Threshold concepts, once learned, are likely to bring together different aspects of the subject that previously did not appear, to the student, to be related.

In engineering the integrative aspect may be seen at two levels.

1. A threshold concept may bring together several troublesome concepts:
Phasors are certainly integrative − relying on connections between complex numbers, sinusoidal properties and exponentials. The application of complex numbers to real components − inductors and capacitors − is initially alien knowledge to students (Meyer and Land, 2003).
                                                                  Holloway, Alpay & Bull (2010)
The confluence of several examples of troublesome knowledge within a threshold concept has been observed by several investigators in researching the teaching of electrical engineering.
Flanagan, Taylor & Meyer (2010), have identified a threshold concept in the mastery of transmission line theory which is characterised by:
  • Troublesome visualisations and abstractions
  • Troublesome oscillation between the abstract and the concrete
  • Complex arithmetic
  • Counter-intuitive entities − reactive power, characteristic impedance
They refer to such a concept as compounded threshold concept

Bernhard & Carstensen (2007), in extensive studies of the teaching of circuit analysis, have developed the idea of complex concepts.

2. There are several concepts, that appear in two or more modules throughout a typical engineering syllabus, which if grasped help integrate the discipline. Some of these, e.g. Laplace transform in circuit analysis, circuit design, control systems, signal processing; phasors in circuit analysis, circuit design, communication systems, power electronics, are troublesome for many students and may be threshold concepts or contribute to a compounded threshold concept.

The integrative element of such threshold concepts may be examined by observing the facilitation of a student’s grasp of the concept in one module after completing an earlier potentially integrative module.


Bernhard, J. and Carstensen, A-K. (2007), Modelling and learning a complex concept - an exploration in light of some examples from electric circuit theory,
Paper presented at ESERA2007, Malmö, August 21-25, 2007.
[   last accessed 25 June 2008]

Flanagan, M. T., Taylor, P. and Meyer, J.H.F. (2010), Compounded Thresholds in Electrical Engineering,
in: Threshold Concepts and Transformational Learning, Land, R., Meyer, J.H.F. and Baillie, C., (eds), Sense Publishers, Rotterdam, pp. 227-239,   [book details].

Holloway, M., Alpay, E. and Bull, A.: (2010), A Quantitative Approach to Identifying Threshold Concepts in Engineering Education,
Engineering Education 2010 (EE2010) Inspiring the next generation of engineers, 6 - 8 July 2010, Aston University
[Higher Education Academy Engineering Subject Centre:   last accessed 16 August 2010]

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