Student Representation of Mathematical Thinking In Mathematical Problem Solving
Abstract
The way students who want to become teachers represent their mathematical reasoning when they solve mathematical problems—using case studies and qualitative techniques. Data were gathered from the vignette results of student work. They are using snowball sampling for subject selection. Three third-semester mathematics education program participants served as the study's research subjects—ways for gathering data, such as interviewing and recording. Three steps of the analysis were completed: presentation of data, elaboration of conclusions and verification. As a consequence of meeting all markers of mathematical thinking representation, the S1 and S2 subjects with high and moderate academic talents had good mathematical thinking representation abilities. Because S3 students with limited intellectual skills cannot still represent mathematical ideas.
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References
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Jaming, P., & Moran, W. (2000). Tensor products and p-induction of representations on Banach spaces. Collect. Math, 51(1), 83–109.
Khaleghi, A., Aghaei, Z., & Mahdavi, M. A. (2021). A gamification framework for cognitive assessment and cognitive training: Qualitative study. JMIR Serious Games, 9(2). https://doi.org/10.2196/21900
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Leksono, I. P., & Fitriatien, S. R. (2021). Development of Mathematic Learning Set Based On Pedagogical Content Knowledge to Improve Mathematics Problem Solving Ability. Journal of Medives?: Journal of Mathematics Education IKIP Veteran Semarang, 5(1). https://doi.org/10.31331/medivesveteran.v5i1.1529
Li, H., Zhang, J., & Zhang, E. (2021). A Three-Dimensional Spatial Metaphorical Representation of Generation Implied in Han Kin Terms. Frontiers in Psychology, 12. https://doi.org/10.3389/fpsyg.2021.656586
Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1). https://doi.org/10.46328/ijemst.1111
NCTM. (2000). Principles and Standards for School Mathematics. In School Science and Mathematics (Vol. 47, Issue 8). https://doi.org/10.1111/j.1949-8594.2001.tb17957.x
Pascual, L. E., & San Pedro, A. B. (2018). Post Secondary Students’ Level of Proficiency in Solving Real World Problems in Mathematics. Journal of Applied Mathematics and Physics, 06(01). https://doi.org/10.4236/jamp.2018.61019
Ping Ong, S., Cholia, S., Jain, A., Brafman, M., Gunter, D., Ceder, G., & Persson, K. A. (2014). The Materials application programming interface (API): A simple, flexible and efficient API for materials data based on REpresentational State Transfer (REST) Principles. http://www.elsevier.com/open-access/userlicense/1.0/
Pratiwi, I. C., Inganah, S., & Putri, O. R. U. (2020). Analysis On Written Mathematical Communication Skills At System Of Linear Equations In Two Variables (SLETV) Material Viewed From Student Learning Styles. Mathematics Education Journal, 3(2). https://doi.org/10.22219/mej.v3i2.11069
Romaito, P., Safitri, I., Sarida, H., Nisah, H., Uswatun, Hasanah, Apriani, D., Afsari, S., Dwichanda, O., & Lucky, Y. (2021). The Mathematics Learning using Geogebra Software to Improve Students’ CreativeThinking Ability. Journal of Physics: Conference Series, 1819(1). https://doi.org/10.1088/1742-6596/1819/1/012008
Saad, A. (2020). Students’ computational thinking skill through cooperative learning based on hands-on, inquiry-based, and student-centric learning approaches. Universal Journal of Educational Research, 8(1). https://doi.org/10.13189/ujer.2020.080135
Samad, I., Ahmad, H., & Febryanti. (2020). The ability to improve mathematical representation through media from lipa’ sa’be mandar. Jurnal Sainsmat, 9(1).
Saputra, A. W., Minggi, I., & Djadir. (2021). The Identification of the Concept Understanding on Limit of Functions Based on Students’ Learning Styles in Mathematics Department at FMIPA UNM. Journal of Physics: Conference Series, 1899(1). https://doi.org/10.1088/1742-6596/1899/1/012130
Selvy, Y., Ikhsan, M., Johar, R., & Saminan. (2020). Improving students’ mathematical creative thinking and motivation through GeoGebra assisted problem based learning. Journal of Physics: Conference Series, 1460(1). https://doi.org/10.1088/1742-6596/1460/1/012004
Suastika, K. (2021). Mathematics Learning Model of Open Problem Solving to Develop Students’ Creativity. International Electronic Journal of Mathematics Education, 12(3). https://doi.org/10.29333/iejme/633
Sullivan, P., Clarke, D., & Clarke, B. (2009). Converting Mathematics Tasks to Learning Opportunities?: An Important Aspect of Knowledge for Mathematics Teaching Plenty of Interesting Ideas but Where are the Interesting. 21(1), 85–105.
Tammeleht, A., Rodríguez-Triana, M. J., Koort, K., & Löfström, E. (2021). Scaffolding Collaborative Case-Based Learning during Research Ethics Training. Journal of Academic Ethics, 19(2). https://doi.org/10.1007/s10805-020-09378-x
Tohir, M., Maswar, M., Moh, A., Saiful, S., & Rizki Pradita, D. A. (2020). Prospective teachers’ expectations of students’ mathematical thinking processes in solving problems. European Journal of Educational Research, 9(4). https://doi.org/10.12973/EU-JER.9.4.1735
Utari, D. T., Utomo, D. P., & Zukhrufurrohmah, Z. (2020). Effectiveness of the application of Quantum Learning Model in terms of students’ written mathematical communication skills. Mathematics Education Journal, 4(2). https://doi.org/10.22219/mej.v4i2.12228
Winarso, W. (2018). A Case Study of Misconceptions Students in the Learning of Mathematics; The Concept Limit Function in High School. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2979460
Wulandari, N. D., Cholily, Y. M., & Azmi, R. D. (2020). Analysis of Students ’Mathematic Ability in Using Open Ended Teaching Materials on Class VII Function Relations Materials. Mathematics Education Journal, 4(2). https://doi.org/10.22219/mej.v4i2.12834
Analysis of Quantum Learning Model with Peer Assessment on Achievement Studentâ€TMs Critical Thinking Skill in Mathematics. (2019). Journal of Primary Education, 9(1). https://doi.org/10.15294/jpe.v11i1.35653
Andriani, S. P., Triyanto, T., & Nurhasanah, F. (2021). DEFRAGMENTATION THINKING STRUCTURE TO OVERCOME ERRORS IN ADDRESSING MATHEMATICAL PROBLEM. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(1). https://doi.org/10.24127/ajpm.v10i1.3441
Bakar, M. A. A., & Ismail, N. (2019). Merging of metacognitive regulation strategies and activity based learning through best seller mathematical learning activities to enhance student’s mastery of mathematics. Universal Journal of Educational Research, 7(9A). https://doi.org/10.13189/ujer.2019.071618
Barthel, R., Ainsworth, S., & Sharples, M. (2013). Collaborative knowledge building with shared video representations. International Journal of Human Computer Studies, 71(1), 59–75. https://doi.org/10.1016/j.ijhcs.2012.02.006
Bernard, M., & Setiawan, W. (2020). Development of Geometry Analysis Using Geogebra Scripting in terms of Student Cognitive Capabilities. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032103
Boote, S. K., & Boote, D. N. (2018). ABC problem in elementary mathematics education: Arithmetic before comprehension. Journal of Mathematics Teacher Education, 21(2), 99–122. https://doi.org/10.1007/s10857-016-9350-2
Boudon, P. A., Muñoz, A. M. A., & Standen, C. H. (2020). Motivation and collaboration as cultural ways of learning among rural Mapuche children of La Araucanía. Psicoperspectivas, 19(3). https://doi.org/10.5027/psicoperspectivas-Vol19-Issue3-fulltext-1862
Chamberlin, M. T. (2005). Teachers’ discussions of students’ thinking: meeting the challenge of attending to students’ thinking. 141–170. https://doi.org/10.1007/s10857-005-4770-4
Cho, M. K., & Kim, M. K. (2020). Investigating elementary students’ problem solving and teacher scaffolding in solving an Ill-structured problem. International Journal of Education in Mathematics, Science and Technology, 8(4). https://doi.org/10.46328/IJEMST.V8I4.1148
Harris, J. B., Mishra, P., & Koehler, M. J. (2009). Teachers’ technological pedagogical content knowledge and learning activity types: Curriculum-based technology integration reframed. Journal of Research on Technology in Education, 41(3), 393–416. https://scholarworks.wm.edu/educationpubs
Herna, Nusantara, T., Subanji, & Mulyati, S. (2016). The Characterization Of True Pseudo Construction In Understanding Concept Of Limit Function. IOSR Journal of Research & Method in Education, 6(5).
Ishabu, L. S., Ketut Budayasa, I., & Eko Siswono, T. Y. (2019). Creative thinking process of female elementary school student with visual learning style in mathematical problem solving. Journal of Physics: Conference Series, 1265(1). https://doi.org/10.1088/1742-6596/1265/1/012018
Izzatin, M., Waluyo, S. B., Rochmad, & Wardono. (2020). Students’ cognitive style in mathematical thinking process. Journal of Physics: Conference Series, 1613(1). https://doi.org/10.1088/1742-6596/1613/1/012055
Jaming, P., & Moran, W. (2000). Tensor products and p-induction of representations on Banach spaces. Collect. Math, 51(1), 83–109.
Khaleghi, A., Aghaei, Z., & Mahdavi, M. A. (2021). A gamification framework for cognitive assessment and cognitive training: Qualitative study. JMIR Serious Games, 9(2). https://doi.org/10.2196/21900
Köklü, Ö., & Jakubowski, E. (2010). From interpretations to graphical representations: A case study investigation of covariational reasoning. Egitim Arastirmalari - Eurasian Journal of Educational Research, 40.
Krawec, J. L. (2014). Problem Representation and Mathematical Problem Solving of Students of Varying Math Ability. Journal of Learning Disabilities. https://doi.org/10.1177/0022219412436976
Lee, T. H., Qu, Y., & Telzer, E. H. (2019). Neural Representation of Parental Monitoring and Links to Adolescent Risk Taking. Frontiers in Neuroscience, 13. https://doi.org/10.3389/fnins.2019.01286
Leksono, I. P., & Fitriatien, S. R. (2021). Development of Mathematic Learning Set Based On Pedagogical Content Knowledge to Improve Mathematics Problem Solving Ability. Journal of Medives?: Journal of Mathematics Education IKIP Veteran Semarang, 5(1). https://doi.org/10.31331/medivesveteran.v5i1.1529
Li, H., Zhang, J., & Zhang, E. (2021). A Three-Dimensional Spatial Metaphorical Representation of Generation Implied in Han Kin Terms. Frontiers in Psychology, 12. https://doi.org/10.3389/fpsyg.2021.656586
Mainali, B. (2021). Representation in teaching and learning mathematics. International Journal of Education in Mathematics, Science and Technology, 9(1). https://doi.org/10.46328/ijemst.1111
NCTM. (2000). Principles and Standards for School Mathematics. In School Science and Mathematics (Vol. 47, Issue 8). https://doi.org/10.1111/j.1949-8594.2001.tb17957.x
Pascual, L. E., & San Pedro, A. B. (2018). Post Secondary Students’ Level of Proficiency in Solving Real World Problems in Mathematics. Journal of Applied Mathematics and Physics, 06(01). https://doi.org/10.4236/jamp.2018.61019
Ping Ong, S., Cholia, S., Jain, A., Brafman, M., Gunter, D., Ceder, G., & Persson, K. A. (2014). The Materials application programming interface (API): A simple, flexible and efficient API for materials data based on REpresentational State Transfer (REST) Principles. http://www.elsevier.com/open-access/userlicense/1.0/
Pratiwi, I. C., Inganah, S., & Putri, O. R. U. (2020). Analysis On Written Mathematical Communication Skills At System Of Linear Equations In Two Variables (SLETV) Material Viewed From Student Learning Styles. Mathematics Education Journal, 3(2). https://doi.org/10.22219/mej.v3i2.11069
Romaito, P., Safitri, I., Sarida, H., Nisah, H., Uswatun, Hasanah, Apriani, D., Afsari, S., Dwichanda, O., & Lucky, Y. (2021). The Mathematics Learning using Geogebra Software to Improve Students’ CreativeThinking Ability. Journal of Physics: Conference Series, 1819(1). https://doi.org/10.1088/1742-6596/1819/1/012008
Saad, A. (2020). Students’ computational thinking skill through cooperative learning based on hands-on, inquiry-based, and student-centric learning approaches. Universal Journal of Educational Research, 8(1). https://doi.org/10.13189/ujer.2020.080135
Samad, I., Ahmad, H., & Febryanti. (2020). The ability to improve mathematical representation through media from lipa’ sa’be mandar. Jurnal Sainsmat, 9(1).
Saputra, A. W., Minggi, I., & Djadir. (2021). The Identification of the Concept Understanding on Limit of Functions Based on Students’ Learning Styles in Mathematics Department at FMIPA UNM. Journal of Physics: Conference Series, 1899(1). https://doi.org/10.1088/1742-6596/1899/1/012130
Selvy, Y., Ikhsan, M., Johar, R., & Saminan. (2020). Improving students’ mathematical creative thinking and motivation through GeoGebra assisted problem based learning. Journal of Physics: Conference Series, 1460(1). https://doi.org/10.1088/1742-6596/1460/1/012004
Suastika, K. (2021). Mathematics Learning Model of Open Problem Solving to Develop Students’ Creativity. International Electronic Journal of Mathematics Education, 12(3). https://doi.org/10.29333/iejme/633
Sullivan, P., Clarke, D., & Clarke, B. (2009). Converting Mathematics Tasks to Learning Opportunities?: An Important Aspect of Knowledge for Mathematics Teaching Plenty of Interesting Ideas but Where are the Interesting. 21(1), 85–105.
Tammeleht, A., Rodríguez-Triana, M. J., Koort, K., & Löfström, E. (2021). Scaffolding Collaborative Case-Based Learning during Research Ethics Training. Journal of Academic Ethics, 19(2). https://doi.org/10.1007/s10805-020-09378-x
Tohir, M., Maswar, M., Moh, A., Saiful, S., & Rizki Pradita, D. A. (2020). Prospective teachers’ expectations of students’ mathematical thinking processes in solving problems. European Journal of Educational Research, 9(4). https://doi.org/10.12973/EU-JER.9.4.1735
Utari, D. T., Utomo, D. P., & Zukhrufurrohmah, Z. (2020). Effectiveness of the application of Quantum Learning Model in terms of students’ written mathematical communication skills. Mathematics Education Journal, 4(2). https://doi.org/10.22219/mej.v4i2.12228
Winarso, W. (2018). A Case Study of Misconceptions Students in the Learning of Mathematics; The Concept Limit Function in High School. SSRN Electronic Journal. https://doi.org/10.2139/ssrn.2979460
Wulandari, N. D., Cholily, Y. M., & Azmi, R. D. (2020). Analysis of Students ’Mathematic Ability in Using Open Ended Teaching Materials on Class VII Function Relations Materials. Mathematics Education Journal, 4(2). https://doi.org/10.22219/mej.v4i2.12834
Published
2023-01-27
How to Cite
BUHAERAH, Buhaerah; NASIR, Muhammad.
Student Representation of Mathematical Thinking In Mathematical Problem Solving.
Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, [S.l.], v. 7, n. 1, p. 57 - 68, jan. 2023.
ISSN 2549-5070.
Available at: <https://www.e-journal.ivet.ac.id/index.php/matematika/article/view/2241>. Date accessed: 06 may 2024.
doi: https://doi.org/10.31331/medivesveteran.v7i1.2241.
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