Kesalahan Konstruksi Konsep Ukuran Pemusatan Data pada Mahasiswa dengan Identitas Matematis Positif
Abstract
Penelitian ini merupakan studi kualitatif yang mengeksplor kesalahan konstruksi konsep dua mahasiswa akuntansi dengan identitas matematis positif. Penelitian dilaksanakan dari bulan Desember 2023 sampai Januari 2024 pada salah satu universitas di Sulawesi Selatan. Data dikumpulkan melalui pemberian tes (soal utama dan soal pelacak yang dirancang khusus untuk mengetahui kesalahan konstruksi konsep) dan wawancara semi terstruktur. Konstruksi konsep diteliti menggunakan kerangka APOS dan mempertimbangkan beberapa kesalahan konstruksi konsep yang mungkin terjadi seperti lubang konstruksi, pseudo construction, mis-logical construction, dan mis-analogical construction. Data dianalisis dengan menggunakan tiga tahapan yaitu kondensasi data, penyajian data, dan pengambilan kesimpulan. Hasil penelitian menunjukkan bahwa bentuk kesalahan konstruksi yang dialami oleh mahasiswa dengan identitas matematis positif adalah lubang konstruksi. Dalam hal ini, mereka tidak mempertimbangkan nilai modus yang bisa lebih dari satu, dan bagaimana pengaruh outlier sehingga mereka mengalami kekeliruan dalam memilih ukuran pemusatan data mana yang paling sesuai untuk menjawab atau memecahkan masalah statistika yang diberikan.
Downloads
References
Afriyani, D., Sa’dijah, C., Subanji, S., & Muksar, M. (2019). Students’ Construction Error in Translation among Mathematical Representations. Journal of Physics: Conference Series, 1157(3).
Anderson, R. (2007). Being a Mathematics Learner: Four Faces of Identity. The Mathematics Educator, 17(1), 7–14.
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). Mental Structures and Mechanisms: APOS Theory and the Construction of Mathematical Knowledge. Dalam APOS Theory (hlm. 17-26). New York: Springer.
Axelsson, G. B. M. (2009). Mathematical Identity in Women: The Concept, Its Components and Relationship to Educative Ability, Achievement and Family Support. International Journal of Lifelong Education, 28(3), 383–406.
Aziz, A. M., & Rosli, R. (2021). A Systematic Literature Review on Developing Students' Statistical Literacy Skills. Journal of Physics: Conference Series, 1806 012102.
Bakker, A. (2003). The Early History of Average Values and Implications for Education. Journal of Statistics Education, 11(1).
Barrera, M. E. A., Pulido, H. G., & Alejo, V. V. (2023). Model-Eliciting Activity with Civil Engineering Students to Solve a Problem Involving Binomial Distribution. Statistics Education Research Journal, 22(3), 3.
Bishop, J. P. (2012). “She’s Always Been the Smart One. I’ve Always Been the Dumb One”: Identities in the Mathematics Classroom. Journal for Research in Mathematics Education, 43(1), 34-74.
Boz-Yaman, B. (2019). Examination of Pre-service Mathematics Teachers’ Mental Constructions of Function Transformation. Acta Didactica Napocensia, 12(1), 33–56.
Buehring, R. S., & Grando, R. C. (2023). Reading and Writing the World with Children: Statistical Thinking and Multivariate Data. Statistics Education Research Journal, 22(2), 6.
Chasanah, N. A., Sisworo, S., & Dwiyana, D. (2019). Meningkatkan Penalaran Matematis Siswa pada Materi Ukuran Pemusatan Data Melalui Pendekatan Problem Posing. Jurnal Pendidikan: Teori, Penelitian, Dan Pengembangan, 4(4), 542-547.
Darragh, L. (2016). Identity Research in Mathematics Education. Educational Studies in Mathematics, 93(1), 19–33.
Dubinsky, E. (2002). Reflective Abstraction in Advanced Mathematical Thinking. In D. Tall (Ed.), Advanced Mathematical Thinking (hlm. 95–126). Netherlands: Springer.
Elder, A. C. (2023). Statistics Attitudes after Using Guided Project-Based Learning as an Andragogical Strategy in a Graduate Statistics Course. Statistics Education Research Journal, 22(3), 4.
English, L. D. (2023). Linking Probability and Statistics in Young Students’ Reasoning with Chance. Statistics Education Research Journal, 22(2), 7.
Fitni, F., Roza, Y., & Maimunah, M. (2020). Analisis Kesalahan Siswa Berdasarkan Newman pada Materi Statistika Ditinjau dari Gaya Belajar. Ilmu Pendidikan: Jurnal Kajian Teori Dan Praktik Kependidikan, 5(1), 1–10.
Gravetter, F. J., & Wallnau, L. B. (2017). Statistics For the Behavioral Sciences, Edisi 10. Cengage Learning.
Grootenboer, P., & Zevenbergen, R. (2008). Identity as a Lens to Understand Learning Mathematics: Developing a Model. Proceedings in the 31st Annual Conference of the Mathematics Education Research Group of Australasia, 243–250.
Groth, R. E., & Bergner, J. A. (2006). Preservice Elementary Teachers’ Conceptual and Procedural Knowledge of Mean, Median, and Mode. Mathematical Thinking and Learning, 8(1), 37–63.
Hijazi, R., & Shaqlaih, A. (2023). Statistical Thinking at Early Primary School Levels: Curriculum Perspectives in UAE Textbooks. Statistics Education Research Journal, 22(2), 13.
Hima, L. R., Nusantara, T., Hidayanto, E., & Rahardjo, S. (2019). Changing in Mathematical Identity of Elementary School Students Through Group Learning Activities. International Electronic Journal of Elementary Education, 11(5), 461–469.
Hirsch, L. S., & O’Donnell, A. M. (2001). Representativeness in Statistical Reasoning: Identifying and Assessing Misconceptions. Journal of Statistics Education, 9(2).
Holt, M. M., & Scariano, S. M. (2009). Mean, Median, and Mode from a Decision Perspective. Journal of Statistics Education, 17(3).
Huber, S., Reinhold, F., Obersteiner, A., & Reiss, K. (2024). Teaching Statistics with Positive Orientations but Limited Knowledge? Teachers’ Professional Competence in Statistics. Statistics Education Research Journal, 23(1), 2.
Ikram, F. Z., & Rosidah, R. (2023). Identitas Matematis: Studi Kasus pada Mahasiswa Akuntansi. SIGMA: Jurnal Pendidikan Matematika, 15(1), 127-136.
Ikram, F. Z., & Rosidah, R. (2024). Kesalahan Mahasiswa Fakultas Keguruan dan Ilmu Pendidikan dalam Menggunakan SPSS. Jurnal MediaTIK, 7(2), 144-149.
Ikram, F. Z., Subanji, S., & Hidayanto, E. (2020) Kesalahan Konstruksi Konsep Mahasiswa dengan Identitas Matematis yang Sangat Negatif pada Materi Ukuran Pemusatan Data. Jurnal Pendidikan Sains, 8(4), 121-129.
Ismail, Z., & Chan, S. W. (2015). Malaysian Students’ Misconceptions About Measures of Central Tendency: An Error Analysis. In AIP Conference Proceedings, 1643(1), 93-100. American Institute of Physics.
Jacobbe, T. (2012). Elementary School Teachers’ Understanding of the Mean and Median. International Journal of Science and Mathematics Education, 10(5), 1143–1161.
Jatisunda, M. G., Nahdi, D. S., & Suciawati, V. (2020). Kemampuan Literasi Statistika Mahasiswa Administrasi Publik. Supremum Journal of Mathematics Education, 4(2), 134–146.
Karatoprak, R., Gülseren, K. A., & Bengü, B. (2015). Prospective Elementary and Secondary School Mathematics Teachers’ Statistical Reasoning. International Electronic Journal of Elementary Education, 7(2), 107–124.
Kaspersen, E., Pepin, B., & Sikko, S. A. (2017). Measuring STEM Students’ Mathematical Identities. Educational Studies in Mathematics, 95(2), 163–179.
Khair, M. S., Subanji, S., & Muksar, M. (2018). Kesalahan Konsep dan Prosedur Siswa dalam Menyelesaikan Soal Persamaan Ditinjau dari Gaya Berpikir. Jurnal Pendidikan: Teori Penelitian dan Pengembangan, 3(5), 620–633.
López, C. C., & Ramírez, M. M. O. (2021). A Diagnosis of Statistical Service Courses in Mexico. Statistics Education Research Journal, 20(2), 10.
Manikandan, S. (2011). Measures of Central Tendency: Median and Mode. Journal of Pharmacology and Pharmacotherapeutics, 2(3), 214.
Maryati, I., & Priatna, N. (2018). Analisis Kemampuan Literasi Statistis Siswa Madrasah Tsanawiyah dalam Materi Statistika. Journal Of Medives: Journal Of Mathematics Education IKIP Veteran Semarang, 2(2), 205-212.
Mathews, D., & Clark, J. (2003). Successful Students’ Conceptions of Mean, Standard Deviation, and the Central Limit Theorem. Dari http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.636.8870&rep=rep1&type=pdf.
Matsuo, H., Nooner, A. L., & Pearce, A. R. (2022). Attitudes Toward Statistics are Better in Traditional Compared to Online Courses, at Least Until COVID-19. Statistics Education Research Journal, 21(3), 2.
McGee, E. O. (2015). Robust and Fragile Mathematical Identities: A Framework for Exploring Racialized Experiences and High Achievement Among Black College Students. Journal for Research in Mathematics Education, 46(5), 599-625.
Mediyani, D., & Mahtuum, Z. A. (2020). Analisis Kesulitan Siswa dalam Menyelesaikan Soal Materi Statistika pada Siswa SMP Kelas VIII. Jurnal Pembelajaran Matematika Inovatif, 3(4), 385–392.
Miles, M. B., Huberman, A. M., & Saldaña, J. (2020). Qualitative Data Analysis: A Methods Sourcebook (4th edition). SAGE.
Mkhize, D. R. (2017). Forming Positive Identities to Enhance Mathematics Learning among Adolescents. Universal Journal of Educational Research, 5(2), 175–180.
Mokros, J., & Russell, S. J. (1995). Children’s Concepts of Average and Representativeness. Journal for Research in Mathematics Education, 26(1), 20-39.
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics.
Netti, S., Nusantara, T., Subanji, S., Abadyo, A., & Anwar, L. (2016). The Failure to Construct Proof Based on Assimilation and Accommodation Framework from Piaget. International Education Studies, 9(12), 12-22.
Oliveira, F. J. D. S., & Reis, D. A. D. F. (2021). The NEPSO and Opinion Educative Survey in Latin America: Discussions on Statistical Literacy in The Perspective of This Approach. Statistics Education Research Journal, 20(2), 4.
OECD (2023). PISA 2022 Results (Volume I): The State of Learning and Equity in Education. OECD Publishing.
Payadnya, I. P. A. A., Noviyanti, P. L., & Wibawa, K. A. (2021). Analisis Kemampuan Pemahaman Konsep Mahasiswa pada Mata Kuliah Metode Statistika I Selama Pandemi COVID-19. Emasains: Jurnal Edukasi Matematika dan Sains, 9(2), 288-296.
Rabin, L. A., Krishnan, A., Bergdoll, R., & Fogel, J. (2021). Correlates of Exam Performance in an Introductory Statistics Course: Basic Math Skills Along with Self-Reported Psychological/Behavioral and Demographic Variables. Statistics Education Research Journal, 20(1), 3.
Rahayu, O. P., & Purwasih, R. (2020). Analisis Kesalahan dalam Materi Statistika pada Siswa SMP Kelas IX Berdasarkan dari Perspektif Gender. Jurnal Pembelajaran Matematika Inovatif, 3(5), 451–462.
Rosidah, Budayasa, I. K., & Juniati, D. (2018). An Analysis of Statistical Reasoning Process of High School Students in Solving the Statistical Problems. Journal of Physics: Conference Series, 1028(1).
Rosidah, R., & Ikram, F. Z. (2021). Measure of Central Tendency: Undergraduate Students’ Error in Decision-Making Perspective. International Journal of Education, 14(1), 39-47.
Rosidah, R., & Ikram, F. Z. (2022). Measure of Spread: Type of Errors that Students Made in Problem-Solving. MaPan: Jurnal Matematika dan Pembelajaran, 10(1), 142-158.
Roy, G. J., Hodges, T. E., & Graul, L. (2016). How Many Jelly Beans are in the Jar? Mathematics Teaching in the Middle School, 21(7), 424-430.
Sfard, A., & Prusak, A. (2005). Telling Identities: In Search of an Analytic Tool for Investigating Learning as a Culturally Shaped Activity. Educational Researcher, 34(4), 14–22.
Sharma, S. (2008). Exploring Fijian High School Students ’Conceptions of Averages. Pacific-Asian Education, 20(2), 29–45.
Solomon, Y. (2009). Mathematical literacy: Developing Identities of Inclusion. Routledge.
Sriwahyuni, K., & Maryati, I. (2022). Kemampuan Pemecahan Masalah Matematis Siswa pada Materi Statistika. Plusminus: Jurnal Pendidikan Matematika, 2(2), 335–344.
Strauss, S., & Bichler, E. (1988). The Development of Children`s Concepts of the Arithmetic Average. Journal for Research in Mathematics Education, 19(1), 64–80.
Subanji, S., & Supratman, A. M. (2015). The Pseudo-Covariational Reasoning Thought Processes in Constructing Graph Function of Reversible Event Dynamics Based on Assimilation and Accommodation Frameworks. Research in Mathematical Education, 19(1), 61–79.
Subanji, S. (2015). Teori Kesalahan Konstruksi Konsep dan Pemecahan Masalah Matematika. Malang: Universitas Negeri Malang (UM Press).
Subanji, S., & Nusantara, T. (2016). Thinking Process of Pseudo Construction in Mathematics Concepts. International Education Studies, 9(2), 17.
Sudirman, S., Subanji, S., Sutawidjaja, A., & Muksar, M. (2015). Proses Berpikir Mahasiswa dalam Mengonstruksi Konsep Komposisi Fungsi. Jurnal Pendidikan Sains, 3(4), 168–178.
Tiro, M. A. (2008). Dasar-dasar Statistika (3rd ed.). Andira Publisher.
Ulusoy, C. A., & Altay, M. K. (2016). Analyzing the Statistical Reasoning Levels of Pre-Service Elementary School Teachers in the Context of a Model Eliciting Activity. International Journal of Research in Education and Science, 3(25311), 20–30.
Vetten, A. D., Keijzer, R., Schoonenboom, J., & Oers, B. V. (2023). Pre-service Primary School Teachers’ Knowledge During Teaching Informal Statistical Inference. Statistics Education Research Journal, 22(2), 12.
von Hippel, P. T. (2005). Mean, Median, and Skew: Correcting a Textbook Rule. Journal of Statistics Education, 13(2).
Zaidan, A., Ismail, Z., Yusof, Y. M., & Kashefi, H. (2012). Misconceptions in Descriptive Statistics Among Postgraduates in Social Sciences. Procedia - Social and Behavioral Sciences, 46, 3535–3540.
Zawojewski, J. S., & Shaughnessy, J. M. (2000). Mean and Median: Are they really so easy?. Mathematics Teaching in the Middle School, 5(7), 436.
Copyright (c) 2025 Fadhil Zil Ikram, Dadan Dasari, Jarnawi Afgani Dahlan, Mei Radia Putri
This work is licensed under a Creative Commons Attribution 4.0 International License.
Jurnal Pendidikan Matematika Unpatti is an Open Access Journal. The authors who publish the manuscript in Jurnal Pendidikan Matematika Unpatti agree to the following terms:
Jurnal Pendidikan Matematika Unpatti is licensed under a Creative Commons Attribution 4.0 International . This permits anyone to copy, redistribute, remix, transmit and adapt the work provided the original work and source is appropriately cited.
This means:
(1) Under the CC-BY license, authors retain ownership of the copyright for their article, but authors grant others permission to use the content of publications in Jurnal Pendidikan Matematika Unpatti in whole or in part provided that the original work is properly cited. Users (redistributors) of Jurnal Pendidikan Matematika Unpatti are required to cite the original source, including the author's names, Jurnal Pendidikan Matematika Unpatti as the initial source of publication, year of publication, volume number, issue, and Digital Object Identifier (DOI); (2) Authors grant Jurnal Pendidikan Matematika Unpatti the right of first publication. Although authors remain the copyright owner.
