Process-Oriented Routines of Students in Heterogeneous Field Dependent-Independent Groups: A Commognitive Perspective on Solving Derivative Tasks
Students are more likely to obtain correct solutions in solving derivative problems. Even though students can complete it correctly, they may not nece.
- Pub. date: October 15, 2021
- Pages: 2017-2032
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Students are more likely to obtain correct solutions in solving derivative problems. Even though students can complete it correctly, they may not necessarily be able to explain the solution well. Cognition and communication by the students will greatly affect the subsequent learning process. The aim of this study is to describe students’ commognition of routine aspects in understanding derivative tasks for heterogeneous groups of cognitive styles-field dependent and independent. This qualitative study involved six third-semester mathematics education students in the city of Palu, Indonesia. We divided the subjects into two groups with field-independent (FI) and field-dependent (FD) cognitive styles. The first group consisted of two FI students and one FD student, and the second group consisted of two FD students and one FI student. Moreover, the subjects also have relatively the same mathematical ability and feminine gender. Data was collected through task-based observations, focused group discussions, and interviews. We conducted data analysis in 3 stages, namely data condensation, data display, and conclusion drawing-verification. The results showed that the subjects were more likely to use routine ritual discourse, namely flexibility on the exemplifying category, by whom the routine is performed on classifying and summarizing categories, applicability on inferring category, and closing conditional on explaining category. The result of ritual routine is a process-oriented routine through individualizing. This result implies that solving the questions is not only oriented towards the correct answers or only being able to answer, but also students need to explain it well.
Keywords: Cognitive style, commognition, derivative, heterogenous groups, routines.
References
Anderson, W. L., & Krathwohl, D. R. (Eds.). (2001). A taxonomy for learning, teaching, and assessing: A Revision of Bloom’s taxonomy of educational objectives. (Abridged ed.). Addison Wesley Longman.
Armstrong, S. J., Peretson, E. R., & Rayner, S. G. (2012). Understanding and defining cognitive style and learning style: A Delphi study in the context of educational Psychology. Educational Studies, 38(4), 449–455. https://doi.org/10.1080/03055698.2011.643110
Bergqvist, E. (2007). Types of reasoning required in university exams in mathematics. The Journal of Mathematical Behavior, 26(4), 348–370. https://doi.org/10.1016/j.jmathb.2007.11.001
David, M. M., & Tomaz, V. S. (2012). The role of visual representations for structuring classroom mathematical activity. Educational Studies in Mathematics, 80, 413–431. https://doi.org/10.1007/s10649-011-9358-6
Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103–131. https://doi.org/10.1007/s10649-006-0400-z
Hiebert, J., & Carpenter, T. P. (1996). Learning and teaching with understanding. National Reston, Virginia Council of Teachers of Mathematics.
Kepner, M. D., & Neimark, E. D. (1984). Test-retest reliability and differential patterns of score change on the Group Embedded Figures Test. Journal of Personality and Social Psychology, 46(6), 1405-1431. https://doi.org/10.1037/0022-3514.46.6.1405
Lavie, I.,Steiner, A., & Sfard, A. (2019). Routines we live by: From ritual to exploration. Educational Studies Mathematics, 101, 53–176. https://doi.org/10.1007/s10649-018-9817-4
Lefrida, R., Siswono, T. Y. E., & Lukito, A. (2020). A commognitive study on field-dependent students’ understanding of derivative. Journal of Physics: Conference Series, 1747, 1-7. https://doi.org/10.1088/1742-6596/1747/1/012025
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis. Sage Publication, Inc.
Nachlieli, T., & Tabach, M. (2012). Growing mathematical objects in the classroom –The case of function. International Journal of Educational Research, 51-52, 10–27. https://doi.org/10.1016/j.ijer.2011.12.007
Nardi, E., Ryve, A., Stadler, E., & Viirman, O. (2014). Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of calculus. Research in Mathematics Education, 16(2), 182–198. https://doi.org/10.1080/14794802.2014.918338
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM
Ng, O. (2016). The interplay between language, gestures, dragging and diagrams in bilingual learners’ mathematical communications. Educational Studies Mathematics, 91, 307–326. http://doi.org/10.1007/s10649-015-9652-9
Ng, O. (2018). Examining technology-mediated communication using a commognitive lens: the case of touchscreen-dragging in dynamic. International Journal of Science and Mathematics Education. 17, 1173–1193. https://doi.org/10.1007/s10763-018-9910-2
Park, J. (2013). Is the derivative a function? If so, how do students talk about it? International Journal of Mathematical Education in Science and Technology, 44(5), 624–640. https://doi.org/10.1080/0020739X.2013.795248.
Piaget, J. (1952). The origins of intelligence of the child (M. Cook, Trans.). W W Norton & Co. https://doi.org/10.1037/11494-000
Riding, R. J., Glass, A., & Douglas, G. (1993). Individual differences in thinking: Cognitive and neurophysiological perspectives. Educational Psychology, 13(3&4), 267-280. https://doi.org/10.1080/0144341930130305
Robert, A., & Roux, K. (2018). A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equations. Pythagoras - Journal of the Association for Mathematics Education of South Africa, 40(1), 1-15. https://doi.org/10.4102/pythagoras.v40i1.438
Sfard, A. (2008). Thinking as communicating: Human development, development of discourses, and mathematizing. Cambridge University Press. https://doi.org/10.1017/CBO9780511499944
Sfard, A. (2020). Commognition. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 91-101). International Publishing Springer Nature. https://doi.org/10.1007/978-3-030-15789-0_100031
Tabach, M., & Nachlieli, T. (2016). Communicational perspectives on learning and teaching mathematics: Prologue. Educational Studies in Mathematics, 91(3), 299–306. https://doi.org/10.1007/s10649-015-9638-7
Tallman, M. A., Carlson, M. P., Bressoud, D. M., & Pearson, M. (2016). A characterization of calculus I final exams in US colleges and universities. International Journal of Research in Undergraduate Mathematics Education, 2(1), 105–133. https://doi.org/10.1007/s40753-015-0023-9.
Thoma, A., & Nardi, E. (2018). Transition from school to university mathematics: Manifestations of unresolved commognitive conflict in first year students’ examination scripts. International Journal of Research in Undergraduate Mathematics Education, 4, 161–180. https://doi.org/10.1007/s40753-017-0064-3
Varberg, D., Purcell, E. J., & Ridgon, S. (2010). Kalkulus (I. Nyoman, Trans.). Prentice Hall, Inc. (Original work published 2007)
Witkin, H. A., Oltman, P., Raskin, E., & Karp, S. (1971). A manual for the embedded figures test. Consulting Psychologists Press. https://doi.org/10.1037/t06471-000
Wittgenstein, L. (1953). Philosophical investigations: The German text, with a revised English translation (G.E.M. Anscombe, Trans). Blackwell Basil. (Original work published 1945)