Computational Thinking Process of Prospective Mathematics Teacher in Solving Diophantine Linear Equation Problems
Neneng Aminah
,
Yohanes Leonardus Sukestiyarno
,
Wardono Wardono
,
Adi Nur Cahyono
Prospective teachers facing the 21st century are expected to have the ability to solve problems with a computer mindset. Problems in learning mathemat.
- Pub. date: July 15, 2022
- Pages: 1495-1507
- 545 Downloads
- 579 Views
- 3 Citations
Prospective teachers facing the 21st century are expected to have the ability to solve problems with a computer mindset. Problems in learning mathematics also require the concept of computational thinking (CT). However, many still find it challenging to solve this problem. The subjects in this study were twenty-one prospective mathematics teachers who took number theory courses, and then two research samples were selected using the purposive sampling technique. This study uses a qualitative descriptive method to describe the thinking process of prospective teachers in solving Diophantine linear equation problems. The results showed that the first subject's thought process was started by turning the problem into a mathematical symbol, looking for the Largest Common Factor (LCF) with the Euclidean algorithm, decomposition process, and evaluation. The second subject does not turn the problem into symbols and does not step back in the algorithm. The researcher found that teacher candidates who found solutions correctly in their thinking process solved mathematical problem used CT components, including reflective abstraction thinking, algorithmic thinking, decomposition, and evaluation. Further research is needed to develop the CT components from the findings of this study on other materials through learning with a CT approach.
Keywords: APOS, computational thinking, mathematical problem.
References
Arikunto, S. (2016). Evaluation basics. Bumi Aksara Press.
Arnon, I., Cottrill, J., Dubinsky, E., Oktaç, A., Fuentes, S. R., Trigueros, M., & Weller, K. (2014). APOS Theory. Springer. https://doi.org/10.1007/978-1-4614-7966-6
Barr, V., & Stephenson, C. (2011). Bringing computational thinking to K-12: What is involved and what is the role of the computer science education community? ACM Inroads, 2(1), 48–54. https://doi.org/10.1145/1929887.1929905
Bintoro, H. S., Mulyono, Sukestiyarno, Y. L., & Walid. (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
Bocconi, S., Chioccariello, A., Dettori, G., Ferrari, A., & Engelhardt, K. (2016). Developing computational thinking in compulsory education-implications for policy and practice. Publication Office of the European Union. https://doi.org/10.2791/792158
Borkulo, S. V., Chytas, C., Drijvers, P., Barendsen, E., & Tolboom, J. (2021). Computational thinking in the mathematics classroom: fostering algorithmic thinking and generalization skills using dynamic mathematics software. In A. Muhling, M. Armoni, & M. Berges (Ed.), The 16th Workshop in Primary and Secondary Computing Education (WiPSCE ’21) (pp. 1-9). ACM Digital Library. https://doi.org/10.1145/3481312.3481319
Cetin, I., & Dubinsky, E. (2017). Reflective abstraction in computational thinking. Journal of Mathematical Behavior, 47(3), 70–80. https://doi.org/10.1016/j.jmathb.2017.06.004
Creswell, J. W., & Plano Clark, V. L. (2018). Core mixed methods design: Designing and conducting mixed methods research approach. SAGE Publication.
Czerkawski, B. C., & Lyman, E. W. (2015). Exploring issues about computational thinking in higher education. TechTrends, 59(2), 57–65. https://doi.org/10.1007/s11528-015-0840-3
Do, H., Melnik, S., & Rahm, E. (2003). Comparison of schema matching evaluations. In: A.B. Chaudhri, E. Rahm, M. Jeckle, & R. Unland (Ed.), Web, Web-Services, and Database Systems. NODe 2002. Lecture Notes in Computer Science (Vol. 2593, p. 1-7). Springer. https://doi.org/10.1007/3-540-36560-5_17
Dubinsky, E. D., & Mcdonald, M. A. (2001). Apos : A constructivist theory of learning in undergraduate mathematics education. The Teaching and Learning of Mathematics at University Level, 7, 275–282. https://doi.org/10.1007/0-306-47231-7_25
Ferrari, P. L. (2003). Abstraction in mathematics. Philosophical Transactions of the Royal Society B: Biological Sciences, 358(1435), 1225–1230. https://doi.org/10.1098/rstb.2003.1316
Fuady, A., Purwanto, Susiswo, & Rahardjo, S. (2019). Abstraction reflective student in problem solving of Mathematics based cognitive style. International Journal of Humanities and Innovation, 2(4), 103–107. https://doi.org/10.33750/ijhi.v2i4.50
Gravemeijer, K. (2011). How concrete is concrete? Journal on Mathematics Education, 2(1), 1–14. https://doi.org/10.22342/jme.2.1.780.1-14
Gray, E. M., & Tall, D. O. (2007). Abstraction as a natural process of mental compression. Mathematics Education Research Journal, 19(2), 23–40. https://doi.org/10.1007/BF03217454
Henderson, P. B., Henderson, P. B., Cortina, T. J., & Wing, J. M. (2007). Computational thinking. ACM SIGCSE Bulletin, 39(1), 195-196. https://doi.org/10.1145/1227310.1227378
Hershkovitz, A., Sitman, R., Israel-fishelson, R., Eguíluz, A., Garaizar, P., & Guenaga, M. (2019). Creativity in the acquisition of computational thinking. Interactive Learning Environments, 27(5-6), 628–644. https://doi.org/10.1080/10494820.2019.1610451
Ioannou, I., & Angeli, C. (2016). A framework and an instructional design model for the development of students’ computational and algorithmic thinking. In A. Lebrocq, & M. Birt (Ed.), Mediterranean Conference on Information Systems (MCIS) (pp. 1–8). AIS Electronic Library. http://aisel.aisnet.org/mcis2016/19
Lavigne, H. J., Lewis-Presser, A., & Rosenfeld, D. (2020). An exploratory approach for investigating the integration of computational thinking and mathematics for preschool children. Journal of Digital Learning in Teacher Education, 36(1), 63–77. https://doi.org/10.1080/21532974.2019.1693940
Lee, I., Grover, S., Martin, F., Pillai, S., & Malyn-Smith, J. (2020). Computational thinking from a disciplinary perspective: integrating computational thinking in K-12 science, technology, engineering, and mathematics education. Journal of Science Education and Technology, 29(1), 1-8. https://doi.org/10.1007/s10956-019-09803-w
Lee, I., Martin, F., Denner, J., Coulter, B., Allan, W., Erickson, J., Malyn-Smith, J., & Werner, L. (2011). Computational thinking for youth in practice. Associate Computing Machinery, 2(1), 32-37. https://doi.org/10.1145/1929887.1929902
Litts, B. K., Lewis, W. E., & Mortensen, C. K. (2020). Engaging youth in computational thinking practices through designing place-based mobile games about local issues. Interactive Learning Environments, 28(3), 302–315. https://doi.org/10.1080/10494820.2019.1674883
Liu, J., & Wang, L. (2010). Computational thinking in discrete mathematics. Education Technology and Computer Science Computational, 42(3), 413–416. https://doi.org/10.1109/ETCS.2010.200
Looi, C. K., How, M. L., Longkai, W., Seow, P., & Liu, L. (2018). Analysis of linkages between an unplugged activity and the development of computational thinking. Computer Science Education, 28(3), 255–279. https://doi.org/10.1080/08993408.2018.1533297
Mitchelmore, M. C., & White, P. (2000). Development of angle concepts by progressive abstraction and generalisation. Educational Studies in Mathematics, 41(2), 209–238. https://doi.org/10.1023/A:1003927811079
Osborne, P. (2004). The reproach of abstraction. Radical Philosophy, 127(2), 21–28. https://bit.ly/3NnQdji
Pala, F. K., & Mıhçı Türker, P. (2019). The effects of different programming trainings on the computational thinking skills. Interactive Learning Environments, 20(4), 1–11. https://doi.org/10.1080/10494820.2019.1635495
Pei, C. (Yu), Weintrop, D., & Wilensky, U. (2018). Cultivating computational thinking practices and mathematical habits of mind in lattice land. Mathematical Thinking and Learning, 20(1), 75–89. https://doi.org/10.1080/10986065.2018.1403543
Rich, K. M., Binkowski, T. A., Strickland, C., & Franklin, D. (2018). Decomposition: A K-8 computational thinking learning trajectory. In A. Korhonen, L. Malmi, R. McCartney (Ed.), ICER 2018 - Proceedings of the 2018 ACM Conference on International Computing Education Research (p.124–132). ACM Digital Library. https://doi.org/10.1145/3230977.3230979
Rich, P., Rich, P. J., Egan, G., & Ellsworth, J. (2019). A framework for decomposition in computational thinking. In B. Scharlau, & R. McDermott (Ed.), ITiCSE '19: Proceedings of the 2019 ACM Conference on Innovation and Technology in Computer Science Education, (pp. 416–421). Association for Computing Machinery. https://doi.org/10.1145/3304221.3319793
Rodríguez-Martínez, J. A., González-Calero, J. A., & Sáez-lópez, M. (2019). Computational thinking and mathematics using Scratch : An experiment with sixth-grade students. Interactive Learning Environments, 20(3), 1–12. https://doi.org/10.1080/10494820.2019.1612448
Sak, U. (2011). Selective problem solving (SPS): A model for teaching creative problem-solving. Gifted Education International, 27(3), 349–357. https://doi.org/10.1177/026142941102700310
Santrock, J. W. (2011). Life-span development. Erlangga.
Selby, C. (2015). Relationships : Computational thinking , pedagogy of programming , and Bloom ’ s Taxonomy. In J. Ezer, J. Vahrenhol, & S. Sentence (Ed.), WiPSCE '15: Proceedings of the Workshop in Primary and Secondary Computing Education (pp. 80–87). Association for Computing Machinery (ACM). https://doi.org/10.1145/2818314.2818315
Selby, C., & Woollard, J. (2013). Computational thinking : The developing definition. In A. Clear, B. Manaris, & D. Finkel (Ed.), ITiCSE '13: Proceedings of the 2013 conference on Innovation & technology in computer science education (pp. 5–8). Association for Computing Machinery (ACM). https://bit.ly/3Mkhovn
Selby, C., & Woollard, J. (2014, December 10). Refining an understanding of computational thinking. University of Southampton Institutional Repository. https://eprints.soton.ac.uk/372410/
Simon, M. A. (2020). Elaborating reflective abstraction for instructional design in mathematics: Postulating a second type of reflective abstraction. Mathematical Thinking and Learning, 22(2), 162–171. https://doi.org/10.1080/10986065.2020.1706217
Sukestiyarno, Y. (2020). Research educational method (1st ed.). UNNES Press.
Susanti, R., & Taufik, M. (2021).Analysis of students computational thinking in social statistic problem. Supremum Journal of Mathematics Education, 5(1), 22-31. https://doi.org/10.35706/sjme.v5i1.4376
Sys, M. M. (2018). From algorithmic to computational thinking : On the way for computing for all students. In V. Dagiene (Ed.), ITiCSE '15: Proceedings of the 2015 Conference on Innovation and Technology in Computer Science Education (p. 1-8). Association for Computing Machinery (ACM). https://doi.org/10.1145/2729094.2742582
Toscano, A. (2008). The culture of abstraction. Theory, Culture & Society, 25(4), 57–75. https://doi.org/10.1177/0263276408091983
Tse, D. (2011). Schema dependent gene activation and memory encoding in neocortex. Science, 333(12), 891–895. https://doi.org/10.1126/science.1205274
Tse, D., Langston, R. F., Kakeyama, M., Bethus, I., Spooner, P. A., Wood, E. R., Witter, M. P., & Morris, R. G. M. (2007). Schemas and memory consolidation. Science, 316(4), 76–82. https://doi.org/10.1126/science.1135935
Van Kesteren, M. T. R., Ruiter, D. J., Fernandez, G., & Henson, R. N. (2012). How schema and novelty augment memory formation. Trends in Neurosciences, 35(4), 211–219. https://doi.org/10.1016/j.tins.2012.02.001
Weintrop, D., Beheshti, E., Horn, M., Orton, K., Jona, K., Trouille, L., & Wilensky, U. (2016). Defining computational thinking for mathematics and science classrooms. Journal of Science Education and Technology, 25(1), 127–147. https://doi.org/10.1007/s10956-015-9581-5
Wing, J. M. (2010). Computational thinking. Communications of the ACM, 49(3), 33-35. https://dl.acm.org/doi/10.1145/1118178.1118215
Wing, J. M. (2015). Computational thinking and thinking about computing. Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences, 366(2), 3717–3725. https://doi.org/10.1098/rsta.2008.0118
Wing, J. M. (2017). Computational thinking ’ s influence on research and education for all Influenza del pensiero computazionale nella ricerca e nell ’ educazione per tutti. Italian Journal of Educational Technology, 25(2), 7–14. https://doi.org/10.17471/2499-4324/922
Worthen, D., & Luiselli, J. K. (2017). Social validity assessment and intervention evaluation of mindfulness education and practices with high school students. Mindfulness, 8(4), 903–910. https://doi.org/10.1007/s12671-016-0664-z
Worthen, M., Veale, A., McKay, S., & Wessells, M. (2019). The transformative and emancipatory potential of participatory evaluation: Reflections from a participatory action research study with war-affected young mothers. Oxford Development Studies, 47(2), 154–170. https://doi.org/10.1080/13600818.2019.1584282
Yadav, A., Hong, H., & Stephenson, C. (2016). Computational thinking for all: Pedagogical approaches to embedding 21st century problem solving in K-12 classrooms. TechTrends, 42(2), 565–568. https://doi.org/10.1007/s11528-016-0087-7