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Kaizen teaching and the learning habits of engineering students in a freshman mathematics course

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Abstract

Which are the teaching methods that actually contribute to the learning of mathematics? The answer to this certainly is the holy grail of didactic and pedagogy, and should be supported by large scale statistical evidence. Our article aims at providing an initial step into this direction by first illustrating a teaching paradigm that is suited for the generation of large scale data sets: based on industry best practice quality assurance standards we introduce the Kaizen teaching paradigm which enforces Kolb’s reflective learning cycle on the students’ side. Second, we present and analyze the data we obtained through our pilot implementation at a engineering freshman mathematics course in the Sultanate of Oman. These emphasize the effectiveness of Kaizen teaching and once again show the necessity of continuous learning. A practice that seems to be forgotten in traditional university engineering courses due to the mere size of the audience. In particular it seems that a Markovian estimator for students’ performance may have to be considered.

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Notes

  1. We refer to the literature, like Bostrm (2011), Coffield et al. (2004), Honey and Mumford (1986) for more details on the over 70 teaching styles that are currently subject to vivid discussion.

  2. As usual the term calculus refers to the set of recipes and is taught to students more or less in a form of copying a presented solution idea to another set of problems which may not even require an in depth understanding of the problem itself. Calculus consist of the basics and the correct way of applying formulas. Although calculus is an essential first step towards mathematics it is to be clearly separated from mathematics. Mathematics has the characteristics of a language for the sciences and demands the autonomous realization of solutions for problems of a previously unknown type. Thus the transfer of techniques has to be taught as well as the modeling of scientific and engineering scenarios.

  3. MUMIE is an acronym for “Multimedial Mathematics in Engineering” and was designed jointly by the RWTH Aachen, TU Berlin and TU Munich, see www.mumie.net for further information. The version used at GUtech enables users to explore and learn mathematics by themselves and gave students the chance to practice together with a full material collection of the lecture’s topics and definitions.

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Authors and Affiliations

  1. Lehrstuhl A für Mathematik, RWTH Aachen, 52056, Aachen, Germany

    Jonas Gallenkämper & Judith Kreuzer

  2. Department of Mathematics and Science, German University of Technology in Oman, Halban Campus, Muscat, Oman

    Bernhard Heim, Florian Rupp, Paul von Stockhausen & Nils Viet

Authors
  1. Jonas Gallenkämper
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  2. Bernhard Heim
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  3. Judith Kreuzer
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  4. Florian Rupp
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  5. Paul von Stockhausen
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  6. Nils Viet
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Correspondence to Jonas Gallenkämper.

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Gallenkämper, J., Heim, B., Kreuzer, J. et al. Kaizen teaching and the learning habits of engineering students in a freshman mathematics course. Cent Eur J Oper Res 24, 1009–1030 (2016). https://doi.org/10.1007/s10100-015-0416-5

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  • DOI: https://doi.org/10.1007/s10100-015-0416-5

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