Exploring of Student’s Algebraic Thinking Process Through Pattern Generalization using Similarity or Proximity Perception

Authors

  • Iva Nurmawanti Universitas Mataram
  • I Made Sulandra Universitas Negeri Malang

DOI:

https://doi.org/10.31980/mosharafa.v9i2.603

Keywords:

algebraic thinking, pattern identification, pattern generalization, perception of proximity, perception of similarity, identifikasi pola, generalisasi pola, pemikiran aljabar, persepsi proximity, persepsi similarity

Abstract

Students' algebraic thinking skills must continue to be developed because they can support success in mathematics. Algebraic thinking relates to generalizing patterns learned at the junior secondary level. During the process of generalizing students use the perception of similarity or proximity. Therefore, the purpose of this study is to describe the algebraic thinking process of junior high school students in generalizing patterns. The approach used is qualitative with 3 research subjects who have different algebraic thought processes. The results showed that junior high school students carried out algebraic thought processes by perceiving images, representing, looking for functional relationships, making generalizations, and applying general formulas. The difference in perception is used early in the activity and in the search for functional relationships. The results of this study can be used in developing mathematics learning strategies so that students' algebraic thinking skills develop.

Kemampuan berpikir aljabar siswa harus terus dikembangkan karena dapat mendukung kesuksesan dalam matematika.  Berpikir aljabar generalisasi dengan generalisasi pola yang dipelajari pada tingkat SMP. Pada saat proses melakukan generalisasi siswa menggunakan persepsi similarity atau proximity. Oleh sebab itu, tujuan penelitian ini yaitu mendeskripsikan proses berpikir aljabar siswa SMP dalam melakukan generalisasi pola. Pendekatan yang digunakan yaitu kualitatif dengan 3 subjek penelitian yang memiliki proses berpikir aljabar yang berbeda. Hasil penelitian menunjukkan bahwa siswa SMP melakukan proses berpikir aljabar dengan mempersepsikan gambar, merepresentasikan, mencari hubungan fungsional, melakukan generalisasi, dan mengaplikasikan rumus umum. Perbedaannya persepsi digunakan di awal kegiatan dan pada kegiatan pencarian hubungan fungsional. Hasil penelitian ini dapat digunakan dalam mengembangkan strategi pembelajaran matematika agar kemampuan berpikir aljabar siswa berkembang.

References

Afriansyah, E. A., Puspitasari, N., Luritawaty, I. P., Mardiani, D., & Sundayana, R. (2019). The analysis of mathematics with ATLAS.ti. Journal of Physics: Conference Series, 1402(7), 077097.

Ayber, G., & Tanışlı, D. (2017). An analysis of middle school mathematics textbooks from the perspective of fostering algebraic thinking through generalization. Kuram ve Uygulamada Egitim Bilimleri, 17(6), 2001–2030.

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

Barbosa, A., Value, I., & Palhares, P. (2009). Exploring generalization with visual petterns: task developed with pre-algebra students. Meeting on Patterns, Maio de 2009, Viana Do Castelo, 1–14.

Chua, B., & Hoyles, C. (2014). Generalisation of linear figural patterns in secondary school mathematics. 15(2), 1–30.

Dundar, S. (2015). An Analysis on the Pattern Generalizations of the Turkish Pre-Service Mathematics Teachers That Are Presented in a Different Structure and Presentation. Educational Research and Reviews, 10(2), 210–224.

Ellis, A. B. (2007). Connections between generalizing and justifying: Students’ reasoning with linear relationships. Journal for Research in Mathematics Education, 38(3), 194–229.

Faturohman, I., & Afriansyah, E. A. (2020). Peningkatan Kemampuan Berpikir Kreatif Matematis Siswa melalui Creative Problem Solving. Mosharafa: Jurnal Pendidikan Matematika, 9(1), 107-118.

Fyfe, E. R., Evans, J. L., Matz, L. E., Hunt, K. M., & Alibali, M. W. (2017). Relations between patterning skill and differing aspects of early mathematics knowledge. Cognitive Development, 44(May 2016), 1–11.

Girit, D., & Akyuz, D. (2016). Algebraic Thinking in Middle School Students at Different Grades: Conceptions about Generalization of Patterns. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 10(2), 243–243.

Goldstone, R. L., Marghetis, T., Weitnauer, E., Ottmar, E. R., & Landy, D. (2017). Adapting Perception, Action, and Technology for Mathematical Reasoning. Current Directions in Psychological Science, 26(5), 434–441.

Kieran, C. (2004). Algebraic thinking in the early grades: What is it. The Mathematics Educator, 8(1), 139–151.

Kılıç, Ç. (2016). Analyzing Middle School Students’ Figural Pattern Generating Strategies Dependıng on a Linear Number Pattern. 12(6), 1205–1230.

Kılıç, Ç. (2017). The Ability of Pre-Service Primary Teachers to Produce Figural Patterns Based on Algebraic Formulas. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 8(2), 261–261.

Lannin, J. K., Barker, D. D., & Townsend, B. E. (2006). Algebraic generalisation strategies: Factors influencing student strategy selection. Mathematics Education Research Journal, 18(3), 3–28.

Lian, L. H., & Yew, W. T. (2012). Assessing algebraic solving ability: A theoretical framework. International Education Studies, 5(6), 177–188.

Lie, S. Z., Zhi, T., & Sean, L. (2017). Generalising The Functional Rule For A Figural Quadratic Pattern.

Maryati, I. (2018). Penerapan Model Pembelajaran Berbasis Masalah Pada Materi Pola Bilangan Di Kelas Vii Sekolah Menengah Pertama. Mosharafa: Jurnal Pendidikan Matematika, 7(1), 63–74.

Mulyani, A., Indah, E. K. N., & Satria, A. P. (2018). Analisis Kemampuan Pemahaman Matematis Siswa Smp Pada Materi Bentuk Aljabar. Mosharafa: Jurnal Pendidikan Matematika, 7(2), 251–262.

Nurmawanti, I., Bambang, E. I., & Sulandra, M. I. (2016). Identifikasi Pola Siswa SMP Berdasarkan Teori Gestalt. Jurnal Pembelajan Matematika, III(2), 154 – 161.

Papic, M. M., Mulligan, J. T., Highfield, K., McKay-Tempest, J., & Garrett, D. (2011). Assessing the Development of Preschoolers’ Mathematical Patterning. Journal for Research in Mathematics Education, 42(3), 237–269.

Radford, L. (2015). Introduction : the Phenomenological, Components of Generalization. 9(3), 129–141.

Ridia, N. S., & Afriansyah, E. A. (2019). Perbandingan Kemampuan Pemahaman Matematis Siswa melalui Auditory Intellectualy Repetition dan Student Teams Achievement Division. Mosharafa: Jurnal Pendidikan Matematika, 8(3), 515-526.

Rivera, F. D. (2018). Pattern generalization processing of elementary students: Cognitive factors affecting the development of exact mathematical structures. Eurasia Journal of Mathematics, Science and Technology Education, 14(9).

Somasundram, P., Akmar, S. N., & Eu, L. K. (2019). Pattern Generalisation by Year Five Pupils. International Electronic Journal of Mathematics Education, 14(2).

Vale, I., Pimentel, T., Cabrita, I., & Barbosa, A. (2012). Pattern Problem Solving Tasks As a Mean To Foster Creativity in Mathematics. Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education, 4(1), 171–178.

Warren, Elizabeth; Cooper, T. (2007). Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking. Educational Stidies in Mathematics, 67(2), 171–185.

Warren, E., Miller, J., & Cooper, T. J. (2013). Exploring Young Student’s Functional Thinking. 4, 75–84.

Wilkie, K. J. (2019). Investigating secondary students’ generalization, graphing, and construction of figural patterns for making sense of quadratic functions. The Journal of Mathematical Behavior, 54, 100689.

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Published

2020-05-30

How to Cite

Nurmawanti, I., & Sulandra, I. M. (2020). Exploring of Student’s Algebraic Thinking Process Through Pattern Generalization using Similarity or Proximity Perception. Mosharafa: Jurnal Pendidikan Matematika, 9(2), 191–202. https://doi.org/10.31980/mosharafa.v9i2.603

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