Systematic Integration of MATLAB into Undergraduate Mathematics Teaching: Summary of Paper Presented at EDUCON 2016

How to cite this study:

Nyamapfene A & Lynch S, Systematic integration of MATLAB into undergraduate mathematics teaching: Preliminary lessons from two UK institutions, IEEE EDUCON, Abu Dhabi, UAE (2016).

Introduction

Computer algebra systems (CAS) are software systems designed for the symbolic manipulation of mathematical objects such as polynomials, integrals and equations [1]. This includes software systems like MATLAB, Mathematica and Maple.  CASs are now routinely integrated into modules in mathematics in most universities [2][3]. Several reasons have been suggested for this high level of CAS use in university level mathematics. This includes perceptions that [2][4]:

  • CASs help to develop mathematical thinking, concepts and skills
  • CASs offer a flexible environment for students to easily explore and experiment with mathematical concepts
  • CASs enable students to visualize mathematical concepts through such features as graph plotting and animation of mathematical functions
  • Pedagogically, CASs help to promote greater conceptual understanding of mathematics by taking away the burden of tedious calculations.

Research Issues

However, despite the relatively high penetration of CASs into university-level education, and their perceived value, it appears that there is significant underutilisation of these technologies [5]. This means that most of the expected benefits of these CASs are not being realised. Therefore, if any benefits are to be realised from investments in CASs in higher education, it is necessary to find out how best to implement CAS use into university level education.

One suggestion has been that most institutions don’t pay proper attention to curriculum design when adopting CASs. Tonkes et al. [6] suggest that  the main reason for this underutilization is that CASs are often added into the existing teaching without proper curriculum design. So a critical question to ask may be: What curriculum design considerations should you make if your CAS implementation is to be successful. We decided to look at two institutions that have integrated MATLAB into their Maths teaching with some measure of success. These two institutions are Manchester Metropolitan University (MMU) and University College London (UCL).   At MMU, MATLAB has been routinely taught as an integral part of their Mathematics undergraduate programmes, and at UCL, the teaching of MATLAB alongside Mathematics has been implemented in to the undergraduate Engineering curriculum.

Our study was guided by these research questions:

  • What are the stated objectives for CAS integration in each of the two institutions?
  • What is the context around the CAS implementation in each institution?
  • What was each institution’s approach to curriculum design during the CAS implementation?
  • What lessons, if any, did the institutions learn from the implementation?

Findings

At UCL the motivation for incorporating MATLAB into Engineering Mathematics was driven by the perception that students often fail to apply the mathematics that they have learnt to the analysis and design of engineering systems. It was hoped that MATLAB would enable students to directly model and solve engineering–related problems within the mathematics course, thereby enabling them to appreciate the role played by mathematics in the study of their disciplines. At Manchester Metropolitan, the main motivation was to improve the employability skills of their Mathematics graduates. It was felt that equipping Mathematics students with MATLAB skills would enable them to understand and appreciate the use of Mathematics in industry. This has turned out to be true, as the employment of their students within 6 months of graduating is now higher than the UK average.

At the time of MATLAB integration at both institutions, there were strong feelings that the then curriculum needed to change. This feeling was shared by both academics and academic leaders. Consequently, in both institutions, MATLAB integration was implemented as part of a wider programme redesign. Teams of academics contributed to the redesign of the entire programmes, and academics collaborated together to design individual lectures, workshop sessions and even the development of course material and assessment questions.

At both institutions, senior management were committed to the programme changes, and resources were made available to support both academics and students. For instance, at UCL a team of postgraduate students was assembled to provide students with out of class support in Mathematics and Matlab. Within the departments, additional staff were deployed to assist lecturers with leading workshop sessions, and with coursework marking.

Recommendations

Based on this study of MATLAB integration at Manchester Metropolitan and UCL, it appears that the following steps can help to improve the chances of a successful MATLAB integration:

  1. Implement MATLAB integration as part of a programme-wide redesign
  2. Ensure students see the benefits of MATLAB
  3. Ensure academics see the need to teach MATLAB
  4. Embed MATLAB into the institutional Maths culture
  5. Provide adequate institutional support for both academics and students

References

  1. Thomson, A. Santaella, and M. Boulat, “Maple and other CAS (Computer Algebra Systems) applied to teaching and assessing mathematics,” School of Doctoral Studies (European Union) Journal, vol. 1, pp. 136-170, 2009.
  2. Buteau, N. Marshall, D. Jarvis, and Z. Lavicza, “Integrating computer algebra systems in post-secondary mathematics education: Preliminary results of a literature review,” International Journal for Technology in Mathematics Education, vol. 17, pp. 57-68, 2010.
  3. Lavicza, “Factors influencing the integration of Computer Algebra Systems into university-level mathematics education,” International Journal for Technology in Mathematics Education, vol. 14, p. 121, 2007.
  4. A. Majid, Z. Huneiti, W. Balachandran, and Y. Balarabe, “MATLAB as a teaching and learning tool for mathematics: a literature review,” International Journal of Arts & Sciences, vol. 6, p. 23, 2013.
  5. Lawrenz, A. Gravely, and A. Ooms, “Perceived helpfulness and amount of use of technology in science and mathematics classes at different grade levels,” School Science and Mathematics, vol. 106, pp. 133-139, 2006.
  6. Tonkes, B. I. Loch, and A. Stace, “An innovative learning model for computation in first year mathematics,” International Journal of Mathematical Education in Science and Technology, vol. 36, pp. 751-759, 2005.
  7. M. Kadijevich, “Neglected critical issues of effective CAS utilization,” Journal of Symbolic Computation, vol. 61, pp. 85-99, 2014.
  8. Bains, J. E. Mitchell, A. Nyamapfene, and E. Tilley, “Work in progress: Multi-displinary curriculum review of engineering education. UCL’s integrated engineering programme,” in Global Engineering Education Conference (EDUCON), 2015 IEEE, 2015, pp. 844-846.
  9. S. Lynch and J. Wilber, MathWorks User Story http://uk.mathworks.com/company/user_stories/manchester-metropolitan-university-students-vote-math-best-overall-course-following-adoption-of-matlab.html    accessed (08/02/16).
  10. S. Lynch, Dynamical Systems with Applications using MATLAB 2nd Ed., Springer International  Publishing, Switzerland, 2014.
  11. Periasamy, “Students’ motivations and actions when they learn mathematics using CAS: a study using an activity theory approach,” PhD. Thesis, Wits School of Education, Faculty of Humanities, University of the Witwatersrand, 2011.
  12. N. G. Lederman and M. L. Niess, “Technology for Technology’s Sake or for the Improvement of Teaching and Learning?,” School Science and Mathematics, vol. 100, pp. 345-348, 2000.

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