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  • 1.
    Bergsten, Christer
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Engelbrecht, Johann
    University of Pretoria, South Africa.
    Kågesten, Owe
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries2015In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, Vol. 46, no 7, p. 979-990Article in journal (Refereed)
    Abstract [en]

    This study forms part of a collaboration project between universities in South Africa and Sweden in which we investigate whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than a traditional more procedurally oriented way of teaching. In this paper, we report in some detail from two interviews with professional engineers, selected to represent two different ‘poles’ of engineering work. The aim was to explore different kinds of arguments regarding the role of mathematics in engineering work, as well as some common across contexts. Both interviewees feel that conceptual mathematics is more important for engineering work, although the role of the procedural aspect was seen by one of the interviewees also to be important, but in a very intricate way.

  • 2.
    Engelbrecht, Johann
    et al.
    University of Pretoria.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Kågesten, Owe
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum: Student Conceptions and Performance2012In: Journal of Engineering Education, ISSN 1069-4730, E-ISSN 1524-4873, Vol. 101, no 1, p. 138-162Article in journal (Refereed)
    Abstract [en]

    BACKGROUND

    Demands by engineering faculties of mathematics departments have traditionally been for teaching    computational skills while also expecting analytic and creative knowledge-based skills. We    report on a project between two institutions, one in South Africa and one in Sweden, that investigated    whether the emphasis in undergraduate mathematics courses for engineering students would    benefit from being more conceptually oriented than the traditional more procedurally oriented way  of teaching.

    PURPOSE (HYPOTHESIS)

    We focus on how second-year engineering students respond to the conceptual-procedural distinction,    comparing performance and confidence between Swedish and South African groups of students in answering    conceptual and procedural mathematics problems. We also compare these students’ conceptions on the  role of conceptual and procedural mathematics problems within and outside their mathematics studies.

    DESIGN/METHOD

    An instrument consisting of procedural and conceptual items as well as items on student opinions on the    roles of the different types of knowledge in their studies was conducted with groups of second-year engineering  students at two universities, one in each country.

    RESULTS

    Although differences between the two countries are small, Swedish students see procedural items to be    more common in their mathematics studies while the South African students find both conceptual and    procedural items common; the latter group see the conceptually oriented items as more common in their  studies outside the mathematics courses.

    CONCLUSIONS

    Students view mathematics as procedural. Conceptual mathematics is seen as relevant outside mathematics.    The use of mathematics in other subjects within engineering education can be experienced differently    by students from different institutions, indicating that the same type of education can handle the application  of mathematics in different ways in different institutions.

  • 3.
    Engelbrecht, Johann
    et al.
    Department of Science, Mathematics and Technology Education, University of Pretoria, Pretoria, South Africa.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Educational Sciences.
    Kågesten, Owe
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, Faculty of Science & Engineering.
    Conceptual and procedural approaches to mathematics in the engineering curriculum: Views of qualified engineers2017In: European Journal of Engineering Education, ISSN 0304-3797, E-ISSN 1469-5898, Vol. 42, no 5, p. 570-586Article in journal (Refereed)
    Abstract [en]

    The research interest underpinning this paper concerns the type ofmathematical knowledge engineering students may acquire during theirspecialised education in terms of the conceptual and proceduraldimensions of doing and using mathematics. This study draws oninterviews with 25 qualified engineers from South Africa and Swedenregarding their views on the role of mathematics in engineeringeducation, with special focus on the conceptual and procedural aspectsof mathematical knowledge. A thematic analysis of the interview dataled to the identification of two main themes. According to theconceptual view a predominantly conceptual approach is needed andvalued more than procedural skills, while the balanced view emphasisesa balance of conceptual understanding and procedural fluency as wellas links between them. It is suggested that the mathematical educationof engineers would need to be more conceptually oriented to preparefor the demands at the workplace.

  • 4.
    Engelbrecht, Johann
    et al.
    University of Pretoria, South Africa.
    Bergsten, Christer
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Kågesten, Owe
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Undergraduate students' preference for procedural to conceptual solutions to mathematical problems2009In: International journal of mathematical education in science and technology, ISSN 0020-739X, E-ISSN 1464-5211, ISSN 0020-739X, Vol. 40, no 7, p. 927-940Article in journal (Refereed)
    Abstract [en]

    This paper reports from a collaboration project between South Africa and Sweden, in which we want to investigate whether the emphasis in undergraduate mathematics courses for engineering students should be more conceptual than the current traditional way of teaching. On the basis of a review of the distinction between conceptual and procedural knowledge, an analysis of student solutions to tasks designed to be solved with a conceptual approach but ‘proceduralized’ by the students sheds some new light on this classical distinction. It is argued that the distinction can be operationalized in test items in a meaningful way but that caution needs to be taken in interpreting the results considering the complex interdependence of these constructs when doing mathematical work.

  • 5.
    Houston, Ken
    et al.
    Math dep University of Ulster.
    Engelbrecht, Johann
    Dept Mathematics Applied Mathematics University of Pretoria.
    Wood, Leigh
    Math dep University of Technology, Sydney.
    Harding, Ansie
    Dept Mathematics Applied Mathematics University of Pretoria.
    Holton, Derek
    Math dep University of Ortago, New Zealand.
    Barton, Bill
    Math dep University of Auckland, New Zealand.
    Kågesten, Owe
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
    Professional development of mathematics academics2006In: 3rd International Conference on the Teaching of Mathematics,2006, Publicerad på CD: Publicerad på CD , 2006Conference paper (Refereed)
    Abstract [en]

    It is almost 30 years since Morris Kline published his wide-ranging critique of undergraduate education in his book, "Why The Professor can't Teach" [1]. In 1999, Steve Krantz, in his book, "How to Teach Mathematics" [2] reported that academics were paying much more attention to their teaching duties than before. Both of these books were largely about the situation in the USA. This paper explores ideas around the early in-service and continuing professional development of academics and uses examples from several countries.  

  • 6.
    Kågesten, Owe
    et al.
    Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
    Bergsten, Christer
    Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
    Engelbrecht, Johann
    University of Pretoia.
    Undergraduate students’ preference for procedural to conceptual solutions to mathematical problems2009In: Accepterat för publicering vid Delta 09, november 2009, 2009Conference paper (Refereed)
    Abstract [en]

    This paper reports from a collaboration project between South Africa and Sweden, in which we want to investigate whether the emphasis in undergraduate mathematics courses for engineering students should be more conceptual than the current traditional way of teaching. Based on a review of the distinction between conceptual and procedural knowledge, an analysis of student solutions to tasks designed to be solved with a conceptual approach but ‘proceduralised’ by the students, sheds some new light on this classical distinction. It is argued that the distinction can be operationalised in test items in a meaningful way but that caution need to be taken in interpreting the results considering the complex interdependence of these constructs when doing mathematical work.

  • 7.
    Kågesten, Owe
    et al.
    Linköping University, Department of Science and Technology, Communications and Transport Systems. Linköping University, The Institute of Technology.
    Engelbrecht, Johann
    University of Pretoria.
    Student group presentations: A learning instrument in undergraduate mathematics for engineering students2007In: European Journal of Engineering Education, ISSN 0304-3797, E-ISSN 1469-5898, Vol. 32, no 3, p. 303-314Article in journal (Refereed)
    Abstract [en]

    In this study we created an environment for peer learning, where students teach students by making oral presentations in groups about solving mathematical problems and explaining theoretical background in mathematics, during the first year of an undergraduate engineering programme at the Norrköping campus of the Linköping University. In order to strengthen the students' understanding and perception of central mathematical concepts, the study was designed to take the students through five different learning experiences, preparing the presentation, presenting the mathematics, listening to others presenting, discussion by all students after the presentation and feedback by the teacher to the small group of students separate from the other students. We study how oral presentations work as a learning and assessment method. The study consisted of three stages.  After a first run of the presentations as a learning instrument, three guidebooks with recommendations to students and teachers were developed in order to assist students as well as teachers about their role in this learning environment. Students’ and teachers’ views on the student presentations as learning instrument were surveyed before and after the intervention.  In stage three, students were interviewed individually to ascertain the relevant success of the different learning experiences.

  • 8.
    Kågesten, Owe
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
    Engelbrecht, Johann
    Dept Mathematics Applied Mathematics University of Pretoria.
    Supplementary explanations in undergraduate mathematics assessment: A forced formative writing activity2006In: European Journal of Engineering Education, ISSN 0304-3797, E-ISSN 1469-5898, Vol. 31, no 6Article in journal (Refereed)
    Abstract [en]

     Engineering students in technical universities in Sweden, as probably in many other countries, tend to treat mathematics as a mechanical subject in which you do calculations and manipulations and very little explanation. In order to create deeper understanding, verbal or written explanations by students can be beneficial. In our study we show a possible way of getting students to reflect about their mechanical solutions to mathematical problems. The method is based on the supplementary written explanations that students may provide in their written examination in what would be a second stage of the examination, a so-called -home exam-. In our project students were forced to rethink their answers, attending to comments and questions posed by the teacher who marked the scripts and supplying further explanation of his/her work and judging from the results of the research, this facet of the project was successful. The additional opportunity to reflect on their responses assisted students in understanding the mathematical concepts deeper and exposed their weaknesses and gaps in their knowledge. 

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