Does Domain of Absolute Value Function Always Positive? Commognitive-Conflict Analysis of Students of First Semester
Keywords:
commognitive analysis; commognitive conflict; absolute function
Abstract
This research aims to analyze the result of students' work in finding the solution to math-problems about absolute functions. Commognitive's analysis was used to analyze student works in this qualitative research. This research's methods were, namely, preparing, collecting data, transcription data, and analyzing data. A total of 25 students from two universities were given math questions, and two were selected as research subjects. The selection of subjects is based on different and exciting work results. The research subjects attended in-depth interviews to learn more about the commognitive's components. The results showed that commognitive conflict occurred in the word use component when the subject experienced errors in interpreting the data on the questions. Subjects cannot correctly describe the graphic requested in the questions (visual mediators). Describing what is known in the problem is also incompatible (narratives). Subjects experienced the incorrect routines. Based on the results of in-depth interviews, it can be said that the commognitive conflicts occurred because of a lack of understanding of the concepts.
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References
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Halim, D., Nurhidayati, S., Zayyadi, M., Lanya, H., & Hasanah, S. I. (2020). Commognitive analysis of the solving problem of logarithm on mathematics prospective teachers. Journal of Physics: Conference Series, 1663(1). https://doi.org/10.1088/1742-6596/1663/1/012002
Heinrich, W. F., Habron, G. B., Johnson, H. L., & Goralnik, L. (2015). Critical Thinking Assessment Across Four Sustainability-Related Experiential Learning Settings. Journal of Experiential Education. https://doi.org/10.1177/1053825915592890
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Ioannou, M. (2017). Investigating the discursive shift in the learning of Group Theory : Analysis of some interdiscursive commognitive conflicts. Retrieved from https://keynote.conference-services.net/resources/444/5118/pdf/CERME10_0167.pdf
Ioannou, M. (2018). Commognitive analysis of undergraduate mathematics students' first encounter with the subgroup test. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-017-0222-6
Jones, T. (2017). Playing Detective to Enhance Critical Thinking. Teaching and Learning in Nursing. https://doi.org/10.1016/j.teln.2016.09.005
Kaya, D., & Aydin, H. (2016). Elementary mathematics teachers' perceptions and lived experiences on mathematical communication. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.12973/eurasia.2014.1203a
Kim, D.-J., Choi, S., Lim, W., Thoma, A., Nardi, E., Viirman, O., … Sfard, A. (2019a). Discourses of Functions – University Mathematics Teaching Through a Commognitive Lens. Educational Studies in Mathematics.
Kim, D.-J., Choi, S., Lim, W., Thoma, A., Nardi, E., Viirman, O., … Sfard, A. (2019b). Discourses of Functions – University Mathematics Teaching Through a Commognitive Lens. Educational Studies in Mathematics, 8(2), 423–430. https://doi.org/10.1007/s10649-015-9676-1
Larsson, K. (2017). Understanding and teaching critical thinking—A new approach. International Journal of Educational Research. https://doi.org/10.1016/j.ijer.2017.05.004
Lu, J., Tao, Y., Xu, J., & Stephens, M. (2020). Commognitive responsibility shift and its visualizing in computer-supported one-to-one tutoring. Interactive Learning Environments. https://doi.org/10.1080/10494820.2020.1777167
Lu, J., Zhang, X., & Stephens, M. (2019). Visualizing the commognitive processes in computer-supported one-to-one tutoring. Interactive Learning Environments. https://doi.org/10.1080/10494820.2019.1610452
Meyer, M. (2018). Options of discovering and verifying mathematical theorems - Task-design from a philosophic-logical point of view. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/92561
Mumford, M. D., Todd, E. M., Higgs, C., & McIntosh, T. (2017). Cognitive skills and leadership performance: The nine critical skills. Leadership Quarterly. https://doi.org/10.1016/j.leaqua.2016.10.012
Nachlieli, T., & Heyd-Metzuyanim, E. (2021). Commognitive conflicts as a learning mechanism towards explorative pedagogical discourse. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-021-09495-3
Nardi, E., Ryve, A., Stadler, E., & Viirman, O. (2014). Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of Calculus. Research in Mathematics Education. https://doi.org/10.1080/14794802.2014.918338
Ngin, C. S. (2018). Examining a teacher's use of multiple representations in the teaching of percentages : A commognitive perspective. Proceedings of the 41st Annual Conference of the Mathematics Education Research Group of Australasia, 591–598.
Park, H. J., Byun, S. Y., Sim, J., Han, H., & Baek, Y. S. (2016). Teachers' perceptions and practices of STEAM education in South Korea. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.12973/eurasia.2016.1531a
Park, J. H., & Lee, K. H. (2018). Introduction to the special issue on abductive reasoning in mathematics education. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/92551
Pratiwi, E., Nusantara, T., Susiswo, S., & Muksar, M. (2020). Textual and contextual commognitive conflict students in solving an improper fraction. Journal for the Education of Gifted Young Scientists. https://doi.org/10.17478/jegys.678528
Presmeg, N. (2016). Commognition as a lens for research. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-015-9676-1
Putut, E., Emanuel, L., & Anam, F. (2022). Sebuah Tinjauan Commognitive : Apakah Matriks Singular ? 7(54), 922–930.
Putut, E., Emanuel, L., Nusantara, T., Rahman, A., & Rahardi, R. (2023). Why am I confused ? Commognitive Conflict in Non-ordinary Question About Number Division. Journal for ReAttach Therapy and Developmental Diversities, 6, 891–901.
Scott, D., Hargreaves, E., & Sfard, A. (2015). Learning, Commognition, and Mathematics. In The SAGE Handbook of Learning. https://doi.org/10.4135/9781473915213.n12
Sfard, A. (2014). University mathematics as a discourse - why, how, and what for? Research in Mathematics Education, 16(2), 199–203. https://doi.org/10.1080/14794802.2014.918339
Sfard, A. (2016). and Mathematics. Learning, Commognition and Mathematics, (January), 129–138.
Sfard, A. (2018). Anna Sfard Department of Mathematics Education, University of Haifa, Haifa, Israel. 1–7.
Sfard, A. (2020). Commognition. In Encyclopedia of Mathematics Education. https://doi.org/10.1007/978-3-030-15789-0_100031
Son, J. W., Han, S. W., Kang, C., & Kwon, O. N. (2016). A comparative analysis of the relationship among quality instruction, teacher self-efficacy, student background, and mathematics achievement in South Korea and the United States. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.12973/eurasia.2016.1532a
Tabach, M., & Nachlieli, T. (2016). Communicational perspectives on learning and teaching mathematics: prologue. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-015-9638-7
Thoma, A., & Nardi, E. (2017). Discursive shifts from school to university mathematics and lecturer assessment practices: Commognitive conflicts regarding variables. Proceedings of the 10th Congress of the European Society for Research in Mathematics Education.
Thoma, A., & Nardi, E. (2018). Transition from School to University Mathematics: Manifestations of Unresolved Commognitive Conflict in First Year Students' Examination Scripts. International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-017-0064-3
Viirman, O. (2011). Discourses of Functions – University Mathematics Teaching Through a Commognitive Lens. Proceedings of the 7th Conference on European Research in Mathematics Education.
Viirman, O. (2014). The functions of function discourse - university mathematics teaching from a commognitive standpoint. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2013.855328
Viirman, O. (2015). Explanation, motivation, and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2015.1034206
Viirman, O., & Nardi, E. (2019a). Negotiating different disciplinary discourses: biology students' ritualized and exploratory participation in mathematical modeling activities. Educational Studies in Mathematics, 101(2), 233–252. https://doi.org/10.1007/s10649-018-9861-0
Viirman, O., & Nardi, E. (2019b). Negotiating different disciplinary discourses: biology students' ritualized and exploratory participation in mathematical modeling activities. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-018-9861-0
Widana, I. W. (2018). Higher Order Thinking Skills Assessment towards Critical Thinking on Mathematics Lesson. International Journal of Social Sciences and Humanities (IJSSH). https://doi.org/10.29332/ijssh.v2n1.74
Wu, W. C., & Perng, Y. H. (2016). Research on the correlations among mobile learning perception, study habits, and continuous learning. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.12973/eurasia.2016.1556a
ZAYYADİ, M. (2020). Content and Pedagogical Knowledge of Prospective Teachers in Mathematics Learning: Commognitive Framework. Journal for the Education of Gifted Young Scientists. https://doi.org/10.17478/jegys.642131
Zayyadi, M., Nusantara, T., Subanji, Hidayanto, E., & Sulandra, I. M. (2019). A commognitive framework: The process of solving mathematical problems of middle school students. International Journal of Learning, Teaching and Educational Research. https://doi.org/10.26803/ijlter.18.2.7
Ampuero, D., Miranda, C. E., Delgado, L. E., Goyen, S., & Weaver, S. (2015). Empathy and critical thinking: primary students solving local environmental problems through outdoor learning. Journal of Adventure Education and Outdoor Learning. https://doi.org/10.1080/14729679.2013.848817
Chikiwa, C., & Schäfer, M. (2018). Promoting critical thinking in multilingual mathematics classes through questioning. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/91832
Cresswell, J. (2013). Qualitative, quantitative, and mixed methods approaches. In Research Design. https://doi.org/10.2307/3152153
Emanuel, E. P. L., & Meilantifa. (2022). Dimanakah Nilai Ekstrim Fungsi Kuadrat Ditinjau dari Lensa Commognitive ? BRILIANT Jurnal Riset Dan Konseptual, 7(54), 269–279.
Erikson, M. G., & Erikson, M. (2019). Learning outcomes and critical thinking–good intentions in conflict. Studies in Higher Education. https://doi.org/10.1080/03075079.2018.1486813
Fazriyah, N., Supriyati, Y., & Rahayu, W. (2018). Watson-Glaser s Critical Thinking Skills Watson-Glaser's Critical Thinking Skills. 2nd International Conference on Statistics, Mathematics, Teaching, and Research, 1–6. Retrieved from https://iopscience.iop.org/article/10.1088/1742-6596/1028/1/012094/pdf
Fernández-León, A., Gavilán-Izquierdo, J. M., González-Regaña, A. J., Martín-Molina, V., & Toscano, R. (2019). Identifying routines in the discourse of undergraduate students when defining. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-019-00301-1
Hafni, R. N. (2017). 21st Century Learner: Be A Critical Thinking. The Second International Conference on Education and Regional Development 2017 (ICERD 2nd), 1(1). Retrieved from http://icerd2017.conference.upi.edu/download/
Halim, D., Nurhidayati, S., Zayyadi, M., Lanya, H., & Hasanah, S. I. (2020). Commognitive analysis of the solving problem of logarithm on mathematics prospective teachers. Journal of Physics: Conference Series, 1663(1). https://doi.org/10.1088/1742-6596/1663/1/012002
Heinrich, W. F., Habron, G. B., Johnson, H. L., & Goralnik, L. (2015). Critical Thinking Assessment Across Four Sustainability-Related Experiential Learning Settings. Journal of Experiential Education. https://doi.org/10.1177/1053825915592890
Im, S., Yoon, H. G., & Cha, J. (2016). Pre-service science teacher education system in South Korea: Prospects and challenges. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.12973/eurasia.2016.1533a
Ioannou, M. (2016). Commognitive Analysis of Undergraduate Mathematics Students' Responses in Proving Subgroup's Non-Emptiness. Opening up Mathematics Education Research (Proceedings of the 39th Annual Conference of the Mathematics Education Research Group of Australasia), 344–351.
Ioannou, M. (2017). Investigating the discursive shift in the learning of Group Theory : Analysis of some interdiscursive commognitive conflicts. Retrieved from https://keynote.conference-services.net/resources/444/5118/pdf/CERME10_0167.pdf
Ioannou, M. (2018). Commognitive analysis of undergraduate mathematics students' first encounter with the subgroup test. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-017-0222-6
Jones, T. (2017). Playing Detective to Enhance Critical Thinking. Teaching and Learning in Nursing. https://doi.org/10.1016/j.teln.2016.09.005
Kaya, D., & Aydin, H. (2016). Elementary mathematics teachers' perceptions and lived experiences on mathematical communication. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.12973/eurasia.2014.1203a
Kim, D.-J., Choi, S., Lim, W., Thoma, A., Nardi, E., Viirman, O., … Sfard, A. (2019a). Discourses of Functions – University Mathematics Teaching Through a Commognitive Lens. Educational Studies in Mathematics.
Kim, D.-J., Choi, S., Lim, W., Thoma, A., Nardi, E., Viirman, O., … Sfard, A. (2019b). Discourses of Functions – University Mathematics Teaching Through a Commognitive Lens. Educational Studies in Mathematics, 8(2), 423–430. https://doi.org/10.1007/s10649-015-9676-1
Larsson, K. (2017). Understanding and teaching critical thinking—A new approach. International Journal of Educational Research. https://doi.org/10.1016/j.ijer.2017.05.004
Lu, J., Tao, Y., Xu, J., & Stephens, M. (2020). Commognitive responsibility shift and its visualizing in computer-supported one-to-one tutoring. Interactive Learning Environments. https://doi.org/10.1080/10494820.2020.1777167
Lu, J., Zhang, X., & Stephens, M. (2019). Visualizing the commognitive processes in computer-supported one-to-one tutoring. Interactive Learning Environments. https://doi.org/10.1080/10494820.2019.1610452
Meyer, M. (2018). Options of discovering and verifying mathematical theorems - Task-design from a philosophic-logical point of view. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/92561
Mumford, M. D., Todd, E. M., Higgs, C., & McIntosh, T. (2017). Cognitive skills and leadership performance: The nine critical skills. Leadership Quarterly. https://doi.org/10.1016/j.leaqua.2016.10.012
Nachlieli, T., & Heyd-Metzuyanim, E. (2021). Commognitive conflicts as a learning mechanism towards explorative pedagogical discourse. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-021-09495-3
Nardi, E., Ryve, A., Stadler, E., & Viirman, O. (2014). Commognitive analyses of the learning and teaching of mathematics at university level: The case of discursive shifts in the study of Calculus. Research in Mathematics Education. https://doi.org/10.1080/14794802.2014.918338
Ngin, C. S. (2018). Examining a teacher's use of multiple representations in the teaching of percentages : A commognitive perspective. Proceedings of the 41st Annual Conference of the Mathematics Education Research Group of Australasia, 591–598.
Park, H. J., Byun, S. Y., Sim, J., Han, H., & Baek, Y. S. (2016). Teachers' perceptions and practices of STEAM education in South Korea. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.12973/eurasia.2016.1531a
Park, J. H., & Lee, K. H. (2018). Introduction to the special issue on abductive reasoning in mathematics education. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/92551
Pratiwi, E., Nusantara, T., Susiswo, S., & Muksar, M. (2020). Textual and contextual commognitive conflict students in solving an improper fraction. Journal for the Education of Gifted Young Scientists. https://doi.org/10.17478/jegys.678528
Presmeg, N. (2016). Commognition as a lens for research. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-015-9676-1
Putut, E., Emanuel, L., & Anam, F. (2022). Sebuah Tinjauan Commognitive : Apakah Matriks Singular ? 7(54), 922–930.
Putut, E., Emanuel, L., Nusantara, T., Rahman, A., & Rahardi, R. (2023). Why am I confused ? Commognitive Conflict in Non-ordinary Question About Number Division. Journal for ReAttach Therapy and Developmental Diversities, 6, 891–901.
Scott, D., Hargreaves, E., & Sfard, A. (2015). Learning, Commognition, and Mathematics. In The SAGE Handbook of Learning. https://doi.org/10.4135/9781473915213.n12
Sfard, A. (2014). University mathematics as a discourse - why, how, and what for? Research in Mathematics Education, 16(2), 199–203. https://doi.org/10.1080/14794802.2014.918339
Sfard, A. (2016). and Mathematics. Learning, Commognition and Mathematics, (January), 129–138.
Sfard, A. (2018). Anna Sfard Department of Mathematics Education, University of Haifa, Haifa, Israel. 1–7.
Sfard, A. (2020). Commognition. In Encyclopedia of Mathematics Education. https://doi.org/10.1007/978-3-030-15789-0_100031
Son, J. W., Han, S. W., Kang, C., & Kwon, O. N. (2016). A comparative analysis of the relationship among quality instruction, teacher self-efficacy, student background, and mathematics achievement in South Korea and the United States. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.12973/eurasia.2016.1532a
Tabach, M., & Nachlieli, T. (2016). Communicational perspectives on learning and teaching mathematics: prologue. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-015-9638-7
Thoma, A., & Nardi, E. (2017). Discursive shifts from school to university mathematics and lecturer assessment practices: Commognitive conflicts regarding variables. Proceedings of the 10th Congress of the European Society for Research in Mathematics Education.
Thoma, A., & Nardi, E. (2018). Transition from School to University Mathematics: Manifestations of Unresolved Commognitive Conflict in First Year Students' Examination Scripts. International Journal of Research in Undergraduate Mathematics Education. https://doi.org/10.1007/s40753-017-0064-3
Viirman, O. (2011). Discourses of Functions – University Mathematics Teaching Through a Commognitive Lens. Proceedings of the 7th Conference on European Research in Mathematics Education.
Viirman, O. (2014). The functions of function discourse - university mathematics teaching from a commognitive standpoint. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2013.855328
Viirman, O. (2015). Explanation, motivation, and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2015.1034206
Viirman, O., & Nardi, E. (2019a). Negotiating different disciplinary discourses: biology students' ritualized and exploratory participation in mathematical modeling activities. Educational Studies in Mathematics, 101(2), 233–252. https://doi.org/10.1007/s10649-018-9861-0
Viirman, O., & Nardi, E. (2019b). Negotiating different disciplinary discourses: biology students' ritualized and exploratory participation in mathematical modeling activities. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-018-9861-0
Widana, I. W. (2018). Higher Order Thinking Skills Assessment towards Critical Thinking on Mathematics Lesson. International Journal of Social Sciences and Humanities (IJSSH). https://doi.org/10.29332/ijssh.v2n1.74
Wu, W. C., & Perng, Y. H. (2016). Research on the correlations among mobile learning perception, study habits, and continuous learning. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.12973/eurasia.2016.1556a
ZAYYADİ, M. (2020). Content and Pedagogical Knowledge of Prospective Teachers in Mathematics Learning: Commognitive Framework. Journal for the Education of Gifted Young Scientists. https://doi.org/10.17478/jegys.642131
Zayyadi, M., Nusantara, T., Subanji, Hidayanto, E., & Sulandra, I. M. (2019). A commognitive framework: The process of solving mathematical problems of middle school students. International Journal of Learning, Teaching and Educational Research. https://doi.org/10.26803/ijlter.18.2.7
Published
2024-07-27
How to Cite
Emanuel, E. P., Nusantara, T., & Rahardi, R. (2024). Does Domain of Absolute Value Function Always Positive? Commognitive-Conflict Analysis of Students of First Semester. QALAMUNA: Jurnal Pendidikan, Sosial, Dan Agama, 16(2), 795-806. https://doi.org/10.37680/qalamuna.v16i2.5169
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Copyright (c) 2024 Endrayana Putut Laksminto Emanuel, Toto Nusantara, Rustanto Rahardi
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