Analysis of Students' Geometrical Thinking from Geometry Task Related to HOTS from PISA


This study intends to analyze geometry tasks related to Higher Order Thinking Skills (HOTS) through geometrical thinking level by Van Hiele which consists of visualization, analysis, abstraction, deduction, and rigor. This study only focuses on visualization, analysis, and abstraction levels. The stages in this study are divided into three steps. Chronologically, the first stage begins with the process of compiling PISA tasks related to geometry and HOTS, especially for examining the students’ spatial abilities. From all the tasks obtained, three tasks match the criteria that were most relevant to Van Hiele’s geometrical thinking level. The second stage was continued by testing the instrument test to 23 students from one of the schools in Tangerang Regency as respondents. In the last stage, analyze the students’ answers based on the steps of their work and compare them with the theory of geometrical thinking from Van Hiele. The results of this study indicate that there are differences between the steps of the students’ answers and theoretical answer steps that are expected in this study. The conclusion that can be drawn is that the students’ learning experiences in understanding geometrical concepts are not theoretically compatible with the principles of spatial ability, especially in completing geometry tasks related to HOTS.

Keywords: Students’ Geometrical Thinking, Geometry Task, PISA

[1] Yenti F. Penerapan model pembelajaran Contextual Teaching and Learning (CTL) terhadap pemahaman konsep matematika siswa kelas VIII SMP Negeri 2 X Koto tahun pelajaran 2014/2015. Curricula. 2016;1(3):1–10. DOI

[2] Subhan M, Nandari F. Analisis hots dan lots soal penilaian akhir semester muatan matematika kelas V Sekolah Dasar. Elem Sch J. 2020;10(3):137–46.

[3] Bloom BS, Airasian P, Cruikshank K, et al. A taxonomy for learning, teaching, and assessing: A revision of bloom’s taxonomy of educational objectives. Longman; 2001.

[4] B.K. Suryapuspitarini, Wardono, and Kartono, “Analisis soal-soal matematika tipe higher order thinking skill (HOTS) pada Kurikulum 2013 untuk mendukung kemampuan literasi siswa.,” Prisma. Prosiding Seminar Nasional Matematika. 2018;1:876–84.

[5] Bursill-Hall P. Why do we study geometry? answers through the ages (lecture at the opening of the faulkes institute). Part Of The Opening Festivities Of The Faulkes Institute For Geometry. Cambridge: University of Cambridge; 2002. pp. 1–33.

[6] M.D. Haryanti, T. Herman, and S. Prabawanto, “Analysis of students’ error in solving mathematical word problems in geometry,.” Journal of Physics: Conference Series. vol. 1157, no. 4, p. 2019.

[7] HershkowitzRina. “About reasoning in geometry.,” Presented at the (1998).

[8] Mammana C. “Geometry and geometry-teaching through the ages.,” Presented at the (1998).

[9] Epelboim J, Suppes P. A model of eye movements and visual working memory during problem solving in geometry. PERGAMON; 2001. pp. 1561–74.

[10] Luneta K. Understanding students’ misconceptions: an analysis of final Grade 12 examination questions in geometry. Pythagoras. 2015;36(1):1–11.

[11] Dosinaeng WB, Leton SI, Lakapu M. Kemampuan mahasiswa dalam menyelesaikan masalah matematis berorientasi HOTS [ Jurnal Nasional Pendidikan Matematika]. JNPM. 2019;3(2):250–64.

[12] Myelnawan M, Setyaningrum W. Kemampuan siswa SMP dalam menyelesaikan soal matematika berbasis HOTS. Jurnal Riset Pendidikan Matematika. 2021;8(1):83–95.

[13] Kurniati D, Harimukti R, Jamil NA. “Kemampuan berpikir tingkat tinggi siswa SMP Di Kabupaten Jember dalam menyelesaikan soal berstandar PISA.,” Jurnal Penelitian dan Evaluasi Pendidikan. vol. 20, no. 2, pp. 142–155, 2016.

[14] Setiawan H. Dafik, and N.D.S. Lestari, “Soal matematika dalam pisa kaitannya dengan literasi matematika dan keterampilan berfikir tingkat tinggi.,” Prosiding Seminar Nasional Matematika. Universitas Jember. 2014;(November):244–51.

[15] Hendroanto A, Fitriyani H, Anggoro RP. Level berpikir van hiele dan kemampuan spasial: apakah pengaruhnya terhadap ketrampilan HOTS mahasiswa? JIPMat. 2019;4(1):1–6.

[16] Griffith DA. Geometry and spatial interaction. Ann Assoc Am Geogr. 1982;72(3):332– 46.

[17] Karaman T, Togrol AY. Relationship between gender, spatial visualization, spatial orientation, flexibility of closure abilities and performance related to plane geometry subject among sixth grade students. Bogaziçi University Journal of Education. 2009;26(1):1–25.

[18] Maier PH. “Spatial geometry and spatial ability–how to make solid geometry solid.,” In: Selected papers from the Annual Conference of Didactics of Mathematics. pp. 63–75 (1996).

[19] Usiskin Z. Van hiele levels and achivements in secondary school geometry. Chicago: The University of Chicago; 1982.

[20] Pavlovicová G, Bocková V, Laššová K. Spatial ability and geometric thinking of the students of teacher training for primary education. TEM Journal. 2022;11(1):388–95.

[21] Nurkaidah IP, Subanti S. “HOTS problem-solving ability and its relation to spatial ability.,” Proceedings of the International Conference of Mathematics and Mathematics Education (I-CMME 2021). vol. 597, pp. 210–216, 2021.

[22] Choi-Koh SS. A student’s learning of geometry using the computer. J Educ Res. 1999;92(5):301–11.

[23] Van Hiele PM. A child’s thought and geometry. English Translation of Selected Writings of Dina Van Hiele-Geldof and Pierre M. Van Hiele. Brooklyn: Brooklyn College; 1984.

[24] M.K. Lutfi, D. Juandi, and A. Jupri, “Students’ ontogenic obstacle on the topic of triangle and quadrilateral,.” Journal of Physics: Conference Series. vol. 1806, no. 1, p. 2021.

[25] M.K. Lutfi and A. Jupri, “Analysis of junior high school students’ spatial ability based on van hiele’s level of geometrical thinking for the topic of triangle similarity,.” Journal of Physics: Conference Series. vol. 1521, no. 3, p. 2020. 6596/1521/3/032026.