Conceptual and Procedural Knowledge of Fractions Among Junior High School Students as Viewed through Cognitive Style

Yunda Devana Tiningsih; Subanji Subanji; Imam Rofiki; Siti Salina Mustakim

doi:10.24014/juring.v9i1.37508

Conceptual and Procedural Knowledge of Fractions Among Junior High School Students as Viewed through Cognitive Style

Yunda Devana Tiningsih, Subanji Subanji, Imam Rofiki, Siti Salina Mustakim

Abstract

This study to describe the conceptual and procedural knowledge of junior high school students on fraction based on reflective and impulsive cognitive styles. This type of research is a descriptive with a qualitative approach. The research subjects were carried out by giving the MFFT Test to 68 prospective subjects, obtained 24 students with reflective cognitive style and 22 students with impulsive cognitive style. Furthermore, two subjects were selected from each category. Qualitative data collection regarding the conceptual and procedural knowledge aspects possessed by the subjects was carried out by providing fraction material test questions and interviews based on assignments. Data analysis uses data collection, data condensation, data presentation, and drawing conclusions/verification. The results showed that subjects with reflective cognitive style understanding of the five aspects of conceptual knowledge related to fractions, fractions as part whole, measurement, quotient, operator, and ratio. In the procedural knowledge, subjects with reflective cognitive style can use all four aspects in carrying out procedures related to fractions, verbalization procedures, applications fraction conversion, applications fraction operations and applications fraction simplification. While subjects with impulsive cognitive style tend not to understand conceptual and procedural knowledge of all aspects.

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References

Abbas, N. A., Abdullah, N. A., Shahrill, M., & Tengah, K. A. (2022). Primary School Pupils’ Performance on the Addition of Fractions: Conceptual and Procedural Knowledge. Jurnal Pendidikan Matematika, 16(2), 227–238. https://doi.org/10.22342/jpm.16.2.17811.227-238

Amir, N. F., & Andong, A. (2022). Kesulitan Siswa dalam Memahami Konsep Pecahan. Journal of Elementary Educational Research, 2(1), 1–12. https://doi.org/10.30984/jeer.v2i1.48

Braithwaite, D. W., & Sprague, L. (2021). Conceptual Knowledge, Procedural Knowledge, and Metacognition in Routine and Nonroutine Problem Solving. Cognitive Sciences, 45(10), Article e13048. https://doi.org/10.1111/cogs.13048

Buyung, B., Wahyuni, R., & Mariyam, M. (2022). Faktor Penyebab Rendahnya Pemahaman Siswa pada Mata Pelajaran Matematika di SD 14 Semperiuk A. Journal of Educational Review and Research, 5(1), 46-51. https://doi.org/10.26737/jerr.v5i1.3538

Celebioglu, B., & Yazgan, Y. (2015). The Investigation of Fourth Graders’ Construction Process of Fractional Multiplication Using Rbc + C Model. Procedia - Social and Behavioral Sciences, 197, 316–319. https://doi.org/10.1016/j.sbspro.2015.07.143

Fadiana, M. (2016). Perbedaan Kemampuan Menyelesaikan Soal Cerita Antara Siswa Bergaya Kognitif Reflektif dan Impulsif. Jramathedu (Journal of Research and Advances in Mathematics Education), 1(1), 79-89. https://doi.org/10.23917/jramathedu.v1i1.1775

Faisal, F., Srimuliati, S., Ulya, K., & Damayanti, L. (2023). Profil Penalaran Matematis Siswa Berdasarkan Gaya Kognitif Reflektif dan Impulsif. Jurnal Ilmiah Pendidikan Matematika Al Qalasadi, 7(1), 94–109. https://doi.org/10.32505/qalasadi.v7i1.6162

Fitri, L., Rachmadwati, L. A., Ayati, J. P. R., & Muliawati, N. E. (2019). Analisis Number Sense Ditinjau dari Gaya Kognitif Reflektif-Impulsif. Jurnal Pendidikan Matematika, 10(2), 131-137. https://doi.org/10.36709/jpm.v10i2.7174

Herianto, & Hamid, N. (2020). Analisis Proses Berpikir Kreatif dalam Pemecahan Masalah Geometri Berdasarkan Gaya Kognitif Reflektif Dan Impulsif Siswa. Pedagogy. Jurnal Pendidikan Matematika, 5(2), 38-49. https://doi.org/10.30605/pedagogy.v5i2.403

Hiebert, J., & Lefevre, P. (1986). Conceptual and Procedural Knowledge in Mathematics: An Introductory Analysis. In J. Hiebert (Ed.), Conceptual and Procedural Knowledge (pp. 1-27). Routledge.

Jhahro, K. F., Trapsilasiwi, D., & Setiawan, T. B. (2018). Pemahaman Konsep Siswa Pada Pemecahan Masalah Soal Geometri Pokok Bahasan Segiempat Ditinjau Dari Gaya Kognitif Reflektif-Impulsif Siswa. Kadikma: Jurnal Matematika Dan Pendidikan Matematika, 9(1), 116–122.

Johnson, B. R., & Schneider, M. (2014). Developing Conceptual and Procedural Knowledge of Mathematics. The Oxford Handbook of Numerical Cognition, 1118–1134. https://doi.org/10.1093/oxfordhb/9780199642342.013.014

Khoiriyah, S. M., & Masriyah, M. (2022). Kemampuan Pemecahan Masalah Siswa Dalam Menyelesaikan Soal Cerita SPLTV Ditinjau dari Gaya Kognitif Reflektif-Impulsif. Mathedunesa, 11(2), 357–367. https://doi.org/10.26740/mathedunesa.v11n2.p357-367

Kieren, T. E. (1976). On the Mathematical, Cognitive and Instructional. In L. A. Lesh & D. A. Bradbard (Eds.), Number and Measurement: Papers from a Research Workshop (Vol. 7418491, pp.101-144).

Lekati, E., Vrahatis, A., & Doukakis, S. (2026). Exploring Conceptual and Procedural Understanding of Fractions in Schools. The International Journal of Science Mathematics and Technology Learning. https://doi.org/10.18848/2327-7971/cgp/a203

Lenz, K., Dreher, A., Holzäpfel, L., & Wittmann, G. (2020). Are Conceptual Knowledge and Procedural Knowledge Empirically Separable? The Case of Fractions. British Journal of Educational Psychology, 90(3), 809–829. https://doi.org/10.1111/bjep.12333

Lenz, K., & Wittmann, G. (2020). Individual Differences in Conceptual and Procedural Fraction Knowledge: What Makes the Difference and What Does it Look Like? International Electronic Journal of Mathematics Education, 16(1), Article em0615. https://doi.org/10.29333/iejme/9282

Lin, C. Y., Becker, J., Byun, M. R., Yang, D. C., & Huang, T. W. (2013). Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction Operations: A Comparative Study of the United States and Taiwan. School Science and Mathematics, 113(1), 41–51. https://doi.org/10.1111/j.1949-8594.2012.00173.x

Magfirotin, E. S., & Amir, M. F. (2024). Elementary School Students’ Conceptual and Procedural Knowledge in Solving Fraction Problems. Jurnal Matematika Kreatif-Inovatif, 15(1), 109–122. https://journal.unnes.ac.id/nju/index.php/kreano.

Miles, M. B., Huberman, A. M., & Saldaña, J. (2020). Qualitative Data Analysis: A Methods Sourcebook. Sage Publication, Inc.

Muliawati, N. E., & Istianah, N. F. (2017). Proses Berpikir Kreatif Siswa dalam Memecahkan Masalah Matematika Ditinjau Dari Gaya Kognitif. P2M (Jurnal Pendidikan Dan Pembelajaran Matematika), 3(2), 118–127. https://doi.org/10.29100/jp2m.v3i2.1768

Nahdi, D. S., & Jatisunda, M. G. (2020). Conceptual Understanding and Procedural Knowledge: A Case Study on Learning Mathematics of Fractional Material in Elementary School. Journal of Physics: Conference Series, 1477(4), Article 042037. https://doi.org/10.1088/1742-6596/1477/4/042037

Nasriadi, A. (2019). Profil Pemecahan Masalah Matematika Siswa SMP Ditinjau dari Gaya Kognitif Reflektif dan Impulsif. Media Eksakta, 18(1), 37–42.

Novita, R., Herman, T., Suryadi, D., Dasari, D., Putra, M., & Fitra, R. (2022). Analisis Pengetahuan Konseptual dan Prosedural Mahasiswa Calon Guru Sekolah Dasar pada Bilangan Rasional. JNPM (Jurnal Nasional Pendidikan Matematika), 6(2), 384-402. https://doi.org/10.33603/jnpm.v6i2.7056

Obersteiner, A., Dresler, T., Bieck, S. M., & Moeller, K. (2019). Understanding Fractions: Integrating Results from Mathematics Education, Cognitive Psychology, and Neuroscience. In A. Norton & M.W. Alibali (Eds.), Constructing number: Merging perspectives from psychology and mathematics education (pp. 135-162). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-00491-0_7

Polya, G. (2004). How to Solve It: A new Aspect of Mathematical Method. Princeton University Press.

Putriana, D., Harun, L., & Utami, R. E. (2024). Analisis Kesalahan Siswa Berdasarkan Tahapan Kastolan dalam Menyelesaikan Soal Materi Perpangkatan dan Bentuk Akar Ditinjau dari Gaya Kognitif Implusif. Imajiner: Jurnal Matematika Dan Pendidikan Matematika, 5(5), 321–327. https://doi.org/10.26877/imajiner.v5i5.15819

Rahayuningsih, S., & Astuti, T. Y. Y. (2021). Analisis Kesalahan Siswa SMP dalam Menyelesaikan Soal Cerita Bilangan Bulat. Likhitaprajna Jurnal Ilmiah, 22(2), 133–141. https://doi.org/10.37303/likhitaprajna.v22i2.185

Sari, I., Zuhri, M. S., & Rubowo, M. R. (2020). Profil Kemampuan Berpikir Kreatif Siswa dalam Memecahkan Masalah Matematika pada Materi SPLTV Ditinjau dari Gaya Kognitif Reflektif dan Impulsif. Imajiner: Jurnal Matematika dan Pendidikan Matematika, 2(5), 391-400. https://doi.org/10.26877/imajiner.v2i5.6548

Sengkey, D. J., Sampoerno, P. D., & Aziz, T. A. (2023). Kemampuan Pemahaman Konsep Matematis: Sebuah Kajian Literatur. Griya Journal of Mathematics Education and Application, 3(1), 67–75. https://doi.org/10.29303/griya.v3i1.265

Styoningtyas, B., & Hariastuti, R. M. (2020). Analisis Pemahaman Matematis Siswa Ditinjau dari Gaya Kognitif Reflektif-Impulsif. Jurnal Emasains: Jurnal Edukasi Matematika dan Sains, 9(1), 9–16. https://doi.org/10.5281/zenodo.3742831

Sunariah, & Rijal, R. (2017). Analisis Kesulitan Belajar Siswa pada Pembelajaran Matematika Materi Pecahan. Jurnal Primary, 09(01), 93–108. http://jurnal.uinbanten.ac.id/index.php/primary/article/view/419/364

Wahyuningsih, S., & Istiandaru, A. (2021). Kesulitan Belajar Materi Pecahan Siswa Kelas VII SMP Muhammadiyah 2 Gamping. Square : Journal of Mathematics and Mathematics Education, 3(2), 99–106. https://doi.org/10.21580/square.2021.3.2.8222

Warli. (2013). Kreativitas Siswa SMP yang Bergaya Kognitif Reflektif atau Impulsif dalam Memecahkan Masalah Geometri. Jurnal Pendidikan dan Pembelajaran, 20(2), 190–201. https://journal.um.ac.id/index.php/pendidikan-dan-pembelajaran/article/view/4396

Yakar, E. A., & Yılmaz, S. (2019). “Matematiğin Üç Dünyası” Teorisine Göre 8. Sınıf Öğrencilerinin Matematiksel Düşünme Becerilerinin Procept Düzeyleri. Batı Anadolu Eğitim Bilimleri Dergisi, 10(1), 1-13. https://dergipark.org.t

DOI: http://dx.doi.org/10.24014/juring.v9i1.37508