TY - JOUR TT - NON-MATHEMATICS STUDENTS’ REASONING IN NON-ROUTINE CALCULUS TASKS AU - Matıć, Ljerka Jukić PY - 2014 DA - May JF - The Eurasia Proceedings of Educational and Social Sciences JO - EPESS PB - ISRES Publishing WT - DergiPark SN - 2587-1730 SP - 124 EP - 134 VL - 1 KW - Calculus KW - reasoning KW - non-mathematics students N2 - This paperinvestigates reasoning of first year non-mathematics students in non-routinecalculus tasks. The students in this study were accustomed to imitative reasoning duringtheir schooling in primary and secondary education. In order tomove from imitative reasoning toward more creative reasoning, the non-routinetasks were implemented as the part of the calculus course. Using qualitativestrategy in a form of interview, we examined reasoning of six students in themiddle of the calculus course and at the end of the course. Analyzed datashowed that creative reasoning develops slowly even when students are exposedto the non-routine tasks. Also, we have found several negative met-befores andmet-afters affecting students’ knowledge and interfering with the reasoningprocess. CR - 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. UR - https://dergipark.org.tr/en/pub/epess/article/333367 L1 - https://dergipark.org.tr/en/download/article-file/332879 ER -