# Engineering students’ instrumental approaches to mathematics; some positive characteristics

More Detail

^{1}Faculty of Engineering Science and Technology, UiT the Arctic University of Norway, Narvik, Norway

^{*}Corresponding Author

EUR J SCI MATH ED, Volume 6, Issue 3, pp. 82-99.
https://doi.org/10.30935/scimath/9525

OPEN ACCESS 1685 Views 985 Downloads

## ABSTRACT

The present paper presents three deliberately chosen mathematical episodes observed in a class of engineering students taking a basic calculus course. By drawing on analyses of instrumental and relational learning strategies, the episodes are shown to illustrate instrumental approaches indicated by the students. The paper discusses positive characteristics about these approaches while further data collections shed light on reasons why such approaches were preferred. Results reveal some positive characteristics, suggesting that instrumental strategies may serve as valuable parts of the learning environment in engineering educations. If students are motivated by instrumental approaches, then utilizing positive aspects about them may be an important starting point in teaching. Awareness of this may provide useful in stimulating for relational learning based on instrumental profits.

## CITATION

Rensaa, R. J. (2018). Engineering students’ instrumental approaches to mathematics; some positive characteristics.

*European Journal of Science and Mathematics Education, 6*(3), 82-99. https://doi.org/10.30935/scimath/9525## REFERENCES

- Adams, R. A. (2006).
*Calculus - A complete course*(6 ed.). Toronto: Pearson Addison Wesley. - Anthony, G. (2000). Factors influencing first-year students' success in mathematics.
*International Journal of Mathematical Education in Science and Technology,***31**(1), 3-14. - Baroody, A. J., Feil, Y., & Johnson, A. (2007). An alternative reconceptualization of procedural and conceptual knowledge.
*Journal for Research in Mathematics Education,***38**(2), 115-131. - Bergqvist, E. (2006). University mathematics teachers' views on the required reasoning in calculus exams. In E. Bergqvist (Ed.), Mathematics and mathematics education; Two sides of the same coin [PhD Thesis]. Umeå, Sweden: Umeå University Sweden.
- Bergsten, C. (2011). Why do students go to lectures? Paper presented at the Seventh Congress of the European Society for Research in Mathematics Education, Rzeszow, Poland. http://www.cerme7.univ.rzeszow.pl/WG/14/CERME7-WG14-Paper---Bergsten-REVISED-Dec2010..pdf
- Blomhøj, M., & Jensen, T. H. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning.
*Teaching Mathematics and its Applications,***22**(3), 123-139. - Brandell, G., Hemmi, K., & Thunberg, H. (2008). The widening gap – A Swedish perspective.
*Mathematics Education Research Journal,***20**(2), 38-56. - Brousseau, G. (1997).
*Theory of Didactical situations in mathematics*(Vol. 19): Kluwer Academic Publishers. - Bryman, A. (2004).
*Social research methods*. Oxford: Oxford University Press. - Cardella, M. (2008). Which mathematics should we teach engineering students? An empirically grounded case for a broad notion of mathematical thinking.
*Teaching Mathematics and its Applications,***27**(3), 150-159. - Carpenter, T. P., & Lehrer, R. (1999). Teaching and learning mathematics with understanding. In E. Fennema & T. A. Romberg (Eds.), Mathematics Classrooms That Promote Understanding (pp. 19-32). Mahwah, NJ: Lawrence Erlbaum Associates.
- Engelbrecht, J., Bergsten, C., & Kågesten, O. (2012). Conceptual and Procedural Approaches to Mathematics in the Engineering Curriculum: Student Conceptions and Performance.
*Journal of Engineering Education,***101**(1), 138-162. - Felder, R. M., & Brent, R. (2005). Understanding Student Differences.
*Journal of engineering education,***94**(1), 57-72. - Gallagher, D. J. (1995). In search for the rightful role of method: reflections on conducting a qualitative dissertation. In T. Tiller, A. Sparkes, S. Kårhus, & F. Dowling Næss (Eds.), The Qualitative Challenge: Reflections on Educational Research (pp. 17-35). Landsås, Norway: Caspar Forlag.
- Hames, E., & Baker, M. (2015). A study of the relationship between learning styles and cognitive abilities in engineering students
*European Journal of Engineering Education,***40**(2), 167-185. - Harris, D., Black, L., Hernandez-Martinez, P., Pepin, B., & Williams, J. (2015). Mathematics and its value for engineering students: what are the implications for teaching?
*International Journal of Mathematical Education in Science and Technology,***46**(3), 321-336. - Hiebert, J. (1986).
*Conceptual and procedural knowledge: The case of mathematics*. Hillesdale, NJ: Erlbaum. - Hiebert, J., & Lefevre, P. (1986). Conceptual and procedural knowledge in mathematics: An introductory analysis. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 1-27). Hillesdale, NJ: Erlbaum.
- Hogstad, N. M., Isabwe, G. M. N., & Vos, P. (2016). Engineering students’ use of visualizations to communicate about representations and applications in a technological environment. Paper presented at the International Network for Didactic Research in University Mathematics, INDRUM 2016 Montpellier. https://hal.archives-ouvertes.fr/INDRUM2016/public/indrum2016proceedings.pdf
- Jaworski, B. (1994).
*Investigating Mathematics Teaching: a Constructivist Enquiry*. London ; Washington, D.C.: Falmer Press. - Kashefi, H., Ismail, Z., & Yusof, Y. M. (2012). Engineering mathematics obstacles and improvements:a comparative sudy of students and lectureres perspectives through creative problem solving.
*Procedia - Social and Behavioral Sciences,***56**, 556-564. - Khiat, H. (2010). A grounded theory approach: Conceptions of understanding in engineering mathematics learning.
*The Qualitative Report,***15**(6), 1459-1488. - 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.
- Mason, J. (1998). Researching from the inside in mathematics education. In A. Sierpinska & J. Kilpatrick (Eds.), Mathematics Education as a Research Domain: A Search for Identity (Vol. 4, pp. 357-377). London: Kluwer Academic Publishers.
- Maull, W., & Berry, J. (2000). A questionnaire to elicit the mathematical concept images of engineering students.
*International Journal of Mathematical Education in Science and Technology,***31**(6), 899-917. - 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. - Mustoe, L. (2002). Mathematics in engineering education.
*European Journal of Engineering Education,***27**(3), 237-240. - Piaget, J., & Inhelder, B. (1969).
*The psychology of the child*. London: Routledge & Kegan Paul. - Pimm, D. (1987).
*Speaking mathematically: Communication in mathematics classrooms*. New York: Routledge and Kegan Paul. - Randahl, M. (2012). First-year engineering students’ use of their mathematics textbook - opportunities and constraints.
*Mathematics Education Research Journal,***24**(3), 239-256. - Randahl, M., & Grevholm, B. (2010). Learning opportunities offered by a classical calculus textbook.
*Nordic Studies in Mathematics Education,***15**(2), 5-27. - Reed, H. C., Drijvers, P., & Kirschner, P. A. (2010). Effects of attitudes and behaviours on learning mathematics with computer tools.
*Computers & Education,***55**(1), 1-15. - Rensaa, R. J. (2011). A task based two-dimensional view of mathematical competency used to analyse a modelling task.
*International Journal of Innovation in Science and Mathematics Education,*19(2), 37-50. - 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. - Rensaa, R. J., & Vos, P. (2017). Interpreting teaching for conceptual and for procedural knowledge in a teaching video about linear algebra
*.*Paper presented at the Norma 17, Stockholm, Sweden. - Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics.
*Educational Psychology Review,***27**, 587-597. - Sazhin, S. S. (1998). Teaching mathematics to engineering students.
*International Journal of Engineering Education,***14**(2), 145-152. - Skemp, R. R. (1978). Relational inderstanding and instrumental understanding.
*The Arithmetic Teacher,***26**(3), 9-15. - Skemp, R. R. (1979a). Goals of Learning and Qualities of Understanding.
*Mathematics Teaching,***88**, 44-49. - Skemp, R. R. (1979b).
*Intelligence, learning, and action : a foundation for theory and practice in education*. Chichester: Wiley. - Skemp, R. R. (1987).
*The psycology of learning mathematics*. London: Penguin Books. - Stake, R. E. (1995).
*The Art Of Case Study Research*: Sage Publications, Inc. - 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.
- UFD. (2011). Forskrift om rammeplan for ingeniørutdanning. Ministry of Education and Research.
- 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. - Varsavsky, C. (2010). Chances of success in and engagement with mathematics for students who enter university with a weak mathematics background.
*International Journal of Mathematical Education in Science and Technology,***41**(8), 1037-1049. - Vinner, S. (2007). Mathematics education: Procedures, rituals and man's search for meaning.
*Journal of Mathematical Behavior,***26**, 1-10. - Wedege, T. (1999). To know or not to know - mathematics, that is a question of context.
*Educational Studies in Mathematics,***39**, 205-227.