Ritualized Non-Mathematics in Drawing Curves
Abstract
This study aimed to investigate students’ mathematical discourse related to the concavity, turning points, and maximum and minimum used in describing graphs on derivative use materials. More specifically, the characteristics of the mathematical discourse based on the commognition perspective is the focus of this study. Data were collected from 70 students who were given assignments on describing function graphs. The results of the students’ assignment work are sorted. Every same answer is in one group. Likewise for different answers. Subjects were selected based on the two groups. Subjects who answered correctly and completely did not become research subjects. Furthermore, interviews were conducted with 11 selected students who were used as research subjects. A qualitative approach was used in this study. The results obtained from the 11 subjects interviewed were different discourses. The research findings revealed the existence of cognitive conflicts. The subject did not build a well-supported narrative. The researcher continued to explore the subject’s ideas and knowledge about the task of describing curves on the derivative application material. There was a misalignment in their task completion and interview results. So that communitive conflicts, especially in ritualized non-mathematics. This is based on the incorrect procedure/statement given by the subject. When completing a task, keywords must first be understood and used properly. Furthermore, using definitions of keywords that have been agreed upon by experts in discourse. In addition, aspects of visual mediators and endorsed narrative are also needed. So that communitive conflict can be overcome.
Keywords: commognitive; ritualized non-mathematical; discourse; curve.
Full Text:
PDFReferences
RADFORD L., & BARWELL R. Language in mathematics education research. In The second handbook of research on the psychology of mathematics education (pp. 275-313). Brill, 2016. https://doi.org/10.1007/978-94-6300-561-6_8
SFARD A. Bewitched by language: Questions on language for mathematics education research. In PLANAS N., MORGAN C., & SCHÜTTE M. (Eds.) Classroom research on mathematics and language: Seeing learners and teachers differently (pp. 41–59). Routledge/Taylor & Francis Group, 2021. https://doi.org/10.4324/9780429260889-4
SFARD A. Learning, discursive faultiness and dialogic engagement. In MERCER N., WEGERIF R., & MAJOR L. (Eds.) The Routledge International Handbook of Research on Dialogic Education. (pp.89–100). Routledge, 2019.
NACHLIELI T., & HEYD-METZUYANIM E. Commognitive conflicts as a learning mechanism towards explorative pedagogical discourse. Journal of Mathematics Teacher Education, 2022, 25: 347–369 https://doi.org/10.1007/s10857-021-09495-3
SFARD A. Commognition. In LERMAN S. (Ed.), Encyclopedia of Mathematics Education (pp. 91-101). International Publishing Springer Nature, 2020.
LAVIE I., STEINER A., & SFARD A. Routines we live by: From ritual to exploration. Educational Studies in Mathematics, 2019, 101(2): 153–176. https://doi.org/10.1007/s10649-018-9817-4
SFARD A. Ritual for Ritual, Exploration for Exploration or what Learners are Offered is What They Present Back to you in Return. In ADLER J., & SFARD A. (Eds.) Research for Educational Change: Transforming researchers' insights into improvement in mathematics teaching and learning (pp. 41-63). Routledge, 2016. https://doi.org/10.4324/9781315643236
SFARD A. On the Need for Theory of Mathematics Learning and the Promise of ‘Commognition’. In ERNEST P. (Ed.) ICME-13 Monographs. The Philosophy of Mathematics Education Today (pp. 219-228). Springer, Cham, 2018, https://doi.org/10.1007/978-3-319-77760-3_13
MPOFU S., & MUDALY V. Grade 11 Rural Learners Understanding of Functions: A Commognition Perspective. African Journal of Research in Mathematics, Science and Technology Education, 2020, 24(2): 156-168. https://doi.org/10.1080/18117295.2020.1798670
SZTAJN P., BORKO H., & SMITH T. Research on mathematics professional development. In CAI J. (Ed.) Compendium for Research in Mathematics Education. (pp. 793-823). Reston, VA: National Council of Teachers of Mathematics, 2017.
HEYD-METZUYANIM E., & COOPER J. When the problem seems answerable yet the solution is unavailable: affective, reactions around an impasse in mathematical discourse. International Journal of Research in Undergraduate Mathematics Education, 2022, 9(3): 605-63. https://doi.org/10.1007/s40753-022-00172-1
EMRE-AKDOGAN E., GÜÇLER B., & ARGÜN Z. The development of two high school students’ discourses on geometric translation in relation to the teacher’s discourse in the classroom. Eurasia Journal of Mathematics, Science and Technology Education, 2018, 14(5): 1605–1619. https://doi.org/10.29333/ejmste/84885
GRAVEN M., & HEYD-METZUYANIM, E. Mathematics identity research: the state of the art and future directions. ZDM Mathematics Education, 2019, 51: 361–377. https://doi.org/10.1007/s11858-019-01050-y
NACHLIELI T., & TABACH M. Ritual-enabling opportunities-to-learn in mathematics classrooms. Educational Studies in Mathematics, 2019, 101(2): 253–271. https://doi.org/10.1007/s10649-018-9848-x
LEFRIDA R., SISWONO T. Y. E., & LUKITO A. Exploring the Field-Independent Student’s in Understanding Derivative Concepts: A Case of Commognitive Perspective. Acta Scientiae, 2023, 25(3): 180-207, https://doi.org/10.17648/acta.scientiae.7097
AKÇAKOCA T., SAĞ G. Y., & ARGÜN Z. Rituals and explorations in students’ mathematical discourses: The case of polynomial inequalities. Participatory Educational Research, 2024, 11(1): 178-197. http://dx.doi.org/10.17275/per.24.11.11.1
HEYD-METZUYANIM E., SMITH M., BILL V., & RESNICK L. B. From ritual to explorative participation in discourse-rich instructional practices: A case study of teacher learning through professional development. Educational Studies in Mathematics, 2019, 101(2): 273-289. https://doi.org/10.1007/s10649-018-9849-9
ROGOVCHENKO S. Mathematical Modelling Problems in a Mathematics Course for Engineers: A Commognitive Perspective. In: LEUNG, F.K.S., STILLMAN, G.A., KAISER, G., WONG, K.L. (Eds.) Mathematical Modelling Education in East and West. International Perspectives on the Teaching and Learning of Mathematical Modelling. (pp. 561-570). Springer, Cham, 2021. https://doi.org/10.1007/978-3-030-66996-6_47
MERRIAM S.B., & TISDELL E.J. Qualitative Research: A Guide to Design and Implementation (4th ed). San Francisco, CA: Jossey-Bass, 2016.
STEWART J. Calculus: Early transcendentals, 8th ed. Cengage Learning, 2015.
MILES M. B., HUBERMAN A. M., & SALDANA J. Qualitative Data Analysis, 4th ed. Sage Publication, 2019.
BERGER M., & BOWIE L. A course on functions for in-service mathematics teachers: Changing the discourse. Education as Change, 2012, 16(2): 217-229. https://doi.org/10.1080/16823206.2012.745751
BACCAGLINI-FRANK A. To tell a story, you need a protagonist: how dynamic interactive mediators can fulfill this role and foster explorative participation to mathematical discourse. Educational Studies in Mathematics, 2021, 106(2): 291-312. https://doi.org/10.1007/s10649-020-10009-w
VARBERG D., PURCELL E.J., and RIGDON S. Calculus, 9th ed. Pearson Education, Inc., 2011.
TONG D.H., UYEN B.P., & QUOC N.V.A. The improvement of 10th students’ mathematical communication skills through learning ellipse topics. Heliyon, 2021, 7(11): e08282. https://doi.org/10.1016/j.heliyon.2021.e08282
AZIZAH N., DARMINTO B.P., & NUGRAHENI P. Analisis Miskonsepsi Siswa pada Materi Turunan Fungsi Aljabar dengan Menggunakan Four-Tier Test. Jurnal Pendidikan Sultan Agung, 2023, 3(1): 1-11. http://dx.doi.org/10.30659/jp-sa.v3i1.28873
TASARA I. Making sense of the teaching of calculus from a commognitive perspective. BERGQVIST E, ÖSTERHOLM M, GRANBERG C and SUMPTER L. (Eds.) Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education, 2018, 4: 267-274.
Refbacks
- There are currently no refbacks.