Mathematical Knowledge of Non-mathematics Students and Their Beliefs about Mathematics

Ljerka Jukic Matic

doi:10.29333/iejme/278

Full Text (PDF)

Ljerka Jukic Matic

More Detail

Abstract

Mathematics is tightly interwoven with science and engineering, where it has numerous applications. In the educational context, there is an ongoing debate who should teach mathematics to non-mathematicians and how this mathematics should be taught. The knowledge gained in mathematics course is used in another course (mathematics, science or engineering), hence students should retain core concepts some time after learning. Beliefs that students have about mathematics significantly influence on their learning, and consequently on the retained knowledge. We investigated retained calculus knowledge and beliefs about mathematics in two groups of first year students coming from the science and engineering study programs. The results showed that both groups of students showed better procedural knowledge than conceptual. Also they showed positive beliefs about mathematics in their study program, but were not certain where this knowledge will be used later. However they differed in the perception of mathematics as being exciting discipline. The educational implications of these findings are also discussed.

Keywords

Calculus
Knowledge
Retention
Beliefs

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 9, Issue 1, January 2014, 13-24

https://doi.org/10.29333/iejme/278

Publication date: 02 Feb 2014

Article Views: 3673

Article Downloads: 2600

Open Access References How to cite this article

References

Allen, K., Kwon, O. N. & Rasmussen, C. (2005). Students‟ retention of mathematical knowledge and skills in differential equations. School Science and Mathematics, 105(5), 227-239.
Arzi, H. J., Ben-Zvi, R., & Ganiel, U. (1986). Forgetting versus savings: The many facets of long-term retention. Science Education, 70(2), 171–188.
Custers, E. J. F. M. (2010). Long-term retention of basic science knowledge: a review study. Advances in Health Sciences Education, 15(1), 109-128
Czocher, J. A, Tague, J. & Baker, G. (2012). Where does the calculus go? An investigation of how calculus ideas are used in later coursework. International Journal of Mathematical Education in Science and Technology, DOI: 10.1080/0020739X.2013.780215
Dart, B. C., Burnett, P. C., Purdie, N., BoultonLewis, G., Campbell, J., & Smith, D. (2000). Students‟ conceptions of learning, the classroom environment, and approaches to learning. The Journal of Educational Research, 93(4), 262-270.
Engelbrecht, J., Harding, A., & Preez, J. D. (2007). Long-term retention of basic mathematical knowledge and skills with engineering students. European Journal of Engineering Education, 32(6), 735-44.
Ernest, P. (2003). The Mathematical Attitudes, Beliefs and Ability of Students. In: Maths for Engineering and Science. LTSN MathsTEAM. 4-5.
Flegg, J., Mallet, D. G., & Lupton, M. (2012). Students' perceptions of the relevance of mathematics in engineering. International Journal of Mathematical Education in Science and Technology, 43(6), pp. 717-732.
Furinghetti, F., & Pehkonen, E. (2002). Rethinking characterizations of beliefs. In G. C. Leder, E. Pehkonen, and G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 39-57). Dordrecht: Kluwer Academic Publishers.
Garner, B. & Garner, L. (2001). Retention of concepts and skills in traditional and reformed applied calculus. Mathematics Education Research Journal, 13(3), 165-184.
Goldin, G., Rösken, B., & Törner, G. (2009). Beliefs - no longer a hidden variable in mathematical teaching and learning processes. In J. Maaß & W. Schlöglmann (Eds.), Beliefs and Attitudes in Mathematics Education: New Research Results (pp. 9-28). Rotterdam: Sense Publisher.
Haapasalo, L., & Kadijevich, D. (2000). Two types of mathematical knowledge and their relation. Journal für Mathematik-Didaktik, 21(2), 139-157.
Helfgott, M. (2004). Five guidelines in the teaching of first-year calculus. Proceedings of the 10th International Congress of Mathematical Education, Copenhagen, Denmark
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, Lawrence Erlbaum Associates, Hillsdale, NJ, 1-27.
Johnston, C. (2001). Student perceptions of learning in first year in an economics and commerce faculty. Higher Education Research and Development, 20(2), 169-184.
Jukić, Lj., & Dahl, B. (2010). The retention of key derivative concepts by university students on calculus courses at a Croatian and Danish university, Proc. 34th Conf. of the Int. Group for the Psychology of Mathematics Education, Brasil, Belo Horizonte: PME
Jukić, Lj., & Dahl, B. (2011). What Affects Retention of Core Calculus Concepts Among University Students? A Study of Different Teaching Approaches in Croatia and Denmark, Proceedings of 7thCongress of the European Society for Research in Mathematics Education (CERME), Rzeszow, Poland
Karsenty R. (2003). What adults remember from their high school mathematics? The case of linear functions. Educational Studies in Mathematics, 51, 117-144.
Kember, D., & Wong, A. (2000). Implications for evaluation from a study of students‟ perceptions of good and poor teaching. Higher Education, 40(1), 69-97.
Krutetskii, V. A. (1976). The Psychology of Mathematical Abilities in Schoolchildren, Chicago: The University of Chicago Press.
Mahavier, William S., & Mahavier, W. T. (2008). Calculus: The Importance of Precise Notation. PRIMUS, 18(4), 349-360.
Matthews, K. E., Adams, P., & Goos, M. (2009). Putting it into perspective: Mathematics in the undergraduate science curriculum. International Journal of Mathematics Education in Science and Technology, 40(7), 891-902
Maull, W., & Berry, J. (2000). A questionnaire to elicit concept images of engineering students. International Journal of Mathematical Education in Science and Technology, 31(6), 899-917.
McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D.A.Grouws (Ed.), Handbook of Research on mathematics teaching and learning, New York Macmillan, 575-596
Orton, A.; & Roper, T. (2000). Science and Mathematics: A Relationship in Need of Counselling?, Studies in Science Education. 35, 123-154.
Sazhin, S. S. (1998) Teaching Mathematics to Engineering Students. International Journal of Engineering Education, 14(2), 145-152
Schumacher, P. & Kennedy, K.T. (2008). Lessons Learned Concerning a Student Centered Teaching Style by University Mathematics Professors from Secondary School Educators. Education, 129(1), 102-109.
Semb, G. B., Ellis, J. A., & Araujo, J. (1993). Long-term memory for knowledge learned in school. Journal of Educational Psychology, 85(2), 305-316.
Sousa, D. A. (2000), How the Brain Learns, 2nd edition, Corwin Press: Thousand Oaks, CA.
Star, J. R. (2005). Re-conceptualizing procedural knowledge. Journal for Research in Mathematics Education, 36(5), 127-155.
Tall, D. (2001). Cognitive Development in Advanced Mathematics Using Technology. Mathematics Education Research Journal, 12(3), 196--218.
Townend, M. S. (2001). Integrating Case Studies in Engineering Mathematics: A response to SARTOR 3. Teaching in Higher Education, 6(2), 203-215.

How to cite this article

APA

Matic, L. J. (2014). Mathematical Knowledge of Non-mathematics Students and Their Beliefs about Mathematics. International Electronic Journal of Mathematics Education, 9(1), 13-24. https://doi.org/10.29333/iejme/278

Vancouver

Matic LJ. Mathematical Knowledge of Non-mathematics Students and Their Beliefs about Mathematics. INT ELECT J MATH ED. 2014;9(1):13-24. https://doi.org/10.29333/iejme/278

AMA

Matic LJ. Mathematical Knowledge of Non-mathematics Students and Their Beliefs about Mathematics. INT ELECT J MATH ED. 2014;9(1), 13-24. https://doi.org/10.29333/iejme/278

Chicago

Matic, Ljerka Jukic. "Mathematical Knowledge of Non-mathematics Students and Their Beliefs about Mathematics". International Electronic Journal of Mathematics Education 2014 9 no. 1 (2014): 13-24. https://doi.org/10.29333/iejme/278

Harvard

Matic, L. J. (2014). Mathematical Knowledge of Non-mathematics Students and Their Beliefs about Mathematics. International Electronic Journal of Mathematics Education, 9(1), pp. 13-24. https://doi.org/10.29333/iejme/278

MLA

Matic, Ljerka Jukic "Mathematical Knowledge of Non-mathematics Students and Their Beliefs about Mathematics". International Electronic Journal of Mathematics Education, vol. 9, no. 1, 2014, pp. 13-24. https://doi.org/10.29333/iejme/278