Textual and Contextual Commognitive Conflict Students in Solving an Improper Fraction

Year 2020, , 731 - 742, 15.06.2020

Enditiyas Pratiwi , Toto Nusantara , Susiswo Susiswo , Makbul Muksar

https://doi.org/10.17478/jegys.678528

Abstract

Commognitive conflict occurs when there are differences in the use of discourse by the interlocutor and becomes a challenge in mathematical communication. For sources of commognitive conflict that have not yet been discussed, therefore the purpose of this study was to reveal source of students’ commognitive conflict in solving problems. This research was to determine the source of the commognitive conflict experienced by first-year students in solving mathematical problems, that is, improper fraction. Commognitve characteristics used in this study are word uses, visual mediators, narratives, and routines. A total of 38 students were given a math problem sheet, and two students were chosen as research participants because they had different and interesting answers. Then the participants participated in a semi-structured in-depth interview to find out the factors that cause commognitive conflict. The results of the research shown that the source of commognitive conflict lies in visual mediators and narratives produced by participants. The visual mediators that are produced should be interpreted contextually, but the indicators undergo a shift in meaning into the textual in the minds of participants.

Keywords

commognitive conflict, commognitive framework, improper fraction, mathematics problem-solving, thinking process

References

• As'ari, A.R., Kurniati, D., Abdullah, A.H., Muksar, M., & Sudirman, S. (2019). Impact of Infusing Truth Seeking and Open-Minded Behaviors on Mathematical Problem-Solving. Journal of the Education of Gifted Young Scientists, 7(4), 1019-1036. DOI: http://dx.doi.org/10.17478/jeygs.606031
• Berger, M., & Bowie, L. (2012). A course of function for in-service mathematics teachers: Changing the discourse. Education as Change, 16(2), 217-229. https://doi.org/10.1080/16823206.2012.745751
• Berger, M. (2013). Examining mathematical discourse to understand in-service teachers’ mathematical activity. Pythagoras, 34(1), 1-10. https://doi.org/10.4102/pythagoras.v34i1.197
• Hackenberg, A. J. (2007). Units coordination and the construction of improper fraction: A revision of the splitting hypothesis. Journal of Mathematical Behavior, 26(2007), 27-47. Doi: 10.1016/j.jmathb.2007.03.002
• Heyd-Metzuyanim, E. (2015). Vicious cycles of identifying and mathematizing: A case study of the development of mathematical failure. Journal of the Learning Science, 24(4), 504-549. https://doi.org/10.1080/10508406.2014.999270
• Ioannou, M. (2016). A commognitive analysis of mathematics undergraduates’ responses to a commutativity verification Group Theory task. Proceeding of the first conference of international network for didactic research in university mathematics. France: University of Montpellier and INDRUM.
• Ioannou, M. (2017). Investigating the discursive shift in the learning of Group Theory: Analysis of some interdiscursive commognitive conflicts. CERME 10, Feb 2017, Dublin, Ireland. hal-01941352
• Ioannou, M. (2018). Commognitive analysis of undergraduate mathematics students’ first encounter with the subgroup test. Mathematics Education Research Journal, 30(2), 117-142. https://doi.org/10.1007/s13394-017-0222-6
• Kieran, C., Forman, E., & Sfard, A. (Eds). (2002). Learning discourse: Discursive approach to research in mathematics education. Kluwer Academic, Dordrecht.
• Lee, G., & Byun, T. 2011. An explanation for the difficulty of leading conceptual change using a counterintuitive demonstration: The relationship between cognitive conflict and responses. Research in Science Education, 42(5), 943-965. https://doi.org/10.1007/s11165-011-9234-5
• Nachlieli, T., & Tabach, M. (2012). Growing mathematical objects in the classroom – the case of function. International Journal Educational Research, 51-52, 10-27. http://doi.org/10.1016/j.ijer.2011.1.2.007
• 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. http://dx.doi.org/10.1080/14794802.2014.918338
• Olive, J., & Steffe, L.P. (2001). The construction of an iterative fractional scheme: The case of Joe. The Journal of Mathematical Behavior, 20, 413-437. Doi:10.1016/s0732-3123(02)00086-x
• Pratiwi, E., Nusantara, T., Susiswo, S., Muksar, M., & Subanji, S. (2019). Characteristic of students' cognitive conflict in solving a problem based on information processing theory. International Journal of Learning, Teaching and Educational Research, 18(2), 76-88. https://doi.org/10.26803/ijlter.18.2.6
• Pratiwi, E., Nusantara, T., Susiswo, S., & Muksar, M. (2019). Students' thinking process when experiencing cognitive conflict. International Journal of Innovation, Creativity and Change, 9(2), 6-16.
• Rabin, J.M., Fuller, E., & Harel, G. (2013). Double negative: The necessity principle, commognitive conflict, and negative number operations. Journal of Mathematical Behaviour, 32(3), 649-659. http://dx.doi.org/10.1016/j.jmathb.2013.08.001
• Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46, 13-57. https://doi.org/10.1023/A:1014097416157
• Sfard, A., & Kieran, C. (2001). Cognition as communication: Rethinking learning-by talking through multi-faceted analysis of students’ mathematical interactions. Mind, Culture, and Activity, 8(1), 42-76. http://dx.doi.org/10.1207/S15327884MCA0801_04
• Sfard, A. (2007) When the rules of discourse change, but nobody tells you: Making sense of mathematics learning from a commognitive standpoint. The Journal of the Learning Sciences, 16(4), 565-613. https://doi.org/10.1080/10508400701525253
• Sfard, A. (2008). Thinking as communication: Human development, development of discourse, and mathematizing. Cambridge University Press, New York.
• Sfard, A. (2018). On the need for theory of mathematics learning and the promise of ‘commognition’. The Philosophy of Mathematics Education Today, 219-228. https://doi.org/10.1007/978-3-319-77760-3_13
• Smith, J.A. (2017). Textual analysis. The International Encyclopedia of Communication Research Methods, 1-7. doi:10.1002/9781118901731.iecrm0248
• Steffe, L.P. (2002). A new hypothesis concerning children’s fractional knowledge. Journal of Mathematical Behavior, 20, 267-307. Doi:10.1016/S0732-3123(02)00075-5
• Suprapto, D. (2010). Contextual Meaning Study of Translation of Children’s Story “The Lion King” from English into Indonesian. Lingua Cultura, 4(1), 1-11.
• Thoma, A., & Nardi, E. (2016). A commognitive analysis of closed-book examination tasks and lecturers’ perspectives. In E. Nardi, C. WinslØw, & T. Hausberger (Eds), Proceedings of the first conference of the international network for didactic research in university mathematics (pp. 306-315). France: University of Montpellier and INDRUM.
• Thoma, A., & Nardi, E. (2017). Discursive shifts from school to university mathematics and lecturer assessment practices: Commognitive conflict regarding variables. CERME 10, Feb 2017, Dublin, Ireland. hal-01941310
• 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(1), 161-180. https://doi.org/10.1007/s40753-017-0064-3
• Tzur, R. (1999). An intergrated study of children’s construction of improper fraction and the teacher’s role in promoting that learning. Journal for Research in Mathematics Education, 30(4), 390-416. Doi: 10.2307/749707
• Viirman, O. (2011). Discourse of Function: University Mathematics Teaching Through a Commognitive Lens. In M. Pytlak, T. Rowland, & E. Soboda (Eds). Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp.2103-2112). Rzeszów, Poland: University of Rzeszów.
• Zayyadi, M., Nusantara, T., Subanji, S., Hidayanto, E., & Sulendra, I. M. (2019). A commognitive framework: The process of solving mathematical problems of middle school students. International Journal of Learning, Teaching and Educational Research, 18(2), 88-102. https://doi.org/10.26803/ijlter.18.2.7
• Zayyadi, M., Nusantara, T., Hidayanto, E., Sulendra, I. M., & Sa’dijah, C. (2020). Content and Pedagogical Knowledge of Prospective Teachers in Mathematics Learning: Commognitive Framework. Journal for the Education of Gifted Young Scientists, 8(1), 515-532. DOI: http://dx.doi.org/10.17478/jegys.642131