Influence of prerequisite concepts understanding and mathematical communication skills toward student’s mathematical proving ability

Ellis Salsabila

doi:10.21831/pg.v14i1.25067

Influence of prerequisite concepts understanding and mathematical communication skills toward student’s mathematical proving ability

Ellis Salsabila, Mathematics Education Program, Universitas Negeri Jakarta, Indonesia

10.21831/pg.v14i1.25067

Abstract

This study aims to describe the influence of prerequisite concepts understanding and mathematical communication skills on the mathematical proving ability of Mathematics Education Program students in the Faculty of Mathematics and Science, State University of Jakarta (FMIPA UNJ). The method used in this study was a survey and correlational techniques. The study population was all students of the Mathematics Education Program FMIPA UNJ in 2018. The study sample was taken with a simple random sampling technique, there were 50 students in total. In this study, the dependent variable was mathematical proving ability (Y) and the independent variables were the prerequisite concepts understanding (X1) and mathematical communication skills (X2). This study based on the inferential statistical analysis of research data by using multiple regression analyses to test the effect of independent variables on the dependent variables. The results obtained were: 1) the prerequisite concepts understanding had a positive effect and significant on students’ mathematical proving ability, 2) mathematical communication skills had a positive effect and significant on students’ mathematical proving ability, and 3) prerequisite concepts understanding and mathematical communication skills simultaneously had a positive effect and significant on mathematical proving ability with effect size of 69.3%.

Pengaruh pemahaman prerequisite concepts dan kemampuan komunikasi matematis terhadap mathematical proving ability mahasiswa

Abstrak

Penelitian ini bertujuan untuk memperoleh informasi tentang pengaruh pemahaman prerequisite concepts dan kemampuan komunikasi matematis terhadap kemampuan membuktikan matematis mahasiswa Pendidikan Matematika di Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Negeri Jakarta (FMIPA UNJ). Metode yang digunakan dalam penelitian ini adalah metode survei dan teknik korelasional. Populasi penelitian adalah seluruh mahasiswa Program Studi Pendidikan Matematika FMIPA UNJ tahun 2018. Sampel penelitian diambil dengan teknik simple random sampling sebanyak 50 mahasiswa. Variabel terikat dalam penelitian ini adalah kemampuan membuktikan matematis (Y) dan variabel bebasnya adalah pemahaman prerequisite concepts (X1) dan kemampuan komunikasi matematis (X2). Penelitian ini berdasarkan analisis statistik inferensial atas data penelitian dengan menggunakan analisis regresi ganda untuk menguji pengaruh variable-variabel bebas terhadap variabel terikat. Hasil yang diperoleh adalah: 1) pemahaman prerequisite concepts berpengaruh positif dan signifikan terhadap kemampuan pembuktian matematis mahasiswa, 2) kemampuan komunikasi matematis berpengaruh positif dan signifikan terhadap kemampuan pembuktian matematis mahasiswa, 3) pemahaman prerequisite concepts dan kemampuan komunikasi matematis secara bersama-sama (simultan) memberikan pengaruh positif dan signifikan terhadap kemampuan pembuktian matematis mahasiswa dengan besar pengaruh sebesar 69,3%.

Keywords

mathematical proving ability; prerequisite concepts understanding; mathematical communication skills; kemampuan pembuktian matematis; pemahaman prerequisite concepts; kemampuan komunikasi matematis

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References

Apino, E., & Retnawati, H. (2017). Developing instructional design to improve mathematical higher order thinking skills of students. Journal of Physics: Conference Series, 812(1), 1-7. doi: http://doi.dx/10.1088/1742-6596/812/1/012100

Arnawa, I. M. (2006). Meningkatkan kemampuan pembuktian mahasiswa dalam aljabar abstrak melalui pembelajaran berdasarkan teori APOS [Improving the proving ability of students in abstract algebra through learning based on APOS theory] (Unpublished doctoral dissertation). Universitas Pendidikan Indonesia, Bandung.

BSNP, (2006). Standar kompetensi dan kompetensi dasar SMA/MA [Competency standards and basic competencies for Senior High School/Islamic Senior High School]. Jakarta: Author.

Epp, S. S. (2003). The role of logic in teaching proof. The American Mathematical Monthly, 110(10), 886-899. doi: https://doi.org/10.1080/00029890.2003.11920029

Halpern, D. F. (2001). Assessing the effectiveness of critical thinking instruction. The Journal of General Education 50(4), 270-286. doi: http://doi.org/10.1353/jge.2001.0024

Hanna, G., & N. Jahnke, (1996). Proof and proving. In A. J. Bishop, K. Clements, C. Keitel., J. Kilpatrick, & C. Laborde (Eds.), International Handbook of Mathematics Education (pp 877-908). Dordrecht: Kluwer Academic Publishers.

Jailani, J., Sugiman, S., & Apino, E. (2017). Implementing the problem-based learning in order to improve the students’ HOTS and characters. Jurnal Riset Pendidikan Matematika, 4(2), 247-259. doi: https://doi.org/10.21831/jrpm.v4i2.17674

Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249–266. doi: https://doi.org/10.1007/BF01273731

Nugraha, T. S., & Mahmudi, A. (2015). Keefektifan pembelajaran berbasis masalah dan problem posing ditinjau dari kemampuan berpikir logis dan kritis [The effectiveness of problem-based learning and problem posing in terms of the ability to think logically and critically]. Jurnal Riset Pendidikan Matematika, 2(1), 107 - 120. doi: https://doi.org/10.21831/jrpm.v2i1.7154

Retnawati, H., Djidu, H., Kartianom, K., Apino, E., & Anazifa, R. D. (2018). Teachers'knowledge about higher-order thinking skills and its learning strategy. Problems of Education in the 21st Century, 76(2), 215-230. Retrieved from http://oaji.net/articles/2017/457-1524597598.pdf

Ruseffendi, E. T. (2006). Pengantar kepada membantu guru mengembangkan kompetensinya dalam pengajaran matematika untuk meningkatkan CBSA [Introduction to helping teachers develop competencies in teaching mathematics to improve CBSA]. Bandung: Tarsito.

Sabri, S. (2003). Prospective secondary school teachers’ conceptions of mathematical proof in indonesia (Unpublished master’s thesis). Curtin University of Technology, Perth.

Sariningsih, R., & Herdiman, I. (2017). Mengembangkan kemampuan penalaran statistik dan berpikir kreatif matematis mahasiswa di Kota Cimahi melalui pendekatan open-ended [Developing the ability of statistical reasoning and mathematical creative thinking of students in the City of Cimahi through an open-ended approach]. Jurnal Riset Pendidikan Matematika, 4(2), 239-246. doi:https://doi.org/10.21831/jrpm.v4i2.16685

Selden, A., & Selden, J. (2003). Validations of proof considered as texts: can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4-36. doi: https://doi.org/10.2307/30034698

Stylianides, G. J., Stylianides, A. J. & Shilling-Traina, L. N. (2013). Prospective teachers’ challenges in teaching reasoning-and-proving. International Journal of Science and Mathematics Education, 11(6), 1463-1490. doi: https://doi.org/10.1007/s10763-013-9409-9

Sumarmo, U. (2005). Pengembangan berfikir matematika tingkat tinggi siswa SLTP dan SMU serta mahasiswa strata satu (S1) melalui berbagai pembelajaran. Laporan Penelitian Lembaga Penelitian Universitas Pendidikan Indonesia [Development of mathematical high-level thinking of junior and senior high school students and undergraduate students through a variety of learning. Research Report of Research Institute Universitas Pendidikan Indonesia]. Retrieved from http://penelitian.lppm.upi.edu/detil/675/pengembangan-berfikir-matematik-tingkat-tinggi-siswa-sltp-dan-smu-serta-mahasiswa-strata-saru-(s1)-melalui-berbagai-pendekatan-pembelajaran

Ülger, K. (2016). The relationship between creative thinking and critical thinking skills of students. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi (H. U. Journal of Education), 31(4), 695-710. doi: https://dx.doi.org/10.16986/HUJE.2016018493

Yerison. (2011). Peningkatan Kemampuan pembuktian dan kemandirian belajar matematik mahasiswa melalui pendekatan M-APOS [The improvement of students’ proving ability and self-regulated learning through the M-APOS approach] (Unpublished doctoral dissertation). Universitas Pendidikan Indonesia, Bandung.

Zaslavsky, O., Nickerson, S.D., Stylianides, A. J., Kidron, I., & Winicki-Landman, G. (2012). The need for proof and proving: mathematical and pedagogical perspectives. In G. Hanna & M. de Villiers (eds.), Proof and proving in mathematics education: New ICMI Study Series 15 (pp. 215-229). Dordrecht: Springer. doi: https://doi.org/10.1007/978-94-007-2129-6

DOI: https://doi.org/10.21831/pg.v14i1.25067