Exploring the Prospective Mathematics Teachers Computational Thinking in Solving Pattern Geometry Problem

Swasti Maharani; Zeni Fadlila Agustina; Muhammad Noor Kholid

doi:10.35445/alishlah.v13i3.1181

Exploring the Prospective Mathematics Teachers Computational Thinking in Solving Pattern Geometry Problem

Swasti Maharani, Zeni Fadlila Agustina, Muhammad Noor Kholid

Abstract

This research aims to describe the characteristic of mathematics prospective teacher's computational thinking (CT) in solving the geometric pattern problem. The subject consists of 65 preservice mathematics teachers in Universitas in Madiun. The instrument was used in this research are geometric pattern problem tests and interview guidelines. The result shows that are three types of mathematics prospective teachers in solving the problem. First, CT substantial, i.e. prospective mathematics teachers use the conceptual knowledge who collaborated with procedural knowledge exactly. They use mathematics iteration to find the pattern and express them to the general form easily. Second, CT Nominal, i.e. prospective mathematics teachers, use manual ways to solve the pattern problem. They count using numeric, not symbolic, of solving the pattern formed. They can understand the design but can't express it to the mathematics model. Third, CT procedural, i.e. mathematics prospective teacher using the procedural knowledge only, not an expert in concept, and following the steps who teaches from experience before. The recommendation for future research is to develop the research to find the other characters in other mathematics subjects, in other students, to develop the learning models who can embody CT.

Keywords

Computational thinking (CT), Geometric pattern, Conceptual knowledge, Procedural knowledge, Generalization

Full Text:

PDF

References

Amit, M., & Neria, D. (2008). ""Rising to the challenge"": Using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM - International Journal on Mathematics Education, 40(1), 111–129. https://doi.org/10.1007/s11858-007-0069-5

Angeli, C., Voogt, J., Fluck, A., Webb, M., Cox, M., Malyn-Smith, J., & Zagami, J. (2016). A K-6 Computational Thinking Curriculum Framework: Implications for Teacher Knowledge. Educational Technology & Society, 19(3), 47–57.

Ansori, M. (2020). Pemikiran Komputasi (Computational Thinking) dalam Pemecahan Masalah. Dirasah : Jurnal Studi Ilmu Dan Manajemen Pendidikan Islam, 3(1), 111–126. https://doi.org/10.29062/dirasah.v3i1.83

Astuti, E. P. (2017). Representasi Matematis Mahasiswa Calon Guru dalam Menyelesaikan Masalah Matematika. Beta Jurnal Tadris Matematika, 10(1), 70. https://doi.org/10.20414/betajtm.v10i1.100

Aziz, L. A. (2021). Analisis Kemampuan Computational Thinking Mahasiswa Dalam Menyelesaikan Masalah Matematika. Jurnal Undikma, 9(1), 34–42.

Barbosa, A., & Vale, I. (2015). Visualization in pattern generalization : Potential and Challenges. Journal of the European Teacher Education Network, 10(1), 57–70.

Bobango, J. . (1993). Geometry for All Student: Phase-Based Instruction. Dalam Cuevas (Eds). Reaching All Students With Mathematics. Virginia: The National Council of Teachers of Mathematics,Inc.

Boonen, A. J. H., Van Wesel, F., Jolles, J., & Van der Schoot, M. (2014). The role of visual representation type, spatial ability, and reading comprehension in word problem solving: An item-level analysis in elementary school children. International Journal of Educational Research, 68, 15–26. https://doi.org/10.1016/j.ijer.2014.08.001

Deliyianni, E., Monoyiou, A., Elia, I., Georgiou, C., & Zannettou, E. (2009). 'Pupils' visual representations in standard and problematic problem solving in mathematics: Their role in the breach of the didactical contract. European Early Childhood Education Research Journal, 17(1), 95–110. https://doi.org/10.1080/13502930802689079

Ellis, A. B. (2007). Connections between generalizing and justifying: 'Students' reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194–229. https://doi.org/10.2307/30034866

Erdogan, T., Akkaya, R., & Çelebi Akkaya, S. (2009). The effect of the Van Hiele model based instruction on the creative thinking levels of 6th grade primary school students. Kuram ve Uygulamada Egitim Bilimleri, 9(1), 181–194.

Garderen, D. Van. (2006). Spatial Visualization, Visual Imagery, and Mathematical Problem Solving of Students With Varying Abilities. JOURNAL OF LEARNING DISABILITIES, 39(6), 496–506.

Garrett, A. J., Mazzocco, M. M. M., & Baker, L. (2006). Development of the Metacognitive Skills of Prediction and Evaluation in Children With or Without Math Disability. Learning Disabilities Research and Practice, 21(2), 77–88. https://doi.org/10.1111/j.1540-5826.2006.00208.x

Hendriana, H., Sumarmo, U., & Rohaeti, E. E. (2013). Kemampuan Komunikasi Matematik Serta Kemampuan dan Disposisi Berpikir Kritis Matematis. Jurnal Matematika Dan Pendidikan Matematika, 2(1), 35–45.

Imswatama, A., & Muhassanah, N. (2016). Analisis Kesalahan Mahasiswa Dalam Menyelesaikan Soal Geometri Analitik Bidang Materi Garis Dan Lingkaran. Suska Journal of Mathematics Education, 2(1), 1. https://doi.org/10.24014/sjme.v2i1.1368

Kashefi, H., Alias, N. A., Kahar, M. F., Buhari, O., & Zakaria, S. (2015). zVisualization in mathematics problem solving meta-analysis research. E-Proceeding of the International Conference on Social Science Research, 2015(June 2015), 803–812. Retrieved from http://worldconferences.net

Kawuri, K. R., Budiharti, R., & Fauzi, A. (2019). Penerapan Computational Thinking untuk Meningkatkan Kemampuan Berpikir Kritis Siswa Kelas X MIA 9 SMA Negeri 1 Surakarta pada Materi Usaha dan Energi 6. Jurnal Materi Dan Pembelajaran Fisika (JMPF), 9(2), 116–121.

Kaya, D., Izgiol, D., & Kesan, C. (2014). The investigation of elementary mathematics teacher 'candidates' problem solving skills according to various variables. International Electronic Journal of Elementary Education, 6(2), 295–313.

Lavy, I. (2007). A case study of dynamic visualization and problem solving. International Journal of Mathematical Education in Science and Technology, 38(8), 1075–1092. https://doi.org/10.1080/00207390601129196

Lockwood, E., & Asay, A. (2016). Algorithmic thinking : An initial characterization of computational thinking in mathematics. The Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (38th, Tucson, AZ, Nov 3-6, 2016), (November).

Masfingatin, T., & Maharani, S. (2019). Computational Thinking : Students On Proving Geometry Theorem. International Journal of Scientific & Technology Research, 8(09), 2216–2223.

Meha, A. M., & Bullu, N. I. (2021). Hubungan Kesiapan Mengajar Dan Proses Praktik Pengalaman Lapangan Dengan Keterampilan Dasar Mengajar Mahasiswa Pendidikan Biologi. Edukatif : Jurnal Ilmu Pendidikan, 3(2), 412–420. https://doi.org/10.31004/edukatif.v3i2.323

Mitchelmore, M., & White, P. (2007). Abstraction in Mathematics Learning The foundational work on hierarchical abstraction theory was done by the late. Mathematics Education Research Journal, 19(2), 1–9.

Mulligan, J., Kemp, C. R., & Highfield, K. (2008). Encouraging Mathematical Thinking through Pattern & Structure: An Intervention in the First Year of Schooling. Australian Primary Mathematics Classroom (APMC), 3(January), 10–15.

Nurfalah, A., & Bernard, M. (2020). Analisis Kesalahan Siswa SMK dalam Menyelesaikan Soal Materi Geometri Dimensi Tiga. Maju, 7(1), 70–75.

Pasandaran, R. F., & Mufidah, M. (2020). Studi Kasus Pembelajaran Geometri Analitik. Pedagogy: Jurnal Pendidikan Matematika, 5(2), 91–105. https://doi.org/10.30605/pedagogy.v5i2.413

Radford, L. (2006). Algebraic Thinking and The Generalization of Patterns: A Semiotic Perspective. Proceedings of the 28th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1–20. https://doi.org/10.5840/jphil20019858

Reflina. (2020). Kesulitan mahasiswa calon guru matematika dalam menyelesaikan soal pembuktian matematis pada mata kuliah geometri. Jurnal Analisa, 6(1), 80–90.

Reiss, K., & Törner, G. (2007). Problem solving in the mathematics classroom: The German perspective. ZDM - International Journal on Mathematics Education, 39(5–6), 431–441. https://doi.org/10.1007/s11858-007-0040-5

Rivera, F. D., & Becker, J. R. (2008). Middle school 'children's cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns. ZDM - International Journal on Mathematics Education, 40(1), 65–82. https://doi.org/10.1007/s11858-007-0062-z

Rösken, B., & Rolka, K. (2006). A picture is worth a 1000 words – The role of zvisualization in mathematics learning. Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, 4(1989), 457–464.

Selby, C. (2013). Computational Thinking : The Developing Definition. ITiCSE Conference 2013, 5–8.

Sengupta, P., Dickes, A., & Farris, A. (2018). Toward a Phenomenology of Computational Thinking in K-12 STEM. In Computational Thinking in STEM Discipline: Foundations and Research Highlights. Springer.

Sudarsono, Mikrayanti, & Murtalib. (2017). Peningkatan Kemampuan Pemahaman dan Pemecahanmasalah Geometri Siswa SMA Melalui Transactional Reading Strategy. Jurnal Pendidikan MIPA, 7(1), 61–74.

Sugiyono, Murdanu, & Murdiyani, N. M. (2014). Pengembangan Perangkat Pembelajaran Matematika Pada Topik Geometri Menggunakan Paradigma Baru Dalam Pembelajaran Matematika. Jurnal Pendidikan Matematika Dan Sains Tahun II, 2(2), 117–125.

van Garderen, D., & Montague, M. (2003). Visual-Spatial Representation, Mathematical Problem Solving, and Students of Varying Abilities. Learning Disabilities Research and Practice, 18(4), 246–254. https://doi.org/10.1111/1540-5826.00079

van Garderen, D., Scheuermann, A., Poch, A., & Murray, M. M. (2018). Visual Representation in Mathematics: Special Education Teachers' Knowledge and Emphasis for Instruction. Teacher Education and Special Education, 41(1), 7–23. https://doi.org/10.1177/0888406416665448

van Oers, B. (2010). Emergent mathematical thinking in the context of play. Educational Studies in Mathematics, 74(1), 23–37. https://doi.org/10.1007/s10649-009-9225-x

Wing, J. M. (2008). Computational thinking and thinking about computing. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 366(1881), 3717–3725. https://doi.org/10.1098/rsta.2008.0118

Wing, J. M. (2011). Computational thinking. Communications of the ACM, 3–3. https://doi.org/10.1109/vlhcc.2011.6070404

Yanty Putri Nasution, E. (2017). Meningkatkan Kemampuan Spasial Siswa Melalui Pembelajaran Geometri Berbantuan Cabri 3D. M A T H L I N E : Jurnal Matematika Dan Pendidikan Matematika, 2(2), 179–194. https://doi.org/10.31943/mathline.v2i2.45

Yuniarti, Y. (2014). Pengembangan Kemampuan Komunikasi Matematis Dalam Pembelajaran Matematika Di Sekolah Dasar. EduHumaniora | Jurnal Pendidikan Dasar Kampus Cibiru, 6(2), 109–114. https://doi.org/10.17509/eh.v6i2.4575

Zhu, Z. (2007). Gender differences in mathematical problem-solving patterns : A review of the literature. Interbational Education Journal, 8(2), 187–203.

DOI: https://doi.org/10.35445/alishlah.v13i3.1181