Research Article

NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS

Volume: 1 September 1, 2014
EN

NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS

Abstract

This paper investigates reasoning of first year non-mathematics students in non-routine calculus tasks. The students in this study were accustomed to imitative reasoning during their schooling in primary and secondary education. In order to move from imitative reasoning toward more creative reasoning, the non-routine tasks were implemented as the part of the calculus course. Using qualitative strategy in a form of interview, we examined reasoning of six students in the middle of the calculus course and at the end of the course. Analyzed data showed that creative reasoning develops slowly even when students are exposed to the non-routine tasks. Also, we have found several negative met-befores and met-afters affecting students’ knowledge and interfering with the reasoning process.

Keywords

References

  1. Arksey, H., & Knight, P. (1999). Interviewing for social scientists. London: Sage. Bergqvist, E. (2007). Types of reasoning required in university exams in mathematics. Journal of Mathematical Behavior, 26(4) 348-370. Bergqvist, E. (2012). University mathematics teachers' views on the required reasoning in calculus exams. The Montana Mathematics Enthusiast, 9(3), 371-408 Boesen, J., Lithner, J., & Palm T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75 (1), 89-105 Chinnappan M., Dinham S., Herrington A., & Scott, D. (2007). Year 12 students and Higher Mathematics: Emerging issues, AARE 2007 International education research conference Cox, W. (1994). Strategic learning in a-level mathematics? Teaching Mathematics and its Applications, 13, 11–21. Ericsson, K., & Simon, H. (1993). Protocol analysis: Verbal reports as data. Cambridge: MIT Press. Haavold, P. (2010). What characterizes high achieving students' mathematical reasoning? In The elements of creativity and giftedness in mathematics. Sense Publisher Hiebert, J. (2003). What research says about the NCTM standards. In Kilpatrick, J., Martin, G., & Schifter, D. (eds) A Research Companion to Principles and Standards for School Mathematics, pp 5-26. Reston Va., National Council of Teachers of Mathematics. Jukić Matić, Lj. (2013). Non-mathematics students’ knowledge and their beliefs about mathematics (under review) Lima R.N. de, & Tall D. (2008). Procedural embodiment and magic in linear equations. Educational Studies in Mathematics, 67(1), 3-18. Lithner, J. (2003). Students’ mathematical reasoning in university textbook exercises. Educational Studies in Mathematics, 52, 29–55. Lithner, J. (2004). Mathematical reasoning in calculus textbook exercises. Journal of Mathematical Behavior, 23, 405–427. Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics 67(3). Lithner, J. (2012). University mathematics students’ learning difficulties, Education Inquiry, 2(2), 289-303 McGowen, M., & Tall, D. (2010). Metaphor or Met-before? The effects of previous experience on the practice and theory of learning mathematics. Journal of Mathematical Behavior, 29, 169--179. McNeal, B. (1995). Learning not to think in a textbook-based mathematics class. Journal of Mathematical Behavior 14 18–32. Niss, M. A. (2003). Quantitative literacy and mathematical competencies. In B. L. Madison, & L. A. Steen (Eds.), Quantitative literacy: why numeracy matters for schools and colleges. (pp. 215-220). Princeton: National Council on Education and the Disciplines. Schoenfeld, A H. (1991). On mathematics as sense-making: An informal attack on the unfortunate divorce of formal and informal mathematics. In J. Voss, D. Perkins, and J. Segal, editors, Informal Reasoning and Education, pages 311–344. Hillsdale, NJ: Lawrence Erlbaum Associates Schoenfeld, A. (1985). Mathematical problem solving. Orlando, FL: Academic Press. Selden, J., Mason, A., & Selden, A. (1998). Can Average Calculus Students Solve Nonrutine Problems? Journal of Mathematical Behavior, 8, 45-50. Tall, D. (1997). Functions and Calculus. In A. J. Bishop et al (Eds.), International Handbook of Mathematics Education, 289–325, Dordrecht: Kluwer. Tall, D. (2006). A Theory of Mathematical Growth through Embodiment, Symbolism and Proof, Annales de Didactique et de Sciences Cognitives, IREM de Strasbourg, 11, pp. 195-215.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Publication Date

September 1, 2014

Submission Date

August 7, 2017

Acceptance Date

-

Published in Issue

Year 2014 Volume: 1

APA
Matıć, L. J. (2014). NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS. The Eurasia Proceedings of Educational and Social Sciences, 1, 124-134. https://izlik.org/JA79UP55AZ
AMA
1.Matıć LJ. NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS. EPESS. 2014;1:124-134. https://izlik.org/JA79UP55AZ
Chicago
Matıć, Ljerka Jukić. 2014. “NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS”. The Eurasia Proceedings of Educational and Social Sciences 1 (May): 124-34. https://izlik.org/JA79UP55AZ.
EndNote
Matıć LJ (May 1, 2014) NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS. The Eurasia Proceedings of Educational and Social Sciences 1 124–134.
IEEE
[1]L. J. Matıć, “NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS”, EPESS, vol. 1, pp. 124–134, May 2014, [Online]. Available: https://izlik.org/JA79UP55AZ
ISNAD
Matıć, Ljerka Jukić. “NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS”. The Eurasia Proceedings of Educational and Social Sciences 1 (May 1, 2014): 124-134. https://izlik.org/JA79UP55AZ.
JAMA
1.Matıć LJ. NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS. EPESS. 2014;1:124–134.
MLA
Matıć, Ljerka Jukić. “NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS”. The Eurasia Proceedings of Educational and Social Sciences, vol. 1, May 2014, pp. 124-3, https://izlik.org/JA79UP55AZ.
Vancouver
1.Ljerka Jukić Matıć. NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS. EPESS [Internet]. 2014 May 1;1:124-3. Available from: https://izlik.org/JA79UP55AZ