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

Year 2014, Volume: 1 , 124 - 134, 01.09.2014

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.

References

  • 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.
Year 2014, Volume: 1 , 124 - 134, 01.09.2014

Abstract

References

  • 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.
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Details

Journal Section Articles
Authors

Ljerka Jukić Matıć

Publication Date September 1, 2014
Published in Issue Year 2014 Volume: 1

Cite

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.