Level Abstraksi Reflektif Mahasiswa dalam Menyelesaikan Masalah Teori Bayes
DOI:
https://doi.org/10.29240/ja.v6i1.9848Keywords:
Reflective abstraction level, Problem solving, Bayes' TheoremAbstract
This study aims to analyze the level of reflective abstraction of prospective teacher students in solving Bayes' theorem problems in the opportunity theory course. Using a qualitative approach, this research data was taken from prospective 5th semester mathematics teachers, as many as 56 students. The subjects of the study were then selected 5 subjects using purposive sampling techniques. The instruments used are problem-solving tests and interview guidelines have been validated by experts. Documentation data in the form of written test results, videos when doing test questions, and videos during interviews. Qualitative analysis is carried out by data reduction, data presentation, data interpretation, and conclusions. The validity test of the data in this study used triangulation of data collected through various sources, namely comparing the results of student answers and in-depth interviews. The results of this study show that there are differences in the level of skill or capacity of students in solving problems regarding Bayes' proposition. This difference was observed based on the way students thought when given a problem in the form of a story problem.
Downloads
References
Agus, Mirian, Maria Pietronilla Penna, Maribel Peró-Cebollero, Joan Guà rdia-Olmos, and Eliano Pessa. 2014. “The Application of Graphical Representations in Estimation of Probabilistic Events.†Journal of Theories and Research in Education 9(1):235–52. doi: 10.6092/issn.1970-2221/4299
Aini, Septi Dariyatul, and Fetty Nuritasari. 2022. “Analisis Kesalahan dalam Menyelesaikan Soal Teorema Bayes.†Pp. 59–67 in Seminar Nasional Pendidikan Matematika Umt 2022
Berrar, Daniel. 2018. “Bayes’ Theorem and Naive Bayes Classifier.†Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics 1–3 (January 2018):403–12. doi: 10.1016/B978-0-12-809633-8.20473-1
Cetin, Ibrahim, and Ed Dubinsky. 2017. “Reflective Abstraction in Computational Thinking.†Journal of Mathematical Behavior 47(July):70–80. doi: 10.1016/j.jmathb.2017.06.004
Clarke, Nicola M. 2014. “A Person-Centred Enquiry into the Teaching and Learning Experiences of Reflection and Reflective Practice - Part One.†Nurse Education Today 34(9):1219–24. doi: 10.1016/j.nedt.2014.05.017
Diaz, Carmen. 2007. “Assesing Students’ Difficulties with Conditional Probability and Bayesian Reasoning.†International Electronic Journal of Mathematics Education 2(3). doi: 10.1021/ed085p1019
Fitriani, Nelly, Didi Suryadi, and Darhim Darhim. 2018. “The Students’ Mathematical Abstraction Ability Through Realistic Mathematics Education With Vba-Microsoft Excel.†Infinity Journal 7(2):123. doi: 10.22460/infinity.v7i2.p123-132
Ingram, Jenni. 2022. “Randomness and Probability: Exploring Student Teachers’ Conceptions.†Mathematical Thinking and Learning 00(00):1–19. doi: 10.1080/10986065.2021.2016029
Johnson, Eric D., and Elisabet Tubau. 2015. “Comprehension and Computation in Bayesian Problem Solving.†Frontiers in Psychology 6(September):1–19. doi: 10.3389/fpsyg.2015.00938
Jojo, Zingiswa Monica Mybert, Aneshkumar Maharaj, and Deonarain Brijlall. 2012. “Reflective Abstraction and Mathematics Education: The Genetic Decomposition of the Chain Rule--Work in Progress.†US-China Education Review B 4 (2012) 4:408–14
Mulligan, Bryce P., and Trevor N. Carniello. 2023. “A Procedure for Predicting, Illustrating, Communicating, and Optimizing Patient-Centered Outcomes of Epilepsy Surgery Using Nomograms and Bayes’ Theorem.†Epilepsy and Behavior 140:109088. doi: 10.1016/j.yebeh.2023.109088
Prayekti, Novi, Toto Nusantara, Sudirman, Hery Susanto, and Imam Rofiki. 2020. “Students’ Mental Models in Mathematics Problem-Solving.†Journal of Critical Reviews 7(12):468–70. doi: 10.31838/jcr.07.12.83
Quilang, Liezl Joy Lazaro, and Lyndon Laborte Lazaro. 2022. “Mathematical Connections Made during Investigative Tasks in Statistics and Probability.†International Journal of Evaluation and Research in Education 11(1):239–49. doi: 10.11591/ijere.v11i1.21730
Salas-Rueda, Ricardo Adan, Erika Patricia Salas-Rueda, and Rodrigo David Salas-Rueda. 2021. “Analysis of the Web Application on Bayes’ Theorem Considering Data Science and Technological Acceptance Model.†Turkish Online Journal of Distance Education 22(3):1–26. doi: 10.17718/tojde.961819
Sandoval-Bravo, Salvador, Pedro Luis Celso-Arellano, Victor Gualajara, and Semei Coronado. 2019. “An Approximation of University Students’ Learning Ability in the Area of Probability.†European Journal of Contemporary Education 8(4):864–78. doi: 10.13187/ejced.2019.4.864
Simon, Martin A. 2022. “Contributions of the Learning through Activity Theoretical Framework to Understanding and Using Manipulatives in the Learning and Teaching of Mathematical Concepts.†Journal of Mathematical Behavior 66(October 2021):100945. doi: 10.1016/j.jmathb.2022.100945
Sui, Jiaming. 2023. “The Application of Bayesian Theorem.†Highlights in Science, Engineering and Technology 49:557–62. doi: 10.54097/hset.v49i.8613
Thompson, David R., and Colin R. Martin. 2017. “Bayes’ Theorem and Its Application to Cardiovascular Nursing.†European Journal of Cardiovascular Nursing 16(8):659–61. doi: 10.1177/1474515117712317
Wafiqoh, Risnina, Yaya Kusumah, and Dadang Juandi. 2020. “Two Parts of Reflective Abstraction: For New Problem Solving and Mathematical Concept.†doi: 10.4108/eai.12-10-2019.2296403
Zahner, Doris, and James E. Corter. 2010. “The Process of Probability Problem Solving: Use of External Visual Representations.†Mathematical Thinking and Learning 12(2):177–204. doi: 10.1080/10986061003654240
Downloads
Additional Files
Published
Issue
Section
Citation Check
License
Copyright (c) 2024 Arfatin Nurrahmah, Andri Suryana, Maya Nurfitriyanti
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors who publish with ARITHMETIC: Academic Journal of Math agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).