Restructuring the Mathematical Power of Students and Teachers: A Case Study in the Misconceptions of Parallelogram Teaching
Abstract
Abstract: Restructuring the Mathematical Power of Students and Teachers: A Case Study in the Misconceptions of Parallelogram Teaching. Objectives: This research aims to (a) investigate cases of misconceptions about understanding parallelograms in mathematics learning and (b) restructure the mathematical power of teachers and students in understanding the concept of parallelograms. Methods: This research is a case study that analyzes in-depth cases of misconceptions in parallelogram learning. The data collection methods are surveys and interviews. This survey involved 120 students and ten teachers as respondents. In the final data analysis, the researcher conducted confirmation and triangulation to ensure the credibility of the findings and conclusions. Findings: The study's findings indicate ontological misconceptions about parallelograms in mathematics learning in elementary and high schools. Students and teachers experience two types of misconceptions, namely preconception errors and modeling errors. Conclusion: The conclusion states that students and teachers have successfully corrected misconceptions through knowledge or mathematical power restructuring so that students and teachers can understand the concept of parallelograms. The process of restructuring mathematical power is characterized by cognitive conflict, scaffolding, and cognitive balance in their thinking processes (teachers and students). The implication is that teachers must correctly instill conceptual knowledge about parallelograms through project-based or inquiry-based learning strategies so that students can build their knowledge based on their learning experiences.
Keywords: case study, mathematical power, misconception, parallelogram.
DOI: http://dx.doi.org/10.23960/jpp.v14.i2.202486
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Aithal, A., & Aithal, P. S. (2020). Development and validation of survey questionnaire and experimental data – A systematical review-based statistical approach. International Journal of Management, Technology, and Social Sciences, 5(2), 233–251. https://doi.org/10.47992/ijmts.2581.6012.0116
Biber, A. Ç., Tuna, A., Daǧdelen, I., & Kepceoǧlu, I. (2019). Students' levels of recognition of parallelogram and establishment of connections. Journal of Curriculum and Teaching, 8(3), 1–14. https://doi.org/10.5430/jct.v8n3p1
Çelik, H. C., & Özdemir, F. (2020). Mathematical thinking as a predictor of critical thinking dispositions of pre-service mathematics teachers. International Journal of Progressive Education, 16(4), 81–98. https://doi.org/10.29329/ijpe.2020.268.6
Creswell, J. W. (2014). Qualitative inquiry and research design: Choosing among five approaches (Second Edi). Thousand Oaks, CA: Sage Publications. https://revistapsicologia.org/public/formato/cuali2.pdf
Darling-Hammond, L., Schachner, A. C. W., Wojcikiewicz, S. K., & Flook, L. (2024). Educating teachers to enact the science of learning and development. Applied Developmental Science, 28(1), 1–21. https://doi.org/10.1080/10888691.2022.2130506
Hennink, M., & Kaiser, B. N. (2022). Sample sizes for saturation in qualitative research: A systematic review of empirical tests. Social Science and Medicine, 292(114523), 1–10. https://doi.org/10.1016/j.socscimed.2021.114523
Jaarsveld, S., & Lachmann, T. (2017). Intelligence and creativity in problem-solving: The importance of test features in cognition research. Frontiers in Psychology, 8, 1–12. https://doi.org/10.3389/fpsyg.2017.00134
Khasawneh, E., Gosling, C., & Williams, B. (2021). What impact does maths anxiety have on university students? BMC Psychology, 9(1), 1–9. https://doi.org/10.1186/s40359-021-00537-2
Kusmaryono, I., Basir, M. A., & Saputro, B. A. (2020). Ontological misconception in mathematics teaching in elementary schools. Infinity Journal, 9(1), 15–30. https://doi.org/10.22460/infinity.v9i1.p15-30
Kusmaryono, I., Suyitno, H., Dwijanto, D., & Dwidayati, N. (2019). The effect of mathematical disposition on mathematical power formation: Review of dispositional mental functions. International Journal of Instruction, 12(1), 343–356. https://doi.org/https://doi.org/10.29333/iji.2019.12123a
Kusmaryono, I., Ubaidah, N., & Basir, M. A. (2022). It doesn't mean that students don't have mathematics anxiety: A case study of mathematics learning with path analysis. European Journal of Educational Research, 11(3), 1683–1697. https://doi.org/10.12973/eu-jer.11.3.1683
Lestary, R., Subanji, S., & Ramadani, I. (2022). Cognitive conflict of relational learners in connecting proportion concepts on three term Rrtio problems. Numerical : Jurnal Matematika Dan Pendidikan Matematika, 6(2), 129–140. https://doi.org/10.25217/numerical.v6i2
Lin Li. (2024). Mathematical symbols in academic writing: The case of incorporating mathematical ideals in academic writing for education researchers. Brock Education Journal, 33(1), 66–84. https://doi.org/10.26522/brocked.v33i1.1122
Maaroof, H. A. Q., & Thujil, R. H. (2023). The concept of cognitive equilibrium and its legal basis in consumption contracts: An analytical study. Migration Letters, 28(S5), 941–953. https://shorturl.at/vIwiH
Makhrus, M., & Busyairi, A. (2022). Reducing misconception of force concepts through learning conceptual change model with cognitive conflict approach. Jurnal Pendidikan Fisika Dan Teknologi, 8(2), 184–192. https://doi.org/10.29303/jpft.v8i2.4332
Mufit, F., Festiyed, Fauzan, A., & Lufri. (2023). The effect of cognitive conflict-based learning model on remediation of misconceptions. Journal of Turkish Science Education, 20(1), 26–49. https://doi.org/10.36681/tused.2023.003
National Council of Teachers of Mathematics. (2014). Principles and standards for school mathematics. In Reston. VA: NCTM.
Naeem, M., Ozuem, W., Howell, K., & Ranfagni, S. (2023). A step-by-step process of thematic Analysis to develop a conceptual model in qualitative research. International Journal of Qualitative Methods, 22, 1–18. https://doi.org/10.1177/16094069231205789
Nendi, F., Rosantri Ermelinda, Jelatu, S., Jundu, R., Ningsi, G. P., & Mandur, K. (2023). The effect of scientific approach contextual teaching and learning on students' mathematical power. Jurnal Pendidikan MIPA, 24(4), 837–845. https://doi.org/10.23960/jpmipa/v24i4.pp837-845
Noble, H., & Heale, R. (2019). Triangulation in research, with examples. Evidence-Based Nursing, 22(3), 67–68. https://doi.org/10.1136/ebnurs-2019-103145
Pilten, P. (2010). Evaluation of mathematical powers of 5th-grade primary school students. Procedia - Social and Behavioral Sciences, 2(2), 2975–2979. https://doi.org/10.1016/j.sbspro.2010.03.450
Rafianti, I., & Pujiastuti, H. (2017). Analysis of students' mathematical power in terms of stifin test. Infinity Journal, 6(1), 29–6. https://doi.org/10.22460/infinity.v6i1.233
Şahin, S. M., & Baki, A. (2010). A new model to assess mathematical power. Procedia - Social and Behavioral Sciences, 9, 1368–1372. https://doi.org/10.1016/j.sbspro.2010.12.336
Saunders, B., Sim, J., Kingstone, T., Baker, S., Waterfield, J., Bartlam, B., Burroughs, H., & Jinks, C. (2018). Saturation in qualitative research: exploring its conceptualization and operationalization. Quality and Quantity, 52(4), 1893–1907. https://doi.org/10.1007/s11135-017-0574-8
Schwichow, M., Anna Hellmann, K., & Mikelskis-Seifert, S. (2022). Pre-service teachers' perception of competence, social relatedness, and autonomy in a flipped classroom: effects on learning to notice student preconceptions. Journal of Science Teacher Education, 33(3), 282–302. https://doi.org/10.1080/1046560X.2021.1913332
Setiawan, B., Sopia, N., & Andri, A. (2022). Development of web-based mathematics learning to improve the mathematical power. Mathematics Education Journal, 6(1), 45–53. https://doi.org/10.22219/mej.v6i1.19699
Singh, P. (2021). The role of teachers in motivating students to learn. Technolearn An International Journal of Educational Technology, 11(1), 29–32. https://doi.org/10.30954/2231-4105.01.2021.6
Soeharto, S., & Csapó, B. (2022). Exploring Indonesian student misconceptions in science concepts. Heliyon, 8(9), 1–10. https://doi.org/10.1016/j.heliyon.2022.e10720
Sovacool, B. K., Iskandarova, M., & Hall, J. (2023). Industrializing theories: A thematic analysis of conceptual frameworks and typologies for industrial sociotechnical change in a low-carbon future. Energy Research and Social Science, 97(102954), 1–36. https://doi.org/10.1016/j.erss.2023.102954
Stemele, B. P., & Jina Asvat, Z. (2024). Exploring learner errors and misconceptions in algebraic expressions with grade 9 learners through the use of algebra tiles. African Journal of Research in Mathematics, Science and Technology Education, 28(1), 153–170. https://doi.org/10.1080/18117295.2024.2334989
Suprapto, N. (2020). Do we experience misconceptions?: An ontological review of misconceptions in science. Studies in Philosophy of Science and Education, 1(2), 50–55. https://doi.org/10.46627/sipose.v1i2.24
Takahashi, A. R. W., & Araujo, L. 2020). Case study research: opening up research opportunities. RAUSP Management Journal, 55(1), 100–111. https://doi.org/10.1108/RAUSP-05-2019-0109
Tsang, S., Royse, C. F., & Terkawi, A. S. (2017). Guidelines for developing, translating, and validating a questionnaire in perioperative and pain medicine. Saudi Journal of Anaesthesia, 11(5), S80–S89. https://doi.org/10.4103/sja.SJA_203_17
Turmuzi, M., Suharta, G. P., Astawa, W. P., & Suparta, N. (2024). Misconceptions of mathematics in higher education universities when learning with google classroom based on learning styles and gender differences. Journal of Technology and Science Education, 14(1), 200–223. https://doi.org/10.3926/jotse.2482
Yavuzsoy-Köse, N., Y. Yilmaz, T., Yeşil, D., & Yildirim, D. (2019). Middle school students' interpretation of definitions of the parallelogram family: Which definition for which parallelogram? International Journal of Research in Education and Science, 5(1), 157–175. https://www.ijres.net/index.php/ijres/article/view/466
Zembat, I. Ö., & Gürhan, S. (2023). Fostering a student's abstraction of the relationship between parallelogram and trapezoid within quadrilateral hierarchy. Investigations in Mathematics Learning, 15(4), 241–265. https://doi.org/10.1080/19477503.2023.2209430
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