A textbook in linear algebra – the use and views of engineering students
DOI:
https://doi.org/10.7146/nomad.v20i3-4.148699Abstract
This paper has a twofold aim. One is to analyse parts of a linear algebra textbook to seek for its relevance to engineering students. Another is to present an analysis of engineering students’ views about this textbook. Results from the textbook analysis indicate that characteristics like motivating examples and visual design of text and pictures may appeal to engineering students. This is confirmed by analysis of students’ views, showing that the textbook is appreciated, with examples as the most valued part. The textbook’s design with theory presented in small portions, often in examples using specific values to illustrate theoretical arguments, seems to be a success factor.
References
Abdulwahed, M., Jaworski, B. & Crowford, A. R. (2012). Innovative approaches to teaching mathematics in higher education: a review and critique. Nordic Studies in Mathematics Education, 17 (2), 49-68.
Anton, H. & Rorres, C. (2014). Elementary linear algebra: with supplemental applications. Hoboken: Wiley.
Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241. https://doi.org/10.1023/A:1024312321077
Bergsten, C. (2011). Why do students go to lectures? In M. Pytlak, T. Rowland & E. Swoboda (Eds.), Proceedings of the seventh congress of the European Society for Research in Mathematics Education (pp. 1960-1970). University of Rzeszów. Retrieved from http://www.mathematik.uni-dortmund.de/~erme/ doc/cerme7/CERME7.pdf
Byrnes, J. P. & Wasik, B. A. (1991). Role of conceptual knowledge in mathematical procedural learning. Developmental Psychology, 27 (5), 777-786. https://doi.org/10.1037/0012-1649.27.5.777
Carberry, A. R. (2008). Learning-by-teaching as a pedagogical approach and its implications on engineering education (Doctoral dissertation). Tufts University.
Carlson, D. (1993). Teaching linear algebra: Must the fog always roll in? College Mathematics Journal, 24 (1), 29-40. https://doi.org/10.1080/07468342.1993.11973503
Dorier, J.-L. (1997). L'Enseignement de l'algèbre linéaire en question. Grenoble: La Pensée Sauvage éditions.
Dorier, J.-L., Robert, A., Robinet, J. & Rogalski, M. (2000). The obstacle of formalism in linear algebra. In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp. 85-94). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47224-4_2
Dorier, J.-L. & Sierpinska, A. (2001). Research into the teaching and learning of linear algebra. In D. Holton (Ed.), The teaching and learning of mathematics at university level: An ICMI study (pp. 255-273). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47231-7_24
Fan, L., Zhu, Y. & Miao, Z. (2013). Textbook research in mathematics education: development status and directions. Zentralblatt für Didaktik der Mathematik, 45, 633-646. https://doi.org/10.1007/s11858-013-0539-x
Glaser, B. G. & Strauss, A. L. (1967). The discovery of grounded theory: Strategies for qualitative research. Chicago: Aldine Publishing Company.
Grevholm, B. (2011). Network for research on mathematics textbooks in the Nordic countries. Nordic Studies in Mathematics Education, 16 (4), 91-102.
Grevholm, B. (2012). Theoretical framework for research on textbooks, 20121008. Retrieved from http://textbookstudy.files.wordpress.com/2013/05/theoreticalframework.pdf
Hiebert, J. & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: an introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge (pp. 1-27). Hillesdale: Erlbaum.
Hjalmarson, M. A. (2007). Engineering students designing a statistical procedure for quantifying variability. Journal of Mathematical Behavior, 26, 178-188. https://doi.org/10.1016/j.jmathb.2007.06.001
Kirkup, L., Wood, L. N., Mather, G. & Logan, P. (2003). Are you being serviced? Promoting quality service teaching. Uniserve Science, 37-42.
Kümmerer, B. (2001). Trying the impossible: Teaching mathematics to physicists and engineers. In D. Holton (Ed.), The teaching and learning of mathematics at university level: an ICMI study (pp. 321-334). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47231-7_29
Lay, D. C. (2014). Linear algebra and its applications (4 ed.). Boston: Addison- Wesley.
Lithner, J. (2003). Students' mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52 (1), 29-55. https://doi.org/10.1023/A:1023683716659
McGregor, R. & Scott, B. (1995). A view on applicable mathematics courses for engineers. In L. Mustoe & S. Hibberd (Eds.), Mathematical education of engineers (pp. 115-129 ). Oxford: Clarendon Press.
Mellin-Olsen, S. (1981). Instrumentalism as an educational concept. Educational Studies in Mathematics, 12, 351-367. https://doi.org/10.1007/BF00311065
Randahl, M. (2012). First-year engineering students' use of their mathematics textbook - opportunities and constraints. Mathematics Education Research Journal, 24 (3), 239-256. https://doi.org/10.1007/s13394-012-0040-9
Randahl, M. & Grevholm, B. (2010). Learning opportunities offered by a classical calculus textbook. Nordic Studies in Mathematics Education, 15 (2), 5-27.
Rensaa, R. J. (2014). The impact of lecture notes on an engineering student's understanding of mathematical concepts. Journal of Mathematical Behavior, 34, 33-57. https://doi.org/10.1016/j.jmathb.2014.01.001
Rensaa, R. J. (in progress). A framework for discussing engineering students' approaches to mathematics.
Rezat, S. & Sträßer, R. (2012). From triangle to tetrahedron: artifacts as fundamental constituents of the didactical situation. ZDM - the International Journal on Mathematics Education, 44 (5), 641-651. https://doi.org/10.1007/s11858-012-0448-4
Rezat, S. & Sträßer, R. (2013). Methodologies in Nordic research on mathematics textbooks. In B. Grevholm, P. S. Hundeland, K. Juter, K. Kislenko & P.-E. Persson (Eds.), Nordic research in didactics of mathematics: past, present and future (pp. 469-482). Oslo: Cappelen Damm AS akademisk.
Rogalski, M. (1990). Pourquoi un tel échec de l'enseignement de l'algèbre linéaire? Enseigner autrement les mathématiques en DEUG Première Année (pp. 279-291). Commission inter-IREM universtité.
Sierpinska, A. (1997). Formats of interaction and model readers. For the Learning of Mathematics, 17 (2), 3-12.
Sierpinska, A. (2000). On some aspects of students' thinking in linear algebra. In J.-L. Dorier (Ed.), On the teaching of linear algebra (pp. 209-246). Dordrecht: Klewer Academic Publisher. https://doi.org/10.1007/0-306-47224-4_8
Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20-26.
Star, J. R. (2005). Reconceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36 (5), 404-411.
Steen, L. A. (2001). Revolution of stealth: redefining university mathematics. In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 303-312). Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47231-7_27
Strauss, A. L. & Corbin, J. M. (1998). Basics of qualitative research: techniques and procedures for developing grounded theory. Thousand Oaks: Sage Publications.
Varsavsky, C. (1995). The design of mathematics curriculum for engineers: a joint venture of the mathematics department and the engineering faculty. European Journal of Engineering Education, 20 (3), 341-345. https://doi.org/10.1080/03043799508923364
Wood, L. (2001). The secondary-tertiary interface. In D. Holton (Ed.), The teaching and learning of mathematics at university level (pp. 87-98). Dordrecht: Kluwer Academic Publisher. https://doi.org/10.1007/0-306-47231-7_9
Ödman, P. J. (1979). Tolkning, förståelse, vetande. Hermeneutik i teori och praktik. [Interpretation, understanding, knowing. Hermeneutics in theory and practice]. Borås: AWE/Gebers.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.