### Exploration of high school students' reasoning in solving trigonometric function problems

#### Abstract

Reasoning has been extensively studied by many experts. However, Research on student reasoning in trigonometric problem solving, particularly those related to logical thinking skills is still sorely needed. This study aimed to explore students' reasoning in solving trigonometric function problems regarding logical thinking skills. The research was conducted using a qualitative approach. The research subjects involved high school students in Palopo, Indonesia. Based on the logical ability test results, three subjects were selected, namely students with high, medium, and low logical abilities. Research instruments in mathematical problem-solving tasks and interview guidelines are valid and reliable. Data collection was carried out through task-based interviews and think-aloud. The results of the study: (1) the reasoning subjects with high and moderate logical abilities in solving trigonometric function problems are the same in every type of question, always starting with inductive reasoning and then doing deductive reasoning (2) the reasoning of subjects with high and medium logical abilities is different in solving trigonometric function problems in the initial identification. Subjects with low logical ability showed no mental activity in solving trigonometric function problems. The research finding is that the subject has a high logical ability and is solving trigonometric function problems first by inductive reasoning and then deductive reasoning. In general, it is concluded that students with high and moderate logical abilities use inductive and deductive thinking patterns interchangeably in solving trigonometric function problems.

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Adu-Gyamfi, K., & Bossé, M. J. (2014). Processes and reasoning in representations of linear functions. International Journal of Science and Mathematics Education, 12(1), 167–192.

Appel, G., Grewal, L., Hadi, R., & Stephen, A. T. (2020). The future of social media in marketing. Journal of the Academy of Marketing Science, 48(1), 79–95.

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology: Qualitative reaserch in psychology (Vol. 3). University of the West of England.

Čadež, T. H., & Kolar, V. M. (2018). How fifth-grade pupils reason about fractions: A reliance on part-whole subconstructs. Educational Studies in Mathematics, 99(3), 335–357.

Çekmez, E. (2020). What generalizations do students achieve with respect to trigonometric functions in the transition from angles in degrees to real numbers?. Journal of Mathematical Behavior, 58(1), 100778.

Choy, B. H., & Dindyal, J. (2018). An approach to teach with variations: Using typical problems. Avances de Investigacion En Educacion Matematica, 13, 21–38.

Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. In Educational Research (Vol. 4).

Elia, I., van den Heuvel-Panhuizen, M., & Kolovou, A. (2009). Exploring strategy use and strategy flexibility in non-routine problem solving by primary school high achievers in mathematics. ZDM - International Journal on Mathematics Education, 41(5), 605–618.

Ellis, A. B., Ozgur, Z., Vinsonhaler, R., Dogan, M. F., Carolan, T., Lockwood, E., Lynch, A., Sabouri, P., Knuth, E., & Zaslavsky, O. (2017). Student thinking with examples: The criteria-affordances-purposes-strategies framework. Journal of Mathematical Behavior, 53(3), 263-283.

Fiallo, J., & Gutiérrez, A. (2017). Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course. Educational Studies in Mathematics, 96(2), 145–167.

García, M., Llinares, S., & Sánchez-Matamoros, G. (2011). Characterizing thematized derivative schema by the underlying emergent structures. International Journal of Science and Mathematics Education, 9(5), 1023–1045.

Hohensee, C. (2016). Teachers’ awareness of the relationship between prior knowledge and new learning. Journal for Research in Mathematics Education, 47(1), 17–27.

Hwang, W. Y., Zhao, L., Shadiev, R., Lin, L. K., Shih, T. K., & Chen, H. R. (2020). Exploring the effects of ubiquitous geometry learning in real situations. Educational Technology Research and Development, 68(3), 1121–1147.

Ikram, M., Purwanto, Parta, I. N., & Susanto, H. (2020). Exploring the potential role of reversible reasoning: Cognitive research on inverse function problems in mathematics. Journal for the Education of Gifted Young Scientists, 8(1), 591–611.

Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1-16.

Job, P., & Schneider, M. (2014). Empirical positivism, an epistemological obstacle in the learning of calculus. ZDM - International Journal on Mathematics Education, 46(4), 635–646.

Kamber, D., & Takaci, D. (2018). On problematic aspects in learning trigonometry. International Journal of Mathematical Education in Science and Technology, 49(2), 161–175.

Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM - Mathematics Education, 49(6), 937–949.

Martín-Fernández, E., Ruiz-Hidalgo, J. F., & Rico, L. (2019). Meaning and understanding of school mathematical concepts by secondary students: The study of sine and cosine. Eurasia Journal of Mathematics, Science and Technology Education, 15(12), 1-16.

Martin, L. C., & Towers, J. (2016). Folding back , thickening and mathematical met-befores. Journal of Mathematical Behavior, 43, 89–97.

Mcgowen, M. A., & Tall, D. O. (2013). Flexible thinking and met-befores : Impact on learning mathematics. Journal of Mathematical Behavior, 32(3), 527–537.

Mejía-Ramos, J. P., & Weber, K. (2020). Using task-based interviews to generate hypotheses about mathematical practice: Mathematics education research on mathematicians’ use of examples in proof-related activities. ZDM - Mathematics Education, 52(6), 1099–1112.

Mesa, V., & Herbst, P. (2011). Designing representations of trigonometry instruction to study the rationality of community college teaching. ZDM - International Journal on Mathematics Education, 43(1), 41–52.

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook (Third Edit). SAGE Publications, Inc.

Misrom, N. B., Muhammad, A., Abdullah, A., Osman, S., Hamzah, M., & Fauzan, A. (2020). Enhancing students’ higher-order thinking skills (HOTS) through an inductive reasoning strategy using geogebra. International Journal of Emerging Technologies in Learning (iJET), 15(3), 156-179.

Moore, K. C. (2014a). Coherence, quantitative reasoning, and the trigonometry of students. Pressbook.

Moore, K. C. (2014b). Quantitative reasoning and the sine function: The case of zac. Journal for Research in Mathematics Education, 45(1), 102–138.

Moore, K. C., Paoletti, T., & Musgrave, S. (2013). Covariational reasoning and invariance among coordinate systems. Journal of Mathematical Behavior, 32(3), 461–473.

Nabie, M. J., Akayuure, P., Ibrahim-Bariham, U. A., & Sofo, S. (2018). Trigonometric concepts: Pre-service teachers’ perceptions and knowledge. Journal on Mathematics Education, 9(2), 169–182.

Norton, A., & D’Ambrosio, B. S. (2008). ZPC and ZPD: Zones of teaching and learning. Journal for Research in Mathematics Education, 39(3), 220–246.

Poon, K. K. (2012). Tour of a simple trigonometry problem. International Journal of Mathematical Education in Science and Technology, 43(4), 449–461.

Post, T. R., Medhanie, A., Harwell, M., Norman, K. W., Dupuis, D. N., Muchlinski, T., Andersen, E., & Monson, D. (2010). The impact of prior mathematics achievement on the relationship between high school mathematics curricula and postsecondary mathematics performance, course-taking, and persistence. Journal for Research in Mathematics Education, 41(3), 274–308.

Rivera, F. D., & Becker, J. R. (2016). Middle school students’ patterning performance on semi-free generalization tasks. Journal of Mathematical Behavior, 43, 53–69.

Rohimah, S. M., & Prabawanto, S. (2019). Student’s difficulty identification in completing the problem of equation and trigonometry identities. International Journal of Trends in Mathematics Education Research, 2(1), 34.

Sangwin, C. J., & Jones, I. (2017). Asymmetry in student achievement on multiple-choice and constructed-response items in reversible mathematics processes. Educational Studies in Mathematics, 94(2), 205–222.

Siyepu, S. W. (2013). An exploration of students ’ errors in derivatives in a university of technology. Journal of Mathematical Behavior, 32(3), 577–592.

Siyepu, S. W. (2015). Analysis of errors in derivatives of trigonometric functions. International Journal of STEM Education, 2(1), 16.

Studies, E. (2022). Upper secondary students ’ mathematical reasoning on a sinusoidal function, Educational Studies in Mathematics, 99(3), 277-291.

Syarifuddin, S., Nusantara, T., Qohar, A., & Muksar, M. (2020). Students’ thinking processes connecting quantities in solving covariation mathematical problems in high school students of Indonesia. Participatory Educational Research, 7(3), 59–78.

Tallman, M. A., & Frank, K. M. (2020). Angle measure, quantitative reasoning, and instructional coherence: an examination of the role of mathematical ways of thinking as a component of teachers’ knowledge base. Journal of Mathematics Teacher Education, 23(1), 69–95.

Vamvakoussi, X. (2017). Using analogies to facilitate conceptual change in mathematics learning. ZDM - Mathematics Education, 49(4), 497–507.

Walkington, C., Clinton, V., & Shivraj, P. (2018). How readability factors are differentially associated with performance for students of different backgrounds when solving mathematics word problems. American Educational Research Journal, 55(2), 362–414.

Wassie, Y. A., & Zergaw, G. A. (2018). Capabilities and contributions of the dynamic math software, geogebra---a review. North American GeoGebra Journal, 7(1), 68–86.

Weber, K. (2008). How mathematicians determine if an argument is a valid proof. Journal for Research in Mathematics Education, 39(4), 431–459.

DOI: http://dx.doi.org/10.24042/ajpm.v13i2.12972

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