Labirin Kognitif Trigonometri: Sebuah Tinjauan Literatur Sistematis berdasarkan Hierarki Newman

Febriani Kurnia Ningsih; Siti Hijriani Limbong; Salmyani Harahap; Nadya Choirunnisa Munthe; Rizka Agustin Harahap

doi:10.61132/bima.v4i2.2838

Authors

Febriani Kurnia Ningsih Universitas Islam Negeri Syekh Ali Hasan Ahmad Addary Padangsidimpuan
Siti Hijriani Limbong Universitas Islam Negeri Syekh Ali Hasan Ahmad Addary Padangsidimpuan
Salmyani Harahap Universitas Islam Negeri Syekh Ali Hasan Ahmad Addary Padangsidimpuan
Nadya Choirunnisa Munthe Universitas Islam Negeri Syekh Ali Hasan Ahmad Addary Padangsidimpuan
Rizka Agustin Harahap Universitas Islam Negeri Syekh Ali Hasan Ahmad Addary Padangsidimpuan

DOI:

https://doi.org/10.61132/bima.v4i2.2838

Keywords:

Cognitive Maze, Mathematics Learning Difficulties, Newman’s Error Analysis, Relational Understanding, Trigonometry

Abstract

Trigonometry is one of the most crucial yet challenging branches of mathematics in both secondary and higher education curricula, as it requires the integration of algebraic reasoning, geometry, and spatial visualization. This study presents a systematic literature review exploring the cognitive labyrinth phenomenon encountered by students when solving trigonometric problems, utilizing the Newman’s Error Analysis (NEA) framework as the primary diagnostic tool. Through a systematic search across various academic databases and the application of the PRISMA protocol, recurring error patterns were identified across the five stages of Newman's hierarchy: reading, comprehension, transformation, process skills, and encoding. Data synthesis results indicate that the greatest cognitive barriers for students reside within the transformation and process skills stages, where the inability to connect abstract concepts with mathematical models frequently serves as the primary cause of failure. Factors such as reliance on instrumental understanding, low angle visualization skills, and the influence of non-cognitive variables like gender and motivation contribute significantly to the complexity of this cognitive labyrinth. The findings of this study emphasize the importance of a pedagogical shift toward strengthening relational understanding and utilizing visualization technology to help students navigate difficulties in trigonometry. Strategic recommendations are provided for educators to implement targeted interventions at each level of the hierarchy to minimize systematic errors and comprehensively enhance students' mathematical proficiency.

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References

Alghadari, F., & Herman, T. (2018). Analysis of senior high school students’ errors in solving trigonometry. Cogent Education, 11(1). https://doi.org/10.1080/2331186X.2024.2385119

Ashcraft, M. H., & Krause, J. A. (2007). Working memory, math performance, and math anxiety. Psychonomic Bulletin & Review, 14(2), 243–248. https://doi.org/10.3758/BF03194059

Bandura, A. (1997). Self-efficacy: The exercise of control. W. H. Freeman.

Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Information Age Publishing. https://doi.org/10.1108/978-1-28141-200-320251013

Jamilah, S. (2021). Analisis kesalahan siswa dalam menyelesaikan soal cerita matematika berdasarkan prosedur Newman di MTsN 4 Banda Aceh [Undergraduate thesis, UIN Ar-Raniry]. https://doi.org/10.30598/jupitekvol4iss1pp36-46

Juniyarti, T., & Sukmawati, P. (2024). Analisis hambatan kognitif siswa pada materi trigonometri menggunakan kerangka kerja Newman. Jurnal Cendekia: Jurnal Pendidikan Matematika, 8(1), 122–135. https://doi.org/10.31004/cendekia.v8i3.3254

Muzangwa, J., & Chifamba, P. (2012). Analysis of student errors in solving trigonometry problems based on the Newman procedure. Kalamatika: Jurnal Pendidikan Matematika, 4(2), 113–126.

Newman, M. A. (1977). An analysis of sixth-grade pupils’ errors on written mathematical tasks. Victorian Institute for Educational Research Bulletin.

Putri, A. S. (2021). Error analysis of learner in solving problem in mathematics course based on Newman Error Analysis (NEA). Jurnal Pendidikan: Teori dan Praktik, 6(1), 45–52.

Rahmaliah, S. (2021). Analisis tipe kesalahan siswa berdasarkan Newman Error Analysis dalam menyelesaikan soal cerita. Jurnal Edukasi Matematika, 12(1), 89–102.

Singh, P., Rahman, A. A., & Hoon, T. S. (2010). Analysis problem solving in mathematical using theory Newman. Eurasia Journal of Mathematics, Science and Technology Education, 6(4), 263–272.

Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.

Sulistyaningsih, E. (2021). Analisis kesulitan belajar matematika pada materi trigonometri ditinjau dari metode Newman. Jurnal Afore, 10(2), 67–78.

Tall, D. (2013). How humans learn to think mathematically: Exploring the three worlds of mathematics. Cambridge University Press. https://doi.org/10.1017/CBO9781139565202

Urinov, K., & Santos, M. (2023). Examining the errors made by high school students while applying the Pythagorean Theorem. Bolema: Boletim de Educação Matemática, 37(75), 189–205. https://doi.org/10.1590/1980-4415v37n75a11