Exploring the Characteristics of Student Transformational Activities in Indonesia in Solving Cognitive Conflict-Based Problems
DOI:
https://doi.org/10.21009/jtp.v25i3.45728Keywords:
Transformational activities, cognitive conflict-based problems, missing a fragment, violation of a rule, an unexpected result, matching problem componentsAbstract
This research aimed to describe the characteristics of the transformational activities of Indonesian students in resolving problems based on cognitive conflict. The research employed a phenomenological approach with five students as subjects. The research instruments included tests and interview guidelines, and the analysis was conducted using the constant comparative method. Change-based activities are a good way to solve cognitive conflict issues, including full rule-based unexpected results, full rule-based matching problem parts, incomplete rule-based unexpected results, and incomplete rule-based matching problem parts. Exploring these characteristics serves as a foundation for instructors to enhance the quality of instructional design. Practically, a profound understanding of these characteristics can provide a solid foundation for educators to enhance their instructional design quality. By exploring and comprehending how students address cognitive conflict, instructors can design more effective learning experiences that align with the student's needs.
References
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Irawati, Zubainur, C. M., & Ali, R. M. (2018). Cognitive conflict strategy to minimize students’ misconception on the topic of addition of algebraic expression. Journal of Physics: Conference Series, 1088. https://doi.org/10.1088/1742-6596/1088/1/012084
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Kieran, C. (2006). The Core of Algebra: Reflections on its Main Activities. The Future of the Teaching and Learning of Algebra The 12th ICMI Study, 21–33. https://doi.org/10.1007/1-4020-8131-6_2
Kieran, C. (2018). Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds (C. Kieran (ed.)). Springer International Publishing. https://doi.org/10.1007/978-3-319-68351-5
Kilpatrick, J., Swafford, J., & Findel, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press. http://www.wakamono-up.jp/top/pdf/Third-party_evaluation_2013_points.pdf
Kolb, S. M. (2012). Grounded Theory and the Constant Comparative Method : Valid Research Strategies for Educators. Journal of Emerging Trends in Educational Research and Policy Studies, 3(1), 83–86. http://jeteraps.scholarlinkresearch.com/articles/Grounded Theory and the Constant Comparative Method.pdf
Lannin, J. K. (2005). Generalization and Justification: The Challenge of Introducing Algebraic Reasoning Through Patterning Activities. Mathematical Thinking and Learning, 7(3), 231–258. https://doi.org/10.1207/s15327833mtl0703_3
Lee, G., & Byun, T. (2012). An Explanation for the Difficulty of Leading Conceptual Change Using a Counterintuitive Demonstration: The Relationship Between Cognitive Conflict and Responses. Research in Science Education, 42(5), 943–965. https://doi.org/10.1007/s11165-011-9234-5
Lee, G., & Kwon, J. (2001). What Do We Know about Students’ Cognitive Conflict in Science Classroom: A Theoretical Model of Cognitive Conflict Process. Proceedings of 2001 AETS Annual Meeting, 309–325.
Levin, M., & Walkoe, J. (2022). Seeds of algebraic thinking: a Knowledge in Pieces perspective on the development of algebraic thinking. ZDM – Mathematics Education, 54(6), 1303–1314. https://doi.org/10.1007/s11858-022-01374-2
Limón, M. (2001). On the cognitive conflict as an instructional strategy for conceptual change: a critical appraisal. Learning and Instruction, 11(4–5), 357–380. https://doi.org/10.1016/S0959-4752(00)00037-2
Maharani, I. P., & Subanji, S. (2018). Scaffolding Based on Cognitive Conflict in Correcting the Students’ Algebra Errors. International Electronic Journal of Mathematics Education, 13(2), 67–74. https://doi.org/10.12973/iejme/2697
Malloy, C., Price, J., Willard, T., & Sloan, L. L. “Butch”. (2002). Pre-Algebra. USA TODAY Snapshots;Dinah-Might Activities, Inc.
Niaz, M. (1995). Cognitive conflict as a teaching strategy in solving chemistry problems: A dialectic–constructivist perspective. Journal of Research in Science Teaching, 32(9), 959–970. https://doi.org/10.1002/tea.3660320907
Palatnik, A., & Koichu, B. (2017). Sense making in the context of algebraic activities. Educational Studies in Mathematics, 95(3), 245–262. https://doi.org/10.1007/s10649-016-9744-1
Pant, V. (2019). Conceptual Understanding and Procedural Knowledge of Fractions : How to Learn and How to Teach. Education Research Highlights in Mathematics, Science and Technology, 17–35.
Pratiwi, E., Nusantara, T., Susiswo, S., & Muksar, M. (2022). Routines’ errors when solving mathematics problems cause cognitive conflict. International Journal of Evaluation and Research in Education (IJERE), 11(2), 773. https://doi.org/10.11591/ijere.v11i2.21911
Pratiwi, E., Nusantara, T., Susiswo, S., Muksar, M., & Subanji, S. (2019). Characteristics of Students’ Cognitive Conflict in Solving a Problem Based on Information Processing Theory. International Journal of Learning, Teaching and Educational Research, 18(2), 76–88. https://doi.org/10.26803/ijlter.18.2.6
Santrock, J. W. (2011). Educational psychology (Fifth). McGraw Hill Companies.
Sela, H. (2008). Coping With Mathematical Contradictions With Peers. Paper Presented at Topic Study Group 18, ICME 11, July, 1–9.
Sela, H., & Zaslavsky, O. (2007). Resolving Cognitive Conflict With Peers – Is There a Difference Between Two and Four? Proceedings of the 31 Conference of the International Group for the Psychology of Mathematics Education, 4, 169–176.
Setiawan, I., Purwanto, P., Sukoriyanto*, S., & Nengah, I. (2023). Cognitive Conflict Based on Thinking Errors in Constructing Mathematical Concept. International Journal of Educational Methodology, 9(4), 631–643. https://doi.org/10.12973/ijem.9.4.631
Sintawati, M., & Mardati, A. (2023). Kemampuan Berpikir Kritis dalam Pembelajaran Matematika. K-Media. http://seminar.uny.ac.id/semnasmatematika/sites/seminar.uny.ac.id.semnasmatematika/files/banner/PM-62.pdf
Strachota, S., Knuth, E., & Blanton, M. (2018). Cycles of Generalizing Activities in the Classroom (Issue January 2018, pp. 351–378). https://doi.org/10.1007/978-3-319-68351-5_15
Sullivan, M. (2008). Algebra & Trigonometry. Pearson Prentice Hall.
Sumadji, S., & Yuwono, T. (2020). Developing Cognitive Conflict to Overcome Students’ Thinking Difficulties. Journal of Education and Learning Mathematics Research (JELMaR), 1(2), 104–113. https://doi.org/10.37303/jelmar.v1i2.38
Susiana, E. (2018). IDEAL Problem Solving dalam Pembelajaran Matematika. KREANO: Jurnal Matematika Kreatif-Inovatif, 1(2), 73–82. https://s.id/-YYLJ
Sutopo. (2014). Counterexample in Cognitive Conflict As Factor Influencing Conceptual Change. QIJIS (Qudus International Journal of Islamic Studies), 2(2), 198–218.
Sutopo, S., Sutawidjaja, A., Sa’dijah, C., & Parta, I. (2019). Cognitive Conflict of IAIN Tulungagung Students with Independent Cognitive Style in Solving Integral Problems. Proceedings of the Proceedings of the 1st International Conference on Business, Law And Pedagogy, ICBLP 2019, 13-15 February 2019, Sidoarjo, Indonesia. https://doi.org/10.4108/eai.16-10-2019.163229
Vermette, S. (2016). Teachers’ Professional Knowledge: The case of Variability. 15(6), 48–60.
Verschaffel, L., Baccaglini-Frank, A., Mulligan, J., van den Heuvel-Panhuizen, M., Xin, Y. P., & Butterworth, B. (2018). Special Needs in Research and Instruction in Whole Number Arithmetic. In New ICMI Study Series (pp. 375–397). https://doi.org/10.1007/978-3-319-63555-2_16
Walida, S. El, Sa’dijah, C., Subanji, & Sisworo. (2022). A Portrait of Controversial Mathematics Problems and Students’ Metacognitive Awareness: A Case of Indonesia. Journal of Higher Education Theory and Practice, 22(12), 51–62. https://doi.org/10.33423/jhetp.v22i12.5462
Watson, J. M. (2002). Inferential reasoning and the influence of cognitive conflict. Educational Studies in Mathematics, 51(3), 225–256. https://doi.org/10.1023/A:1023622017006
Wyrasti, A. F., Sa’Dijah, C., As’Ari, A. R., & Sulandra, I. M. (2019). An autocognitive conflict and its mapping in solving mathematics problem. Journal of Physics: Conference Series, 1157(2). https://doi.org/10.1088/1742-6596/1157/2/022126
Wyrasti, Andi Fajeriani, Sa’dijah, C., & Anwar, L. (2017). The Assessment of Students’ Cognitive Conflict by Using Student’s Cognitive Map in Solving Mathematics Problem. International Conference on Education, 2006, 72–82.
Wyrasti, Andi Fajeriani, Sa’dijah, C., As’ari, A. R., & Sulandra, I. M. (2018). The Misanalogical Construction of Undergraduate Students in Solving Cognitive Conflict Identification Task. International Electronic Journal of Mathematics Education, 14(1). https://doi.org/10.12973/iejme/3961
Apsari, R. A., Putri, R. I. I., Sariyasa, S., Abels, M., & Prayitno, S. (2019). Geometry Representation To Develop Algebraic Thinking: A Recommendation For A Pattern Investigation In Pre-Algebra Class. Journal on Mathematics Education, 11(1), 45–58. https://doi.org/10.22342/jme.11.1.9535.45-58
Barile, M. (2023). ‘Characterization.’ From MathWorld-A Wolfram Web Resource. In MathWorld website (p. http://www.wolframalpha.com). http://mathworld.wolfram.com
Bittinger, M. L., & Beecher, J. A. (2012). Developmental mathematics: college mathematics and introductory algebra. PEARSON.
Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM, 40(1), 3–22. https://doi.org/10.1007/s11858-007-0067-7
Chow, T.-C. F., & Treagust, D. F. (2013). An Intervention Study Using Cognitive Conflict to Foster Conceptual Change. Journal of Science and Mathematics, 36(1), 44–64.
Ellis, A. B. (2011). Generalizing-promoting actions: How classroom collaborations can support students’ mathematical generalizations. Journal for Research in Mathematics Education, 42(4), 308–345. https://doi.org/10.5951/jresematheduc.42.4.0308
Falduto, V., Gross, R., Lippman, D., Rasmussen, M., Norwood, R., Belloit, N., Magnier, J.-M., Whipple, H., & Fernandez, C. (2017). College Algebra (1 st). Rice University.
Fraser, D. (2007). Using cognitive conflict to promote a structural understanding of grade 11 algebra. ProQuest Dissertations and Theses, 174. https://search.proquest.com/dissertations-theses/using-cognitive-conflict-promote-structural/docview/304720957/se-2?accountid=13042%0Ahttp://oxfordsfx.hosted.exlibrisgroup.com/oxford?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&genre=
Fujii, T. (2003). Probing students’ understanding of Variables through cognitive conflict problems? Is the concept ofavariable so difficult for students to understand? In Neil A. Pateman, B. J. Dougherty, & J. T. Zilliox (Eds.), Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education held jointly with the 25th Conference of PME-NA (pp. 1–65). CRDG, College of Education, University of Hawai‘i.
Fujii, Toshiakira. (1987). The role of cognitive conflict in understanding mathematics. In Begeron, J., Herscovics, N., Kieran, C. (Eds.)Proceedings of the Eleventh International Conference for the Psychology of Mathematics Education. Volume III, 141–147.
Gal, H. (2019a). When the use of cognitive conflict is ineffective—problematic learning situations in geometry. Educational Studies in Mathematics, 102(2), 239–256. https://doi.org/10.1007/s10649-019-09904-8
Gal, H. (2019b). When the use of cognitive conflict is ineffective—problematic learning situations in geometry. Educational Studies in Mathematics, 102(2), 239–256. https://doi.org/10.1007/s10649-019-09904-8
Glaser, B. G., & Strauss, A. L. (1967). The Discovery of Grounded Theory, Strategies for Qualitative Research. AldineTransaction.
Halimah, Subanji, & Septi Nur Afifah, D. (2019). Student’s cognitive conflict form problem solving on mathematics. Journal of Physics: Conference Series, 1339(1), 012127. https://doi.org/10.1088/1742-6596/1339/1/012127
Irawati, Zubainur, C. M., & Ali, R. M. (2018). Cognitive conflict strategy to minimize students’ misconception on the topic of addition of algebraic expression. Journal of Physics: Conference Series, 1088. https://doi.org/10.1088/1742-6596/1088/1/012084
Jonassen, D. H. (2010). Learning to Solve Problems. In Angewandte Chemie International Edition, 6(11), 951–952. (Issue Mi). Routledge. https://doi.org/10.4324/9780203847527
Kieran, C. (2004). Algebraic Thinking in the Early Grades : What Is It? Mathematics Educator, 8(1), 139–151.
Kieran, C. (2006). The Core of Algebra: Reflections on its Main Activities. The Future of the Teaching and Learning of Algebra The 12th ICMI Study, 21–33. https://doi.org/10.1007/1-4020-8131-6_2
Kieran, C. (2018). Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds (C. Kieran (ed.)). Springer International Publishing. https://doi.org/10.1007/978-3-319-68351-5
Kilpatrick, J., Swafford, J., & Findel, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press. http://www.wakamono-up.jp/top/pdf/Third-party_evaluation_2013_points.pdf
Kolb, S. M. (2012). Grounded Theory and the Constant Comparative Method : Valid Research Strategies for Educators. Journal of Emerging Trends in Educational Research and Policy Studies, 3(1), 83–86. http://jeteraps.scholarlinkresearch.com/articles/Grounded Theory and the Constant Comparative Method.pdf
Lannin, J. K. (2005). Generalization and Justification: The Challenge of Introducing Algebraic Reasoning Through Patterning Activities. Mathematical Thinking and Learning, 7(3), 231–258. https://doi.org/10.1207/s15327833mtl0703_3
Lee, G., & Byun, T. (2012). An Explanation for the Difficulty of Leading Conceptual Change Using a Counterintuitive Demonstration: The Relationship Between Cognitive Conflict and Responses. Research in Science Education, 42(5), 943–965. https://doi.org/10.1007/s11165-011-9234-5
Lee, G., & Kwon, J. (2001). What Do We Know about Students’ Cognitive Conflict in Science Classroom: A Theoretical Model of Cognitive Conflict Process. Proceedings of 2001 AETS Annual Meeting, 309–325.
Levin, M., & Walkoe, J. (2022). Seeds of algebraic thinking: a Knowledge in Pieces perspective on the development of algebraic thinking. ZDM – Mathematics Education, 54(6), 1303–1314. https://doi.org/10.1007/s11858-022-01374-2
Limón, M. (2001). On the cognitive conflict as an instructional strategy for conceptual change: a critical appraisal. Learning and Instruction, 11(4–5), 357–380. https://doi.org/10.1016/S0959-4752(00)00037-2
Maharani, I. P., & Subanji, S. (2018). Scaffolding Based on Cognitive Conflict in Correcting the Students’ Algebra Errors. International Electronic Journal of Mathematics Education, 13(2), 67–74. https://doi.org/10.12973/iejme/2697
Malloy, C., Price, J., Willard, T., & Sloan, L. L. “Butch”. (2002). Pre-Algebra. USA TODAY Snapshots;Dinah-Might Activities, Inc.
Niaz, M. (1995). Cognitive conflict as a teaching strategy in solving chemistry problems: A dialectic–constructivist perspective. Journal of Research in Science Teaching, 32(9), 959–970. https://doi.org/10.1002/tea.3660320907
Palatnik, A., & Koichu, B. (2017). Sense making in the context of algebraic activities. Educational Studies in Mathematics, 95(3), 245–262. https://doi.org/10.1007/s10649-016-9744-1
Pant, V. (2019). Conceptual Understanding and Procedural Knowledge of Fractions : How to Learn and How to Teach. Education Research Highlights in Mathematics, Science and Technology, 17–35.
Pratiwi, E., Nusantara, T., Susiswo, S., & Muksar, M. (2022). Routines’ errors when solving mathematics problems cause cognitive conflict. International Journal of Evaluation and Research in Education (IJERE), 11(2), 773. https://doi.org/10.11591/ijere.v11i2.21911
Pratiwi, E., Nusantara, T., Susiswo, S., Muksar, M., & Subanji, S. (2019). Characteristics of Students’ Cognitive Conflict in Solving a Problem Based on Information Processing Theory. International Journal of Learning, Teaching and Educational Research, 18(2), 76–88. https://doi.org/10.26803/ijlter.18.2.6
Santrock, J. W. (2011). Educational psychology (Fifth). McGraw Hill Companies.
Sela, H. (2008). Coping With Mathematical Contradictions With Peers. Paper Presented at Topic Study Group 18, ICME 11, July, 1–9.
Sela, H., & Zaslavsky, O. (2007). Resolving Cognitive Conflict With Peers – Is There a Difference Between Two and Four? Proceedings of the 31 Conference of the International Group for the Psychology of Mathematics Education, 4, 169–176.
Setiawan, I., Purwanto, P., Sukoriyanto*, S., & Nengah, I. (2023). Cognitive Conflict Based on Thinking Errors in Constructing Mathematical Concept. International Journal of Educational Methodology, 9(4), 631–643. https://doi.org/10.12973/ijem.9.4.631
Sintawati, M., & Mardati, A. (2023). Kemampuan Berpikir Kritis dalam Pembelajaran Matematika. K-Media. http://seminar.uny.ac.id/semnasmatematika/sites/seminar.uny.ac.id.semnasmatematika/files/banner/PM-62.pdf
Strachota, S., Knuth, E., & Blanton, M. (2018). Cycles of Generalizing Activities in the Classroom (Issue January 2018, pp. 351–378). https://doi.org/10.1007/978-3-319-68351-5_15
Sullivan, M. (2008). Algebra & Trigonometry. Pearson Prentice Hall.
Sumadji, S., & Yuwono, T. (2020). Developing Cognitive Conflict to Overcome Students’ Thinking Difficulties. Journal of Education and Learning Mathematics Research (JELMaR), 1(2), 104–113. https://doi.org/10.37303/jelmar.v1i2.38
Susiana, E. (2018). IDEAL Problem Solving dalam Pembelajaran Matematika. KREANO: Jurnal Matematika Kreatif-Inovatif, 1(2), 73–82. https://s.id/-YYLJ
Sutopo. (2014). Counterexample in Cognitive Conflict As Factor Influencing Conceptual Change. QIJIS (Qudus International Journal of Islamic Studies), 2(2), 198–218.
Sutopo, S., Sutawidjaja, A., Sa’dijah, C., & Parta, I. (2019). Cognitive Conflict of IAIN Tulungagung Students with Independent Cognitive Style in Solving Integral Problems. Proceedings of the Proceedings of the 1st International Conference on Business, Law And Pedagogy, ICBLP 2019, 13-15 February 2019, Sidoarjo, Indonesia. https://doi.org/10.4108/eai.16-10-2019.163229
Vermette, S. (2016). Teachers’ Professional Knowledge: The case of Variability. 15(6), 48–60.
Verschaffel, L., Baccaglini-Frank, A., Mulligan, J., van den Heuvel-Panhuizen, M., Xin, Y. P., & Butterworth, B. (2018). Special Needs in Research and Instruction in Whole Number Arithmetic. In New ICMI Study Series (pp. 375–397). https://doi.org/10.1007/978-3-319-63555-2_16
Walida, S. El, Sa’dijah, C., Subanji, & Sisworo. (2022). A Portrait of Controversial Mathematics Problems and Students’ Metacognitive Awareness: A Case of Indonesia. Journal of Higher Education Theory and Practice, 22(12), 51–62. https://doi.org/10.33423/jhetp.v22i12.5462
Watson, J. M. (2002). Inferential reasoning and the influence of cognitive conflict. Educational Studies in Mathematics, 51(3), 225–256. https://doi.org/10.1023/A:1023622017006
Wyrasti, A. F., Sa’Dijah, C., As’Ari, A. R., & Sulandra, I. M. (2019). An autocognitive conflict and its mapping in solving mathematics problem. Journal of Physics: Conference Series, 1157(2). https://doi.org/10.1088/1742-6596/1157/2/022126
Wyrasti, Andi Fajeriani, Sa’dijah, C., & Anwar, L. (2017). The Assessment of Students’ Cognitive Conflict by Using Student’s Cognitive Map in Solving Mathematics Problem. International Conference on Education, 2006, 72–82.
Wyrasti, Andi Fajeriani, Sa’dijah, C., As’ari, A. R., & Sulandra, I. M. (2018). The Misanalogical Construction of Undergraduate Students in Solving Cognitive Conflict Identification Task. International Electronic Journal of Mathematics Education, 14(1). https://doi.org/10.12973/iejme/3961
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Published
2023-12-31
How to Cite
Rosimanidar, Purwanto, Hidayanto, E. ., & Sulandra, I. M. . (2023). Exploring the Characteristics of Student Transformational Activities in Indonesia in Solving Cognitive Conflict-Based Problems. JTP - Jurnal Teknologi Pendidikan, 25(3), 552–568. https://doi.org/10.21009/jtp.v25i3.45728
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