Session Information
24 SES 01, Mathematics in Transition.
Paper Session
Contribution
This paper examines the transfer of mathematics learning from pre-university mathematics courses to its use in electrical engineering degrees. It considers how apparently small changes in context, problem and the expression of mathematics can lead to disconnection from mathematics amongst students when they move on to university. Commonalities and differences in mathematics assessment pre and during university give rise to mathematical boundary objects (Star, 1989) that carry with the student as they move from their pre-university to their university learning context. Such boundary objects are neither the mathematics of the school mathematics classroom, nor the mathematics of the university lecturer, but rather an emergent evolution of understanding. How can such mathematical boundary objects be understood and how can they be used to facilitate better conceptual understanding of mathematics in order to solve problems of engineering?
The paper examines how mathematics is used by students in the context of problem solving during their electrical engineering degree, by identifying and examining the use of such mathematical boundary objects. In order to do this we examine how electrical engineering students mathematise in the context of solving problems of electrical engineering during the first year of the university degree course.
The aim is to provide concrete examples of students’ practice drawn across three case studies of electrical-engineering students in three higher education institutions situated in the North of England, so as to make explicit students’ mathematisation and their use of models and metaphors as they make mathematics. Students reflect upon their use of mathematics and how their understanding of the mathematics concerned has changed in the context of their engineering degree. Students are also asked about their identification with mathematics. Whilst, for some, such data takes the form of post-hoc reflections, for others a series of longitudinal interviews provides an historical account of their changing perspectives and reported mathematical practices.
There have been various studies into the transfer of specific mathematics skills and/or mathematical knowledge by university students into new subject areas including science (Britton, New, Sharma & Yardley; 2005) and engineering (Hirst, Williamson & Bishop, 2004; Fadali, Velasquez-Bryant & Robinson, 2004; Gynnild, Tyssedal & Lorentzen, 2005) and our students spoke about these processes. Following Williams and Wake (2006) we examine the process of transfer or transition (Beach, 1999) at the boundary between two learning contexts, the former school or pre-university mathematics context and the context of the use of mathematics during the degree (different activity systems).
Conceptually, it draws on theories of mathematical genre, after Bakhtin (1981) and Wake and Williams (2006); use of models and metaphor, after the work of Freudenthal and the Freudenthal Institute, which has shown how models and modelling problems drawn from the culture can be significant in the service of abstracting mathematics and building new mathematics, through ‘horizontal’ and ‘vertical’ mathematisation (Freudenthal, 1983; Gravemeijer et al., 1999; Streefland, 1991; Treffers, 1987, Lamon et al., 2003), and third generation Activity Theory (Engestrom, 1987), which provides a conceptual framework with which to understand the boundary mathematical activity.
Method
Expected Outcomes
References
Bahktin, M. (1981) The Dialogic Imagination: Four Essays by M. M. Bahktin. (ed. M. Holquist). Austin, Texas University Press. Britton, S., New, P. B., Sharma, M. D. and Yardley, D. (2005) 'A case study of the transfer of mathematics skills by university students', International Journal of Mathematical Education in Science and Technology, 36: 1, 1 - 13 Beach, K. D. (1999). Consequential transitions: A sociocultural expedition beyond transfer in education. In Review of Research in Education, Vol. 24. Washington, D.C.: American Educational Research Association. Engeström, Y. (1987) Learning by Expanding: an activity-theoretical approach to developmental research. Helsinki: Orienta-Konsultit. Gravemeijer, K. P. E. & Doorman, L. M. (1999). Context problems in realistic mathematics education: A calculus course as an example. Educational Studies in Mathematics, 39 (1–3), 111–129. Gynnild, V., Tyssedal, J. & Lorentzen, L. (2005). Approaches to study and the quality of learning. Some empirical evidence from engineering education. International Journal of Science and Mathematics Education, 3 (4), 587-607. Lamon, S. J., Parker, W. A. & Houston, S. K. (Eds.) (2003). Mathematical modelling: a way of life. Chichester: Horwood Publishing. Sfard, A., & Prusak, A. (2005). Telling identities: in search of an analytic tool for investigating learning as a culturally shaped activity. Educational Researcher, 34 (4), 14-22. Star, S. L. (1989) ‘The structure of ill-structured solutions: boundary objects and heterogeneous distributed problem solving’, in L. Gasser and M. Huhns (eds) Distributed artificial intelligence, Vol. II, London, Pitman. Wake, G. & Williams, J. S. (2006). "Metaphors and models in translation between College and Workplace mathematics." Educational Studies in Mathematics 64 (3), 345-371. Williams, J. S., Davis, P. S. & Black, L. (2007). "Subjectivities in School: Socio-cultural and Activity Theory Perspectives." International Journal of Educational Research Special Issue on Subjectivities in School: Socio-cultural and Activity Theory Perspectives 46 (1-2).
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