Students' mathematical reasoning abilities are viewed from Van Hiele’s theory
Abstract
Mathematical reasoning is the ability of a person's brain that includes the presentation of statements, making conjectures, performing mathematical manipulations, and presenting conclusions. This study aims to analyze or describe the ability of mathematical reasoning in solving trigonometric problems based on Van Hiele's level of thinking among high school students. This research uses a descriptive qualitative method. Data collection techniques consist of tests and interviews. Data analysis involves data presentation, reduction, and conclusion. The results of this study show that students at level 0 (visualization) of Van Hiele's level of thinking have one indicator of mathematical reasoning ability, which is to present statements. Students at level 1 (analysis) of Van Hiele's level of thinking have two indicators of mathematical reasoning: presenting statements and making conjectures. Students at level 2 (informal cut) of Van Hiele's level of thinking have three indicators of mathematical reasoning: presenting statements, making conjectures, and mathematical manipulations. Students at level 3 (deduction) of Van Hiele's level of thinking have four indicators of mathematical reasoning ability: presenting statements, making conjectures, mathematical manipulations, and drawing conclusions. Therefore, the higher the thinking level of the students at Van Hiele, the higher their mathematical reasoning ability. Whereas, the lower the Van Hiele thinking level of students, the lower their mathematical reasoning ability.
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Alpian, Rudi, and Bambang Sri Anggoro. 2020. “Analisis penalaran matematis peserta didik berdasarkan teori van hiele.” Indonesian Journal of Science and Mathematics Education 3 (1): 96–105. https://doi.org/10.24042/ijsme.v3i1.4761.
Ariati, Chelsi, and Dadang Juandi. 2022. “Kemampuan penalaran matematis: systematic literature review.” Jurnal Lemma 8 (2): 61–75. https://doi.org/10.22202/jl.2022.v8i2.5745.
Astuti, Reni, Didi Suryadi, and Turmudi Turmudi. 2019. “Analysis of the geometric understanding ability of junior high school students in congruence subject based on the level of van hiele thinking.” https://doi.org/10.4108/eai.19-10-2018.2281321.
Gradini, Ega, Bettri Yustinaningrum, and Dina Safitri. 2022. “Kesalahan siswa dalam memecahkan masalah trigonometri ditinjau dari indikator polya.” Mosharafa: Jurnal Pendidikan Matematika 11 (1): 49–60. https://doi.org/10.31980/mosharafa.v11i1.686.
Gusmania, Yesi, and Nina Agustyaningrum. 2020. “Analisis pemahaman konsep matematis mahasiswa pada mata kuliah trigonometri.” Jurnal Gantang 5 (2): 123–32. https://doi.org/10.31629/jg.v5i2.2493.
Hadi, Windia, and Ayu Faradillah. 2020. “Application of discovery learning method in mathematical proof of students in trigonometry.” Desimal: Jurnal Matematika 3 (1): 73–82. https://doi.org/10.24042/djm.v3i1.5713.
Hidayat, Wahyu, Euis Eti Rohaeti, Agie Ginanjar, and Ratu Ilma Indra Putri. 2022. “An epub learning module and students’ mathematical reasoning ability: a development study.” Journal on Mathematics Education 13 (1): 103–18. https://doi.org/10.22342/jme.v13i1.pp103-118.
Insani, Maya Isna, and Gida Kadarisma. 2020. “Analisis epistemological obstacle siswa sma pada materi trigonometri.” Jurnal Pembelajaran Matematika Inovatif 3 (5): 547–58. https://doi.org/10.22460/jpmi.v3i5.547-558.
Kurnia Putri, Dinda, Joko Sulianto, and Mira Azizah. 2019. “Kemampuan penalaran matematis ditinjau dari kemampuan pemecahan masalah.” International Journal of Elementary Education 3 (3): 351. https://doi.org/10.23887/ijee.v3i3.19497.
Lestari, Martha, Subanji Subanji, and Santi Irawati. 2022. “Analisis kemampuan analisis kemampuan penalaran matematis siswa sma pada materi matriks.” AKSIOMA: Jurnal Program Studi Pendidikan Matematika 11 (1): 550. https://doi.org/10.24127/ajpm.v11i1.4577.
Linola, Delima Mei, Retno Marsitin, and Tri Candra Wulandari. 2017. “Analisis kemampuan penalaran matematis peserta didik dalam menyelesaikan soal cerita di sman 6 malang.” Pi: Mathematics Education Journal 1 (1): 27–33. https://doi.org/10.21067/pmej.v1i1.2003.
Mahendra, As’ari Eka, Caswita Caswita, and Haninda Bharata. 2019. “Pengembangan lembar kerja peserta didik berbasis problem based learning untuk meningkatkan kemampuan penalaran matematika.” Desimal: Jurnal Matematika 2 (2): 141–46. https://doi.org/10.24042/djm.v2i2.4238.
Maphutha, Kgaladi, Satsope Maoto, and Israel Kibirige. 2022. “The effect of the activity-based approach on grade 11 learners’ performance in solving two-dimensional trigonometric problems.” Eurasia Journal of Mathematics, Science and Technology Education 18 (10). https://doi.org/10.29333/ejmste/12405.
Miatun, Asih, Hikmatul Khusna, and Slamet. 2021. “Van hiele levels: errors in solving geometry problems from mathematical disposition.” Journal of Physics: Conference Series 1933 (1). https://doi.org/10.1088/1742-6596/1933/1/012115.
Muslimin, Muslimin, and Sunardi Sunardi. 2019. “Analisis kemampuan penalaran matematika siswa sma pada materi geometri ruang.” Kreano, Jurnal Matematika Kreatif-Inovatif 10 (2): 171–78. https://doi.org/10.15294/kreano.v10i2.18323.
Nofita Telung, Oltje T. Sambuaga, and Derel F. Kaunang. 2022. “Perancangan pembelajaran peluang menggunakan pendekatan pendidikan matematika realistik indonesia.” Khatulistiwa: Jurnal Pendidikan Dan Sosial Humaniora 2 (4): 73–83. https://doi.org/10.55606/khatulistiwa.v2i4.757.
Novianti, Vina, and Marchasan Lexbin Elvi Judah Riajanto. 2021. “Analisis kesulitan siswa smk dalam menyelesaikan soal materi trigonometri.” Jurnal Pembelajaran Matematika Inovatif 4 (1): 161–68. https://doi.org/10.22460/jpmi.v4i1.161-168.
Nur’aini, Indah Linda, Erwin Harahap, Farid H. Badruzzaman, and Deni Darmawan. 2017. “Pembelajaran matematika geometri secara realistis dengan geogebra.” Matematika 16 (2): 1–6. https://doi.org/10.29313/jmtm.v16i2.3900.
Oktaviana, Veronika, and Indrie Noor Aini. 2021. “Deskripsi kemampuan penalaran matematis siswa smp kelas VIII.” Jurnal Pembelajaran Matematika Inovatif 4 (3): 588. https://doi.org/10.22460/jpmi.v4i3.587-600.
Pradini, Meysah Rani, and Nila Kesumawati. 2022. On mathematical reasoning ability in the circle material.” Desimal; Jurnal Matematika 5 (3): 235–46. https://doi.org/10.24042/djm.
Ramdan, M Gina Auliah Ramdan, and Lessa Roesdiana. 2022. “Analisis kemampuan penalaran matematis siswa smp pada materi teorema phytagoras.” Jurnal Educatio FKIP UNMA 8 (1): 386–95. https://doi.org/10.31949/educatio.v8i1.1996.
Samo, Damianus Dao. 2017. “Kemampuan pemecahan masalah matematika mahasiswa tahun pertama dalam memecahkan masalah geometri konteks budaya.” Jurnal Riset Pendidikan Matematika 4 (2): 141. https://doi.org/10.21831/jrpm.v4i2.13470.
Sutama, Sutama, Gilang Ary Sandy, and Djalal Fuadi. 2017. “Pengelolaan penilaian autentik kurikulum 2013 mata pelajaran matematika di sma.” Manajemen Pendidikan 12 (1): 105–14. https://doi.org/10.23917/jmp.v12i1.2967.
Umami, Insan Nuri, and Orin Asdarina. 2024. “Analisis level berpikir geometris siswa smp dalam menyelesaikan soal lingkaran berdasarkan teori van hiele.” Kognitif: Jurnal Riset HOTS Pendidikan Matematika 4 (1): 460–71. https://doi.org/10.51574/kognitif.v4i1.1554.
Wulandari, Tia Ayu, and Naufal Ishartono. 2022. “Analisis kemampuan representasi matematika siswa sma dalam menyelesaikan soal geometri berdasarkan level berpikir van hiele.” JNPM (Jurnal Nasional Pendidikan Matematika) 6 (1): 97. https://doi.org/10.33603/jnpm.v6i1.5330.
DOI: http://dx.doi.org/10.24042/djm.v7i2.23646
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