

Robinson, C.L. (2004) New Initiatives in Teaching Mathematics to Students of Sports Technology, Proceedings of the 12th SEFI Maths Working Group Seminar, Vienna University of Technology pp127 – 134.

Jaworski B. (2006). Theory and practice in mathematics teaching development: Critical inquiry as a mode of learning in teaching. Journal of Mathematics Teacher Education, 9, 187-211.

Jaworski, B. (2008) Building and sustaining inquiry communities in mathematics teaching development: Teachers and didacticians in collaboration. In K. Krainer & T. Wood (Eds.), Participants in mathematics teacher education: Individuals, teams, communities and networks. Volume 3 of the International Handbook of Mathematics Teacher Education (pp. 335-361). The Netherlands: Sense Publishers.

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Introducing group projects in the teaching of engineering