A Systematic Literature Review on Algebraic Reasoning in Mathematics Instruction

Yumna Warifdah; Imam Sujadi; Rubono Setiawan; Farida Nurhasanah

doi:10.31980/mosharafa.v13i4.2536

Authors

Yumna Warifdah Sebelas Maret University
Imam Sujadi Universitas Sebelas Maret
Rubono Setiawan Universitas Sebelas Maret
Farida Nurhasanah Universitas Sebelas Maret

DOI:

https://doi.org/10.31980/mosharafa.v13i4.2536

Keywords:

mathematics, algebraic reasoning, middle school, matematika, penalaran aljabar, smp

Abstract

Abstrak

Penalaran aljabar menjadi topik hangat dalam dua dekade terakhir, tetapi siswa sekolah menengah mengalami kesulitan dalam mempelajari hal ini, sebab mengalami transformasi dari pemikiran aritmatika ke pemikiran aljabar yang abstrak. Penelitian ini menganalisis artikel penalaran aljabar dari basis data Scopus berdasarkan tahun penelitian, metode, dan sebaran geografis dalam satu dekade. Penelitian disajikan melalui tinjauan literatur sistematis dengan menggunakan protokol PRISMA meliputi Preferred Reporting Item for Systematic Reviews and Meta-Analytic. Dari proses seleksi, didapatkan 29 artikel yang memenuhi kriteria inklusi dan lolos tiga tahap penyaringan. Penelitian dengan topik ini cenderung mengalami penurunan, terutama dalam 4 tahun terakhir. Metode yang paling sering digunakan adalah metode penelitian kualitatif karena dianggap peneliti sangat cocok untuk meneliti kemampuan berpikir. Dari 8 wilayah yang melakukan penelitian penalaran aljabar, Indonesia merupakan negara yang paling banyak melakukannya. Hal ini dilatarbelakangi rendahnya penalaran aljabar siswa. Peluang penelitian pada topik ini masih terbuka lebar dengan menggunakan penelitian ini sebagai rujukan.

Abstract

Algebraic reasoning has become a hot topic in the last two decades, but high school students have difficulty in learning it, because they experience a transformation from arithmetic thinking to abstract algebraic thinking. This study analyzes algebraic reasoning articles from the Scopus database based on the year of research, methods, and geographical distribution in one decade. The research is presented through a systematic literature review using the PRISMA protocol including the Preferred Reporting Item for Systematic Reviews and Meta-Analytic. From the selection process, 29 articles were obtained that met the inclusion criteria and passed three stages of screening. Research on this topic tends to decline, especially in the last 4 years. The most frequently used method is the qualitative research method because researchers consider it very suitable for researching thinking skills. Of the 8 regions that conduct algebraic reasoning research, Indonesia is the country that does it the most. This is due to the low algebraic reasoning of students. Research opportunities on this topic are still wide open by using this research as a reference.

References

Agoestanto, A., & Rinachyuan, W. (2020). Student Error Analysis in Global Meta-Level Algebraic Thinking on Treffinger Learning Assisted by Scaffolding. Journal of Physics: Conference Series, 1567(2), 022092.

https://doi.org/10.1088/1742-6596/1567/2/022092

Agoestanto, A., Sukestiyarno, Y. L., Isnarto, I., Rochmad, R., & Lestari, M. D. (2019). The Position and Causes of Students Errors in Algebraic Thinking Based on Cognitive Style. International Journal of Instruction, 12(1), 1431–1444. https://doi.org/10.29333/iji.2019.12191a

Agoestanto, A., Sukestiyarno, Y. L., Isnarto, & Rochmad. (2019). An Analysis on Generational, Transformational, Global Meta-Level Algebraic Thinking Ability in Junior High School Students. Journal of Physics: Conference Series, 1321(3), 032082. https://doi.org/10.1088/1742-6596/1321/3/032082

Andriani, P. (2015). Penalaran Aljabar dalam Pembelajaran Matematika. Beta, 8(1), 1–13.

Ayber, G. (2017). An Analysis of Middle School Mathematics Textbooks from the Perspective of Fostering Algebraic Thinking through Generalization. Educational Sciences: Theory & Practice, 17(6), 2001–2030. https://doi.org/10.12738/estp.2017.6.0506

Blanton, M. L., & Kaput, J. J. (2005). Characterizing a Classroom Practice That Promotes Algebraic Reasoning. Journal for Research in Mathematics Education, 36(5), 412–446. https://doi.org/https://doi.org/10.2307/30034944

Carpenter, T. P., & Levi, L. (2000). Developing Conceptions of Algebraic Reasoning in the Primary Grades. Research Report. Research Report: National Center For Improving Student Learning and Achievement In Mathematics and Science, 5, 1–22.

Carraher, D. W., Schliemann, A. D., Brizuela, B. M., & Earnest, D. (2006). Arithmetic and Algebra in Early Mathematics Education. Journal for Research in Mathematics Education, 37(2), 87–115.

Chimoni, M., & Pitta-Pantazi, D. (2017). Parsing the Notion of algebraic thinking within a Cognitive Perspective. Educational Psychology, 37(10), 1186–1205. https://doi.org/10.1080/01443410.2017.1347252

Da Silva Melo, C. B., & Bisognin, E. (2024). Development of Algebraic Thinking in Elementary School: An Analysis from Design-Based Research. Acta Scientiae, 26(1), 69–94.

https://doi.org/10.17648/acta.scientiae.7806

DİNÇER, B., & CANTÜRK GÜNHAN, B. (2020). The Effects of Educational Robotics Applications on Linear Equations about Algebraic Reasoning. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(2), 492–527.

https://doi.org/10.16949/turkbilmat.600379

Doucette, L. (2017). Quantitative Methods and Inferential Statistics: Capacity and Development for Librarians. Evidence Based Library and Information Practice, 12(2), 53–58. https://doi.org/10.18438/B82940

Dougherty, B., Bryant, D. P., Bryant, B. R., Darrough, R. L., & Pfannenstiel, K. H. (2015). Developing Concepts and Generalizations to Build Algebraic Thinking. Intervention in School and Clinic, 50(5), 273–281. https://doi.org/10.1177/1053451214560892

Ellis, A., Ely, R., Singleton, B., & Tasova, H. (2020). Scaling-continuous Variation: Supporting Students’ Algebraic Reasoning. Educational Studies in Mathematics, 104(1), 87–103. https://doi.org/10.1007/s10649-020-09951-6

Faradillah, A., Jusra, H., & Pradipta, T. R. (2021). Validity and Reliability Analysis of Algebraic Reasoning Test Instrument. Journal of Physics: Conference Series, 1933(1), 012116. https://doi.org/10.1088/1742-6596/1933/1/012116

Girit, D., & AKYÜZ, 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(1), 243–272.

Hidayanto, E., & Lathifa, N. A. (2021). Level of Ability Thinking Mathematically on the Transition Process from Arithmetic Thinking To Algebraic Thinking. AIP Conference Proceedings, 2330, 040029. https://doi.org/10.1063/5.0043372

Hitt, F., Saboya, M., & Cortés Zavala, C. (2016). An Arithmetic-Algebraic Work Space For The Promotion Of Arithmetic And Algebraic Thinking: Triangular Numbers. ZDM, 48(6), 775–791. https://doi.org/10.1007/s11858-015-0749-5

Hitt, F., Saboya, M., & Zavala, C. C. (2017). Rupture or Continuity: The Arithmetico-Algebraic Thinking as an Alternative in a Modelling Process in a Paper and Pencil and Technology Environment. Educational Studies in Mathematics, 94(1), 97–116. https://doi.org/10.1007/s10649-016-9717-4

Indraswari, N. F., Budayasa, I. K., & Ekawati, R. (2018). Algebraic Reasoning in Solving Mathematical Problem Based on Learning Style. Journal of Physics: Conference Series, 947(1), 012061. https://doi.org/10.1088/1742-6596/947/1/012061

Irfiani, V., Junaedi, I., & Waluya, S. B. (2023). Systematic Literature Review: Kemampuan Berpikir Kritis Matematis Siswa Ditinjau dari Adversity Quotient. Jurnal Pendidikan Matematika, 1(2), 11. https://doi.org/10.47134/ppm.v1i2.157

Kaliski, B. S. (1975). Algebra or Arithmetic? The Journal of Business Education, 50(7), 289–290.

https://doi.org/10.1080/00219444.1975.10534653

Kaput, J. J. (2000). Transforming Algebra from an Engine of Inequity to an Engine of Mathematical Power by" Algebrafying" the K-12 Curriculum. ERIC

Kaput, J. J., Carraher, D. W., & Blanton, M. L. (2008). Algebra in the Early Grades. In Sustainability. London: Lawrence Erlbaum Associates.

Kusumaningsih, W., Darhim, D., Herman, T., & Turmudi, T. (2018a). Improvement Algebraic Thinking Ability Using Multiple Representation Strategy On Realistic Mathematics Education. Journal on Mathematics Education, 9(2), 281–290.

https://doi.org/10.22342/jme.9.2.5404.281-290

Kusumaningsih, W., Darhim, Herman, T., & Turmudi. (2018b). Gender Differences in Algebraic Thinking Ability to Solve Mathematics Problems. Journal of Physics: Conference Series, 1013(1), 012143. https://doi.org/10.1088/1742-6596/1013/1/012143

Lepak, J. R., Wernet, J. L. W., & Ayieko, R. A. (2018). Capturing and Characterizing Students’ Strategic Algebraic Reasoning Through Cognitively Demanding Tasks with Focus on Representations. The Journal of Mathematical Behavior, 50, 57–73. https://doi.org/10.1016/j.jmathb.2018.01.003

Levin, M., & Walkoe, J. (2022). Seeds of Algebraic Thinking: a Knowledge in Pieces Perspective on the Development of Algebraic Thinking. ZDM – Mathematics Education, 54(6), 1303–1314. https://doi.org/10.1007/s11858-022-01374-2

Mustaffa, N. (2018). The Effect of Integrating Algebraic Thinking in Problem-Based Learning via Virtual Environment Among Secondary School Students. ICCE 2018 - 26th International Conference on Computers in Education, Main Conference Proceedings, 187–192.

Muthmainnah, M., Priatna, N., & Priatna, B. A. (2017). Analysis of Students’ Error in Algebraic Thinking Test. Journal of Physics: Conference Series, 895(1), 012089. https://doi.org/10.1088/1742-6596/895/1/012089

Nada, Y. H., Prabawanto, S., & Suhendra. (2020). Characteristics of Students’ Mathematical Representation in Solving Algebraic Thinking Problems. Journal of Physics: Conference Series, 1521(3), 032009.

https://doi.org/10.1088/1742-6596/1521/3/032009

NCTM. (2000). Principles and Standards for School Mathematics.

Nurhayati, D. M., Herman, T., & Suhendra, S. (2017). Analysis of Secondary School Students’ Algebraic Thinking and Math-Talk Learning Community to Help Students Learn. Journal of Physics: Conference Series, 895(1), 012054. https://doi.org/10.1088/1742-6596/895/1/012054

Olivia, R., Rahmi, D., Yuniati, S., & Kurniati, A. (2024). Systematic Literature Review: Kemampuan Berpikir Kritis Siswa Ditinjau Dari Gaya Belajar. Jurnal Ilmiah Profesi Pendidikan, 9(2), 896–903. https://doi.org/10.29303/jipp.v9i2.2167

Ontario, M. of E. (2013). Paying attention to algebraic reasoning, K-12: Support document for paying attention to mathematical education.

Pati, D., & Lorusso, L. N. (2018). How to Write a Systematic Review of the Literature. HERD: Health Environments Research & Design Journal, 11(1), 15–30. https://doi.org/10.1177/1937586717747384

Pitta-Pantazi, D., Chimoni, M., & Christou, C. (2020). Different Types of Algebraic Thinking: an Empirical Study Focusing on Middle School Students. International Journal of Science and Mathematics Education, 18(5), 965–984. https://doi.org/10.1007/s10763-019-10003-6

Pratiwi, W. D., Kurniadi, E., & Astuti, P. (2019). Learning Design for Transition from Arithmetic Thinking to Algebraic Thinking. Journal of Physics: Conference Series, 1166(1), 012031. https://doi.org/10.1088/1742-6596/1166/1/012031

Raharjo, S., Pradja, B. P., & Istiqomah, D. (2020). Analisis Kemampuan Penalaran Aljabar Siswa SMP dalam Pemecahan Masalah Pola Bilangan. JIPMat, 5(2), 147–158. https://doi.org/10.26877/jipmat.v5i2.6546

Rahmawati, D. I. (2018). Characteristics of Algebraic Thinking of Junior High School Students. Journal of Physics: Conference Series, 1097(1), 012110. https://doi.org/10.1088/1742-6596/1097/1/012110

Rahmawati, D. I., Priatna, N., & Juandi, D. (2019). Algebraic Thinking Characteristics of Eighth Grade Junior High School Students based on Superitem Test of SOLO model. Journal of Physics: Conference Series, 1157(4), 042087. https://doi.org/10.1088/1742-6596/1157/4/042087

Rivera, F. D., & Becker, J. R. (2020). Algebraic Reasoning through Patterns. Mathematics Teaching in the Middle School, 15(4), 212–221. https://doi.org/10.5951/mtms.15.4.0212

Setiawan, Y. B., Hapizah, H., & Hiltrimartin, C. (2018). Kesalahan Siswa dalam Menyelesaikan Soal Olimpiade SMP Konten Aljabar. Jurnal Riset Pendidikan Matematika, 5(2), 233–243. https://doi.org/10.21831/jrpm.v5i2.18191

Sibgatullin, I. R., Korzhuev, A. V., Khairullina, E. R., Sadykova, A. R., Baturina, R. V., & Chauzova, V. (2022). A Systematic Review on Algebraic Thinking in Education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), em2065. https://doi.org/10.29333/ejmste/11486

Sugilar, H., Kariadinata, R., & Sobarningsih, N. (2019). Spektrum Symbol dan Structure Sense Matematika Siswa Madrasah Tsanawiyah. KALAMATIKA: Jurnal Pendidikan Matematika, 4(1), 37–48. https://doi.org/10.22236/KALAMATIKA.vol4no1.2019pp37-48

Suhaedi, D. (2020). Realistic Mathematics Education: A Learning Innovation in Enhancing Students’ Algebraic Thinking Ability. Proceedings of the Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019, 12 October 2019, Bandung, West Java, Indonesia. https://doi.org/10.4108/eai.12-10-2019.2296293

Susac, A., Bubic, A., Vrbanc, A., & Planinic, M. (2014). Development of abstract mathematical reasoning: the case of algebra. Frontiers in Human Neuroscience, 8, 1–10. https://doi.org/10.3389/fnhum.2014.00679

TIMSS. (2012). TIMSS 2011 International Results in Mathematics, 43.

Ünal, Z. E., Ala, A. M., Kartal, G., Özel, S., & Geary, D. C. (2023). Visual and Symbolic Representations as Components of Algebraic Reasoning. Journal of Numerical Cognition, 9(2), 327–345. https://doi.org/10.5964/jnc.11151

Valenti, A., Bacciu, D., & Vergari, A. (2024). ChemAlgebra: Algebraic Reasoning on Chemical Reactions. 2024 International Joint Conference on Neural Networks (IJCNN), 1–8.

https://doi.org/10.1109/IJCNN60899.2024.10650037

Walle, J. A. Van de, Karp, K. S., & Bay-Williams, J. M. (2009). Elementary and Middle School Mathematics: Teaching Developmentally. In Book1 (7th ed.).

Wilujeng, H., Kusumah, Y. S., & Darhim, D. (2019). The Students’ Achievement of Algebraic Thinking Ability Using Merrill’s First Principles of Instruction. Journal of Physics: Conference Series, 1188(1), 012039.

https://doi.org/10.1088/1742-6596/1188/1/012039