Commognitive View: Analysis Of Students' Work Results In Using Definite Integrals To Solve Contextual Problems

Endrayana Putut Laksminto Emanuel; Herfa Maulina  Dewi Soewardini; Meilantifa

doi:10.46306/jurinotep.v4i2.189

Authors

Endrayana Putut Laksminto Emanuel Universitas Wijaya Kusuma Surabaya
Herfa Maulina Dewi Soewardini Universitas Wijaya Kusuma Surabaya
Meilantifa Universitas Wijaya Kusuma Surabaya

DOI:

https://doi.org/10.46306/jurinotep.v4i2.189

Keywords:

tennis, service ability, junior athletes, Manonjaya Tennis Club.

Abstract

The purpose of this study is to describe students’ commognitive processes when solving contextual problems on definite integrals related to the area between curves. The research method was carried out through several stages, namely preparation, data collection, analysis, and drawing conclusions. The research subjects were ten students from a private university in Indonesia who were asked to solve a contextual mathematics problem within 30 minutes, specifically on definite integrals to determine the area bounded by two curves. Based on their work, one student was selected as the main subject to be analyzed using a commognitive approach and interviewed in depth to obtain more detailed information. The results of the study showed that the subject was able to translate the problem statements into mathematical form accurately. The subject was also able to use mathematical terms and symbols correctly (words use), illustrate the given conditions into graphs appropriately (visual mediators), and apply problem-solving steps systematically based on prior knowledge (routines). In addition, the subject was able to draw correct conclusions supported by valid mathematical arguments. Based on these findings, it can be concluded that students are capable of solving contextual mathematics problems successfully. Furthermore, it is expected that students can improve their understanding of course materials so that they are able to solve given problems more optimally and support the achievement of learning objectives.

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References

Aini, F. N., Emanuel, E. P. L., & Chamidah, A. (2021). Efektivitas Penerapan Model Blended Learning Berbasis Google Classroom Ditinjau Dari Motivasi Belajar Dan Hasil Belajar Siswa Pada Pokok Bahasan Trigonometri Kelas XI IPA-1 SMA Hang Tuah 4 Surabaya. Briliant: Jurnal Riset Dan Konseptual, 6(2), 303. https://doi.org/10.28926/briliant.v6i2.629

Çelik Demirci, S., & Baki, A. (2023). Characterizing mathematical discourse according to teacher and student interactions: The core of mathematical discourse. Journal of Pedagogical Research, 7(4), 144–164. https://doi.org/10.33902/JPR.202321852

Chikiwa, C., & Schäfer, M. (2018). Promoting critical thinking in multilingual mathematics classes through questioning. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/91832

Cresswel, J. (2013). Qualitative, quantitative, and mixed methods approaches. In Research design. https://doi.org/10.2307/3152153

Emanuel, E. P.L., Kirana, A., & Chamidah, A. (2021). Enhancing students’ ability to solve word problems in Mathematics. Journal of Physics: Conference Series, 1832(1). https://doi.org/10.1088/1742-6596/1832/1/012056

Emanuel, Endrayana Putut Laksminto, Meidiana, Y. G., & Suhartono. (2021). Studi Komparasi Penggunaan Google Meet Dan Whatsapp Group Terhadap Hasil Belajar Siswa SMA Hangtuah 4 Surabaya. Briliant: Jurnal Riset Dan Konseptual, 6(4), 849–853.

Emanuel, Endrayana Putut Laksminto, & Meilantifa. (2022). Dimanakah Nilai Ekstrim Fungsi Kuadrat Ditinjau dari Lensa Commognitive ? BRILIANT Jurnal Riset Dan Konseptual, 7(54), 269–279.

Erikson, M. G., & Erikson, M. (2019). Learning outcomes and critical thinking–good intentions in conflict. Studies in Higher Education. https://doi.org/10.1080/03075079.2018.1486813

Fajriyah, E., Mulyono, & Asikin, M. (2019). Mathematical Literacy Ability Reviewed from Cognitive Style of Students on Double Loop Problem Solving Model with RME Approach. Unnes Journal of Mathematics Education Research, 8(1), 57–64. Retrieved from https://journal.unnes.ac.id/sju/index.php/ujmer/article/view/26959

Firdaus, F., Kailani, I., Bakar, M. N. Bin, & Bakry, B. (2015). Developing Critical Thinking Skills of Students in Mathematics Learning. Journal of Education and Learning (EduLearn), 9(3), 226. https://doi.org/10.11591/edulearn.v9i3.1830

Heinrich, W. F., Habron, G. B., Johnson, H. L., & Goralnik, L. (2015). Critical Thinking Assessment Across Four Sustainability-Related Experiential Learning Settings. Journal of Experiential Education. https://doi.org/10.1177/1053825915592890

Heyd-Metzuyanim, E., & Tabach, M. (2018). The commognitive theory framework: From theory to implementation. In K-12 Mathematics Education In Israel: Issues and Innovations. https://doi.org/10.1142/9789813231191_0038

Ioannou, M. (2018). Commognitive analysis of undergraduate mathematics students’ first encounter with the subgroup test. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-017-0222-6

Jones, T. (2017). Playing Detective to Enhance Critical Thinking. Teaching and Learning in Nursing. https://doi.org/10.1016/j.teln.2016.09.005

Kim, D.-J., Choi, S., Lim, W., Thoma, A., Nardi, E., Viirman, O., … Sfard, A. (2019a). Discourses of Functions – University Mathematics Teaching Through a Commognitive Lens. Educational Studies in Mathematics.

Kim, D.-J., Choi, S., Lim, W., Thoma, A., Nardi, E., Viirman, O., … Sfard, A. (2019b). Discourses of Functions – University Mathematics Teaching Through a Commognitive Lens. Educational Studies in Mathematics, 8(2), 423–430. https://doi.org/10.1007/s10649-015-9676-1

Lu, J., Zhang, X., & Stephens, M. (2019). Visualizing the commognitive processes in computer-supported one-to-one tutoring. Interactive Learning Environments. https://doi.org/10.1080/10494820.2019.1610452

Nachlieli, T., & Heyd-Metzuyanim, E. (2021). Commognitive conflicts as a learning mechanism towards explorative pedagogical discourse. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-021-09495-3

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. https://doi.org/10.1080/14794802.2014.918338

Pratiwi, E., Nusantara, T., Susiswo, S., & Muksar, M. (2020). Textual and contextual commognitive conflict students in solving an improper fraction. Journal for the Education of Gifted Young Scientists. https://doi.org/10.17478/jegys.678528

Presmeg, N. (2016). Commognition as a lens for research. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-015-9676-1

Putut, E., Emanuel, L., & Anam, F. (2022). Sebuah Tinjauan Commognitive : Apakah Matriks Singular ? BRILIANT Jurnal Riset Dan Konseptual, 7(54), 922–930. https://doi.org/http://dx.doi.org/10.28926/briliant.v7i4.1073

Putut, E., Emanuel, L., Nusantara, T., & Rahardi, R. (2024). Does Domain of Absolute Value Function Always Positive ? Commognitive-Conflict Analysis of Students of First Semester. Qalamuna: Jurnal Pendidikan, Agama, Dan Sosial, 16(2), 795–806. https://doi.org/10.37680/qalamuna.v16i2.5169

Putut, E., Emanuel, L., Nusantara, T., Rahman, A., & Rahardi, R. (2023). Why am I confused ? Commognitive Conflict in Non-ordinary Question About Number Division. Journal for ReAttach Therapy and Developmental Diversities, 6(5s), 891–901. Retrieved from https://jrtdd.com/index.php/journal/article/view/644

Roberts, A., & le Roux, K. (2018). A commognitive perspective on Grade 8 and Grade 9 learner thinking about linear equations. Pythagoras. https://doi.org/10.4102/pythagoras.v40i1.438

Schüler-Meyer, A. (2019). How Do Students Revisit School Mathematics in Modular Arithmetic? Conditions and Affordances of the Transition to Tertiary Mathematics with a Focus on Learning Processes. International Journal of Research in Undergraduate Mathematics Education, 5(2), 163–182. https://doi.org/10.1007/s40753-019-00088-3

Scott, D., Hargreaves, E., & Sfard, A. (2015). Learning, Commognition and Mathematics. In The SAGE Handbook of Learning. https://doi.org/10.4135/9781473915213.n12

Sfard, A. (2008). Thinking as Communicating. In Thinking as Communicating. https://doi.org/10.1017/cbo9780511499944

Sfard, A. (2018). Commognition. In Encyclopedia of Mathematics Education. https://doi.org/10.1007/978-3-319-77487-9_100031-1

Sudarsana, I. K., Nakayanti, A. R., Sapta, A., Haimah, Satria, E., Saddhono, K., … Mursalin, M. (2019). Technology Application in Education and Learning Process. Journal of Physics: Conference Series, 1363(1). https://doi.org/10.1088/1742-6596/1363/1/012061

Thoma, A., & Nardi, E. (2016). Routines in the didactical and mathematical discourses of closed-book examination tasks A commognitive analysis of closed-book examination tasks and lecturers’ perspectives. First Conference of International Network for Didactic Research in University Mathematics.

Thoma, A., & Nardi, E. (2017). Discursive shifts from school to university mathematics and lecturer assessment practices: Commognitive conflicts regarding variables. Proceedings of the 10th Congress of the European Society for Research in Mathematics Education.

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. https://doi.org/10.1007/s40753-017-0064-3

Toscano, R., Gavilán-Izquierdo, J. M., & Sánchez, V. (2019). A study of pre-service primary teachers’ discourse when solving didactic-mathematical tasks. Eurasia Journal of Mathematics, Science and Technology Education, 15(11). https://doi.org/10.29333/ejmste/108631

Tuset, G. A. (2018). A commognitive lens to study pre-service teachers ’ teaching in the context of achieving a goal of ambitious mathematics teaching. Proceeding, Congress of the European Society for Research in Mathematics Education.

Viirman, O. (2015). Explanation, motivation and question posing routines in university mathematics teachers’ pedagogical discourse: a commognitive analysis. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2015.1034206

Viirman, O., & Nardi, E. (2019). Negotiating different disciplinary discourses: biology students’ ritualized and exploratory participation in mathematical modeling activities. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-018-9861-0

Widana, I. W. (2018). Higher Order Thinking Skills Assessment towards Critical Thinking on Mathematics Lesson. International Journal of Social Sciences and Humanities (IJSSH). https://doi.org/10.29332/ijssh.v2n1.74

Witness, S., Monwabisi, S., & Ralarala, K. (2014). Making Sense of Mathematical Discourse: Implications for Success in the Learning of Differentiation in a University Classroom. Alternation Special Edition No, 12(12), 326–357.

Yazar Soyadı, B. B. (2015). Creative and Critical Thinking Skills in Problem-based Learning Environments. Journal of Gifted Education and Creativity. https://doi.org/10.18200/jgedc.2015214253