KESALAHAN REPRESENTASI PECAHAN PADA GARIS BILANGAN
(1) Universitas Kanjuruhan
(2) Universitas Negeri Malang
(3) Universitas Negeri Malang
(4) Universitas Negeri Malang
(5) Universitas Kanjuruhan
(*) Corresponding Author
Abstract
Penelitian tentang analisis kesalahan representasi pecahan calon guru matematika penting karena pecahan berguna dalam kehidupan sehari-hari. Tujuan penelitian untuk menyelidiki kesalahan calon guru matematika dalam representasi tugas kepekaan pecahan pada garis bilangan. Tipe kesalahan dan indikator menunjukkan keterampilan representasi pecahan. Penelitian ini menggunakan pendekatan deskriptif kualitatif dengan 19 calon guru matematika sebagai calon subjek. Wawancara dilakukan pada 5 subjek yang dipilih. Pada wawancara, kami meminta mereka untuk mendeskripsikan jawaban mereka dalam merepresentasikan tugas kepekaan pecahan pada garis bilangan dan faktor-faktor yang menyebabkan kesalahan. Hasil penelitian menunjukkan dua kesalahan terbesar pada calon guru matematika, yaitu tidak terampil menggunakan estimasi, dan tidak terampil menggunakan benchmark. Temuan lain menunjukkan lebih banyak calon guru matematika yang melakukan kesalahan dalam representasi pecahan negatif daripada pecahan positif pada garis bilangan. Hal ini disebabkan adanya hambatan kognitif calon guru matematika dari pengetahuan sebelumnya dalam domain pecahan positif ketika diterapkan pada domain pecahan negatif. Sehingga lebih banyak calon guru matematika yang melakukan kesalahan dalam representasi pecahan negatif daripada pecahan positif pada garis bilangan. Faktor-faktor penyebabkan kesalahan representasi dari penugasan kepekaan pecahan pada garis bilangan adalah calon guru menganggap materi pecahan sulit, sulit membayangkan pecahan, mengalami kebingungan dan lupa dengan materi pecahan. Intervensi berbantuan media direkomendasikan untuk mengatasi ketidakmampuan calon guru menggunakan estimasi dan bencmark terutama dalam domain pecahan negatif.
Keywords
Full Text:
PDF (Bahasa Indonesia)References
Aliustaoğlu, F., Tuna, A., & Biber, A. Ç. (2018). Misconceptions of sixth grade secondary school students on fractions. International Electronic Journal of Elementary Education, 10(5), 591–599.
Boyce, S., & Moss, D. (2017). Role of representation in prospective teachers’ fraction schemes. In E. Galindo & J. Newton (Eds.), Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. (pp. 829–836). Indianapolis, IN: Hoosier Association of Mathematics Teacher Educators.
Cortina, J. L., Visnovska, J., & Zúñiga, C. (2014). Equipartition as a didactical obstacle in fraction instruction. Acta Didactica Universitatis Comenianae Mathematics, (14), 1–18.
Courtney-Clarke, M., & Wessels, H. (2014). Number sense of final year pre-service primary school teachers. Pythagoras, 35(1), 1–9.
Deringöl, Y. (2019). Misconceptions of primary school students about the subject of fractions: Views of primary teachers and primary pre-service teachers. International Journal of Evaluation and Research in Education (IJERE), 8(1), 29-38.
Izsák, A., Beckmann, S., & Bradshaw, L. (2016). Preservice teacher education. Proceedings of the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Tucson, AZ: The University of Arizona.
Kara, F., & Incikabi, L. (2018). Sixth grade students’ skills of using multiple representations in addition and subtraction operations in fractions. International Electronic Journal of Elementary Education, 10(4), 463–474.
Kor, L.-K., Teoh, S.-H., Binti Mohamed, S. S. E., & Singh, P. (2018). Learning to make sense of fractions: Some insights from the Malaysian primary 4 pupils. International Electronic Journal of Mathematics Education, 14(1), 169–182.
Lamberg, T., & Wiest, L. R. (2014). Dividing fractions using an area model: A look at in-service teachers’ understanding. Mathematics Teacher Education and Development, 17(1), 30–43.
Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why is learning fraction and decimal arithmetic so difficult? Developmental Review, 38(1), 201–221.
Manfreda Kolar, V., Hodnik Čadež, T., & Vula, E. (2018). Primary teacher students’ understanding of fraction representational knowledge in Slovenia and Kosovo. Center for Educational Policy Studies Journal, 8(2), 71–96.
Miles, M.B., Huberman, A.M., and Saldara, J. (2014). Qualitative data analysis, a methods sourcebook. USA: Sage Publication.
Mousley, K., & Kelly, R. R. (2017). Developing deaf students fraction skills requires understanding magnitude and whole number division. Journal of Education and Learning, 7(2), 12-20.
Murniasih, T. R., Sa’dijah, C., Muksar, M., & Susiswo, S. (2018). Errors in representation translation in solving problems related to number sense of pre-service math teachers. In A. G. Abdullah, R. Rusfandi, U. Jawas, & A. B. D. Nandiyanto (Eds.), Proceedings of the Annual Conference on Social Sciences and Humanities (ANCOSH) (pp. 393–399). SCITEPRESS – Science and Technology Publications, Lda. A.
Prediger, S. (2008). The relevance of didactic categories for analysing obstacles in conceptual change: revisiting the case of multiplication of fractions. Learning and Instruction, 18(1), 3–17.
Rodrigues, J., Dyson, N. I., Hansen, N., & Jordan, N. C. (2017). Preparing for algebra by building fraction sense. Teaching Exceptional Children, 49(2), 134–141.
Sa’dijah, C. (2013). Kepekaan bilangan siswa SMP melalui pembelajaran matematika kontekstual dan mengintegrasikan ketrampilan berpikir kreatif. Jurnal Pendidikan Dan Pembelajaran, 20(2), 222–227.
Sengul, S., & Gulbagci, H. (2012). An investigation of 5th grade Turkish students’ performance in number sense on the topic of decimal numbers. Procedia - Social and Behavioral Sciences, 46, 2289–2293.
Shodikin, A. (2017). Effect of learning with abductive-deductive strategy towards the achievement of reasoning ability of high school students. Infinity Journal, 6(2), 111-120.
Shumway, J. (2011). Number sense routines: building numerical literacy every day in grades K-3. Stenhouse Publishing.
Son, J.-W., & Lee, J.-E. (2016). Pre-service teachers’ understanding of fraction multiplication, representational knowledge, and computational skills. Mathematics Teacher Education and Development, 18(2), 5–28.
Suryowati, E. (2015). Kesalahan Siswa Sekolah Dasar Dalam Merepresentasikan Pecahan Pada Garis Bilangan. AKSIOMA Journal of Mathematics Education, 4(1), 38–52.
Sutiarso, S. (2019). Mengapa Sulit Menyelesaikan Soal Pecahan 2/x + 3/y = 2/3? AKSIOMA Journal of Mathematics Education, 8(3), 420–428.
Tian, J., & Siegler, R. S. (2017). Fractions Learning in Children With Mathematics Difficulties. Journal of Learning Disabilities, 50(6), 614–620.
Tsao, Y.-L., & Pan, T.-R. (2013). The Computational Estimation and Instructional Perspectives of Elementary School Teachers. Journal of Instructional Pedagogies, 11(1), 1-15.
Tuba, A. İ. (2017). The problems posed and models employed by primary school teachers in subtraction with fractions. Educational Research and Reviews, 12(5), 239–250.
Tucker, S. I. (2014). REFractions. APCM, 19(1), 29–34.
Way, J. (2011). Developing Fraction Sense Using Digital Learning Objects. The Australian Association of Mathematics Teachers Inc.
Whitacre, I., & Nickerson, S. D. (2016). Investigating the Improvement of Prospective Elementary Teachers’ Number Sense in Reasoning about Fraction Magnitude. Journal of Mathematics Teacher Education, 19(1), 57–77.
Wong, M. (2013). Locating fractions on a number line. Australian Primary Mathematics Classroom, 2(3), 22–27.
Yaman, H. (2015). The Mathematics Education I and II Courses’ Effect on Teacher Candidates’ Development of Number Sense. Educational Sciences: Theory & Practice, 15(4), 1119–1135.
DOI: http://dx.doi.org/10.24127/ajpm.v9i2.2740
Refbacks
- There are currently no refbacks.