How Self-Efficacy Shapes Mathematical Analytical Thinking: A Qualitative Study using Action-Process-Object-Schema Theory
), Ferry Ferdianto(2), Reni Untarti(3), Lukmanul Akhsani(4)
| 
Country:
(1) Universitas Muhammadiyah Purwokerto, Indonesia
(2) Universitas Swadaya Gunung Jati Cirebon, Indonesia
(3) Universitas Muhammadiyah Purwokerto, Indonesia
(4) Universitas Muhammadiyah Purwokerto, Indonesia
Corresponding Author
Analytical thinking enables students to solve complex problems in a systematic and measurable manner. This study examined students' analytical thinking processes in relation to self-efficacy using the Action-Process-Object-Schema (APOS) theory. The researchers employed a qualitative method with an explanatory approach. They selected mathematics education students from Universitas Muhammadiyah Purwokerto who were enrolled in a sequence convergence course as research subjects. To collect data, the researchers used analytical thinking tests, questionnaires, and interviews. Based on the self-efficacy questionnaire, the researchers classified students into high, medium, and low self-efficacy groups. They selected one informant from each category using purposive sampling. The data analysis involved three stages: data reduction, presentation of findings, and interpretation. The analytical thinking process included collecting, differentiating, organizing, and attributing. The findings showed that students in the high and medium self-efficacy groups demonstrated strong analytical thinking skills. They successfully completed all stages—collecting, differentiating, organizing, and attributing. In contrast, students with low self-efficacy lacked adequate prior knowledge and required assistance in applying mathematical concepts and completing proofs during the organizing stage. These students gathered only limited information at the collection stage due to a poor understanding of the main problem. As a result, they could only partially complete each stage of the analytical thinking process.
Keywords: analytic thinking process, APOS theory, self-efficacy.
Anderson, L. W., & Krathwohl, D. R. (Eds.). (2001). A taxonomy for learning, teaching, and assessing: A revision of bloom’s taxonomy of educational objectives. New York: Longman.
Anwar, B., & Mumthas. (2014). Taking triarchic teaching to classrooms: giving everybody a fair chance. International Journal of Advanced Research, 2(5), 455–458.
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). From piaget’s theory to apos theory: reflective abstraction in learning mathematics and the historical development of APOS Theory. In APOS Theory (pp. 5–15). Springer New York. https://doi.org/10.1007/978-1-4614-7966-6_2
Asiala, M., Brown, A., DeVries, D. J., Dubinsky, E., Mathews, D., & Thomas, K. (1997). A framework for research and curriculum development in undergraduate mathematics education. Maa Notes, 2, 37–54.
Bandura, A., Freeman, W. H., & Lightsey, R. (1999). Self-efficacy: The exercise of control.
Baysal, Z. N., Arkan, K., & Yıldırım, A. (2010). Preservice elementary teachers’ perceptions of their self-efficacy in teaching thinking skills. Procedia - Social and Behavioral Sciences, 2(2), 4250–4254. https://doi.org/10.1016/ j.sbspro.2010.03.673
Bintoro, H. S., Sukestiyarno, Y. L., Mulyono, M., & Walid, W. (2021). The spatial thinking process of the field-independent students based on action-process-object-schema theory. European Journal of Educational Research, 10(4), 1807–1823. https://doi.org/10.12973/eu-jer.10.4.1807
Borji, V., Font, V., Alamolhodaei, H., & Sánchez, A. (2018). Application of the complementarities of two theories, apos and osa, for the analysis of the university students’ understanding on the graph of the function and its derivative. EURASIA Journal of Mathematics, Science and Technology Education, 14(6). https://doi.org/10.29333/ejmste/89514
Brandt, W. C., & Lorié, W. (2024). Measuring student success skills: a review of the literature on analytical thinking. competencies of the future. National Center for the Improvement of Educational Assessment.
Chonkaew, P., Sukhummek, B., & Faikhamta, C. (2016). Development of analytical thinking ability and attitudes towards science learning of grade-11 students through science technology engineering and mathematics (STEM education) in the study of stoichiometry. Chemistry Education Research and Practice, 17(4), 842–861. https://doi.org/10.1039/C6RP00074F
Demir, E. (2022). An examination of high school students' critical thinking dispositions and analytical thinking skills. Journal of Pedagogical Research, 6(4), 190-200. https://doi.org/10.33902/JPR.202217357
Dilekli, Y. (2019). What are the dimensions of thinking skills in Turkish literature? A content analysis study. International Journal of Evaluation and Research in Education, 8(1), 110–118. https://doi.org/10.11591/ijere.v8.i1.pp110-118
Dubinsky, E. (2016). A theory and practice of learning college mathematics. In Mathematical thinking and problem solving (pp. 221–256). Routledge.
Gao, J. (2020). Sources of Mathematics Self-Efficacy in Chinese Students: a Mixed-Method Study with Q-Sorting Procedure. International Journal of Science and Mathematics Education, 18(4), 713–732. https://doi.org/10.1007/s10763-019-09984-1
Gloudemans, H. A., Schalk, R. M. J. D., & Reynaert, W. (2013). The relationship between critical thinking skills and self-efficacy beliefs in mental health nurses. Nurse Education Today, 33(3), 275–280. https://doi.org/10.1016/j.nedt.2012.05.006
Gunbatar, M. S. (2018). Examination of undergraduate and associate degree students’ computer programming attitude and self-efficacy according to thinking style, gender and experience. Contemporary Educational Technology, 9(4), 354–373. https://doi.org/10.30935/cet.471004
Harahsheh, A. H. (2017). Perceived self-efficacy and its relationship to achievement motivation among parallel program students at prince sattam university. International Journal of Psychological Studies, 9(3), 21. https://doi.org/10.5539/ijps.v9n3p21
Hendriana, H., Rohaeti, E. E., & Sumarmo, U. (2017). Hard skills and soft skills matematik siswa. Bandung: Refika Aditama
Herminarto, S., Sofyan, H., Soenarto, S., Mutohhari, F., & Nurtanto, M. (2022). Students’ career decision-making during online learning: the mediating roles of self-efficacy in vocational education. European Journal of Educational Research, 11(3), 1669–1682. https://doi.org/10.12973/eu-jer.11.3.1669
Kao, C. (2014). Exploring the relationships between analogical, analytical, and creative thinking. Thinking Skills and Creativity, 13, 80–88. https://doi.org/10.1016/ j.tsc.2014.03.006
Maharaj, A. (2014). An APOS analysis of natural science students’ understanding of integration. Journal of Research in Mathematics Education, 3(1), 54–73. https://doi.org/10.4471/redimat.2014.40
Miele, D. B., & Wigfield, A. (2014). Quantitative and qualitative relations between motivation and critical-analytic thinking. Educational psychology review, 26(4), 519-541. https://doi.org/10.1007/s10648-014-9282-2
Mudrikah, A. (2015). Problem-based learning associated by action-process-object-schema (apos) theory to enhance students’ high order mathematical thinking ability. International Journal of Research in Education and Science, 2(1), 125. https://doi.org/10.21890/ijres.88952
Nurhayati, H., & Nyayu, N. (2023). The use of collaborative strategies to improve students’ writing ability and self-efficacy: a mixed method study. European Journal of Educational Research, 12(1), 265–280. https://doi.org/10.12973/eu-jer.12.1.265
Öztürk, M., Akkan, Y., & Kaplan, A. (2020). Reading comprehension, Mathematics self-efficacy perception, and Mathematics attitude as correlates of students’ non-routine Mathematics problem-solving skills in Turkey. International Journal of Mathematical Education in Science and Technology, 51(7), 1042–1058. https://doi.org/10.1080/0020739X.2019.1648893
Paleeri, S. (2015). Setting objectives of value education in constructivist approach in the light of revised blooms taxonomy (RBT). I-Manager’s Journal on School Educational Technology, 10(3), 7–12. https://doi.org/10.26634/jsch.10.3.3126
Qolfathiriyus, A., Sujadi, I., & Indriati, D. (2019). Characteristic profile of analytical thinking in mathematics problem solving. Journal of Physics: Conference Series, 1157, 032123. https://doi.org/10.1088/1742-6596/1157/3/032123
Rahayu, R., Kartono*, K., Dwijanto, D., & Agoestanto, A. (2023). Problem-solving process of students with a reflective cognitive style based on the action-process-object-schema theory. European Journal of Educational Research, 12(1), 41–58. https://doi.org/10.12973/eu-jer.12.1.41
Ramadani, A. S., Supardi, Z. A. I., & Hariyono, E. (2021). Profile of analytical thinking skills through inquiry-based learning in science subjects. Studies in Learning and Teaching, 2(3), 45-60. https://doi.org/10.46627/silet.v2i3.83
Robbins, J. K. (2011). Problem solving, reasoning, and analytical thinking in a classroom environment. The Behavior Analyst Today, 12(1), 41–48. https://doi.org/10.1037/h0100710
Schumacher, C., & Ifenthaler, D. (2018). Features students really expect from learning analytics. Computers in Human Behavior, 78(1), 397-407. https://doi.org/10.1016/j.chb.2017.06.030
Šorgo, A., Lamanauskas, V., Šašić, S. Š., Ersozlu, Z. N., Tomažič, I., Kubiatko, M., Prokop, P., Ersozlu, A., Fančovičova, J., Bilek, M., & Usak, M. (2017). Cross-national study on relations between motivation for science courses, pedagogy courses and general self-efficacy. EURASIA Journal of Mathematics, Science and Technology Education, 13(10). https://doi.org/10.12973/ejmste/76970
Subanji, S., & Nusantara, T. (2016). Thinking process of pseudo construction in mathematics concepts. International Education Studies, 9(2), 17. https://doi.org/10.5539/ies.v9n2p17
Suyatman, S., Saputro, S., Sunarno, W., & Sukarmin, S. (2021). Profile of student analytical thinking skills in the natural sciences by implementing problem-based learning model. Journal of Educational, Cultural and Psychological Studies (ECPS Journal), 23(1), 89-111. https://doi.org/10.7358/ecps-2021-023-suya
Theabthueng, P., Khamsong, J., & Worapun, W. (2022). The development of grade 8 student analytical thinking and learning achievement using the integrated problem-based learning and think-pair-share technique. Journal of Educational Issues, 8(1), 420-429. https://doi.org/10.5296/jei.v8i1.19711
Veeck, A., Quareshi, Z. A., O’Reilly, K., Mumuni, A. G., MacMillan, A., Luqmani, Z., Luqmani, M., & Xie, H. (2023). Interventions to assess and address the self-efficacy of marketing students toward acquiring analytical skills. Marketing Education Review, 33(3), 211–225. https://doi.org/10.1080/10528008.2022.2112533
Widmer, M. A., Duerden, M. D., & Taniguchi, S. T. (2014). Increasing and generalizing self-efficacy. Journal of Leisure Research, 46(2), 165–183. https://doi.org/10.1080/00222216.2014.11950318
Wijaya, A. P., Nusantara, T., Sudirman, S., & Hidayanto, E. (2023). How are students’ prior knowledge differentiate analytical thinking process in identifying the convergence of real number sequences? International Journal of Instruction, 16(1), 205–218. https://doi.org/10.29333/iji.2023.16112a
Yilmaz, O., & Saribay, S. A. (2017). Activating analytic thinking enhances the value given to individualizing moral foundations. Cognition, 165(8), 88-96. https://doi.org/10.1016/j.cognition.2017.05.009
Yulina, I. K., Permanasari, A., Hernani, H., & Setiawan, W. (2019). Analytical thinking skill profile and perception of pre service chemistry teachers in analytical chemistry learning. Journal of Physics: Conference Series, 1157, 042046. https://doi.org/10.1088/1742-6596/1157/4/042046
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.