Student’s Covariational Reasoning in Solving Covariational Problems of Dynamic Events

Sandie Sandie; Utin Desy Susiaty

doi:10.26737/jetl.v5i2.2092

Student’s Covariational Reasoning in Solving Covariational Problems of Dynamic Events

Sandie Sandie, Utin Desy Susiaty

Abstract

One of the reasons for learners to have poor covariational reasoning is because learners understand covariation to the extent that it is procedural, while conceptually it is not fully understood. The goal to be achieved is to describe the process of student covariational reasoning in constructing graphs. This research uses a qualitative approach. This type of research is qualitative research in which the main data is written and/or spoken words. The subjects in this study were odd semester students consisting of 3, 5, and 7 Mathematics Education Study Programs, Faculty of Mathematics, Natural Sciences and Technology IKIP-PGRI Pontianak. The research instrument consists of the main instrument, namely the researcher himself and the supporting instrument, namely the task of covariational problems in the form of a written test and interview guidelines. Data analysis by processing and preparing data from the assignment results to interpreting the data and making conclusions. This study examines the process of student covariational reasoning in solving dynamic incident problems. Students initially experience a pseudo error, however, along with the problem-solving process students can eliminate pseudo thinking that was initially experienced. Students have been able to solve covariational problems at Level 5, where these problems require students to be able to coordinate changes in the value of one variable against changes in the value of other variables. The problem at level 5 also requires students to be able to see changes in time and changes in water level that occur continuously by paying attention to the irregular shape of the bottle. The existence of the Covid-19 pandemic provides a limit for researchers in collecting data that should have been done directly online. This limits researchers to dig deeper into what students think in depth. The number of students who can solve this problem needs to pay attention to the IKIP PGRI Pontianak Institute to compile a curriculum or learning media that instils the concept of reasoning.

Keywords

Dynamic Events; Covariational; Covariational Reasoning

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References

Carlson, M. P. (1998). A cross-sectional investigation of the development of the function concept. CBMS Issues in Mathematics Education, 7, 114–162. https://doi.org/10.1090/cbmath/007/04

Carlson, M. P., Jacobs, S., Coe, E., Larsen, S., & Hsu, E. (2002). Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study. Journal for Research in Mathematics Education, 33(5), 352. https://doi.org/10.2307/4149958

Carlson, M. P., Madison, B., & West, R. D. (2015). A Study of Students’ Readiness to Learn Calculus. International Journal of Research in Undergraduate Mathematics Education, 1(2), 209–233. https://doi.org/10.1007/s40753-015-0013-y

Creswell, J. W. (2014). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (Fourth Edi; V. Knight, J. Young, K. Koscielak, B. Bauhaus, & M. Markanich, eds.). Washington, DC: SAGE Publication.

Dogbey, J. (2016). Using Variables in School Mathematics: Do School Mathematics Curricula Provide Support for Teachers? International Journal of Science and Mathematics Education, 14(6), 1175–1196. https://doi.org/10.1007/s10763-015-9643-4

Ellis, A. B., Ozgur, Z., Kulow, T., Dogan, M. F., & Amidon, J. (2016). An Exponential Growth Learning Trajectory: Students’ Emerging Understanding of Exponential Growth Through Covariation. Mathematical Thinking and Learning, 18(3), 151–181. https://doi.org/10.1080/10986065.2016.1183090

Ellis, A. B., Özgür, Z., Kulow, T., Williams, C. C., & Amidon, J. (2015). Quantifying exponential growth: Three conceptual shifts in coordinating multiplicative and additive growth. Journal of Mathematical Behavior, 39, 135–155. https://doi.org/10.1016/j.jmathb.2015.06.004

Fennel, F., & Rowan, T. (2001). Representation: An important process for teaching and learning mathematics. Teaching Children Mathematics, 7(5), 288–292.

Ferrari-Escolá, M., Martínez-Sierra, G., & Méndez-Guevara, M. E. M. (2016). “Multiply by adding”: Development of logarithmic-exponential covariational reasoning in high school students. Journal of Mathematical Behavior, 42, 92–108. https://doi.org/10.1016/j.jmathb.2016.03.003

Gyamfi, K. ., & Bosse, M. . (2013). Processes and Reasoning in Representations of Linear Functions. International Journal of Science and Mathematics Education, 12(1), 167–192. https://doi.org/10.1007/s10763-013-9416-x

Herbert, S., & Pierce, R. (2012). Revealing educationally critical aspects of rate. Educational Studies in Mathematics, 81(1), 85–101. https://doi.org/10.1007/s10649-011-9368-4

Johnson, H. L., McClintock, E., & Hornbein, P. (2017). Ferris wheels and filling bottles: a case of a student’s transfer of covariational reasoning across tasks with different backgrounds and features. ZDM - Mathematics Education, 49(6), 851–864. https://doi.org/10.1007/s11858-017-0866-4

Lobato, J., & Siebert, D. (2002). Quantitative reasoning in a reconceived view of transfer. Journal of Mathematical Behavior, 21(1), 87–116. https://doi.org/10.1016/S0732-3123(02)00105-0

Moore, K. C. (2014). Quantitative Reasoning and the Sine Function: The Case of Zac. Journal for Research in Mathematics Education, 45(1), 102. https://doi.org/10.5951/jresematheduc.45.1.0102

Moore, K. C., & Carlson, M. P. (2012). Students’ images of problem contexts when solving applied problems. Journal of Mathematical Behavior, 31(1), 48–59. https://doi.org/10.1016/j.jmathb.2011.09.001

Moore, K. C., Silverman, J., II, D. R. L., Musgrave, S., Paoletti, T., & LaForest, K. R. (2013). Pre-service teachers ’ meanings and non-canonical graphs. In M. Martines & A. Castro Superfine (Eds.), Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 441–448). Retrieved from http://pmena.org/2013/proceedings.html

Moore, K. C., Stevens, I. E., Paoletti, T., Hobson, N. L. F., & Liang, B. (2019). Pre-service teacher’s figurative and operative graphing actions. The Journal of Mathematical Behavior. https://doi.org/10.1016/j.jmathb.2019.01.008

Paoletti, T., & Moore, K. C. (2017). The parametric nature of two students’ covariational reasoning. Journal of Mathematical Behavior, 48(April), 137–151. https://doi.org/10.1016/j.jmathb.2017.08.003

Polya, G. (1973). How to Solve it: A New Aspect of Mathematical Method (2nd ed.). Princeton, New Jersey: Princeton University Press.

Saldanha, L. A., & Thompson, P. W. (1998). Re-thinking covariation from a quantitative perspective: simultaneous continuous variation. In S. B. Berensah & W. N. Coulombe (Eds.), Proceedings of the Annual Meeting of the Psychology of Mathematics Education - North America. Raleigh, NC: North Carolina State University.

Sandie, Purwanto, Subanji, & Hidayanto, E. (2019a). Student Difficulties when Constructing a Hidden Bridge to Solve Dynamic Event Problems. In Habiddin, S. Majid, S. Ibnu, N. Farida, & I. W. Dasna (Eds.), The 3rd International Conference on Mathematics and Sciences Education (ICoMSE) 2019 (pp. 0600261–0600265). Malang: AIP Publishing.

Sandie, S., Purwanto, P., Subanji, S., & Hidayanto, E. (2019b). Student difficulties in solving covariational problems. International Journal of Humanities and Innovation (IJHI), 2(2), 25–30. https://doi.org/10.33750/ijhi.v2i2.38

Subanji. (2007). Proses Berpikir Penalaran Kovariasional Pseudo dalam Mengonstruksi Grafik Fungsi Kejadian Dinamik Berkebalikan. Surabaya.

Subanji. (2011). Teori Berpikir Pseudo Penalaran Kovariasional. Malang, Indonesia: UM Press.

Thompson, P. W. (1994). Students, functions, and the undergraduate curriculum. In E. Dubinsky, A. H. Schoenfeld, & J. J. Kaput (Eds.), Research in Collegiate Mathematics Education, 4, 21–44. https://doi.org/10.2307/2687592

Thompson, P. W., & Carlson, M. P. (2017). Variation, Covariation and Functions: Foundation ways of thinking mathematically. Compendium for Research in Mathematics Education, (January), 421–456.

Thompson, P. W., Hatfield, N. J., Yoon, H., Joshua, S., & Byerley, C. (2017). Covariational reasoning among U.S. and South Korean secondary mathematics teachers. Journal of Mathematical Behavior, 48(August), 95–111. https://doi.org/10.1016/j.jmathb.2017.08.001

Weber, E., & Thompson, P. W. (2014). Students’ images of two-variable functions and their graphs. Educational Studies in Mathematics, 87(1), 67–85. https://doi.org/10.1007/s10649-014-9548-0

Wilkie, K. J. (2019). Investigating Students’ Attention to Covariation Features of their Constructed Graphs in a Figural Pattern Generalisation Context. International Journal of Science and Mathematics Education, 47–49. https://doi.org/10.1007/s10763-019-09955-6

Yemen-Karpuzcu, S., Ulusoy, F., & Işıksal-Bostan, M. (2015). Prospective Middle School Mathematics Teachers’ Covariational Reasoning for Interpreting Dynamic Events During Peer Interactions. International Journal of Science and Mathematics Education, 15(1), 89–108. https://doi.org/10.1007/s10763-015-9668-8

DOI: http://dx.doi.org/10.26737/jetl.v5i2.2092

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