Dampak Pendekatan Matriks Enam Sel untuk Meningkatkan Kemampuan Pembuktian Calon Guru Matematika
Keywords:
Pernyataan Berkuantor, Pembuktian, Matriks Enam Sel
Abstract
Matriks enam sel merupakan kerangka dalam memahami struktur logika dari pernyataan matematika berkuantor. Tujuan penelitian ini adalah untuk menganalisis dampak penggunaan matriks enam sel dalam meningkatkan kemampuan pembuktian pernyataan berkuantor calon guru matematika. Penelitian ini menggunakan desain pre-experimental dengan pre-test dan post-test pada satu kelompok tidak acak. Sampel penelitian ini adalah 35 calon guru matematika. Pengumpulan data pre-test dan post-test menggunakan soal tes yang terdiri dari enam pernyataan matematika berkuantor. Data dianalisis dengan menggunakan statistik deskriptif dan uji Wilcoxon signed ranks. Hasil penelitian menunjukkan bahwa penggunaan matriks enam sel dalam pembelajaran dapat meningkatkan kemampuan pembuktian pernyataan berkuantor calon guru matematika. Secara khusus, kemampuan pembuktian calon guru matematika meningkat secara signifikan pada pernyataan berkuantor eksistensial.
Downloads
Download data is not yet available.
References
Creswell, J. . (2012). Educational Research: Planning, Conducting, and Evaluating. Quantitative and Qualitative Research, 4nd edition (4th ed.). Boston: Pearson.
Dawkins, P. C. (2017). On the Importance of Set-Based Meanings for Categories and Connectives in Mathematical Logic. International Journal of Research in Undergraduate Mathematics Education, 3(3), 496–522. https://doi.org/10.1007/s40753-017-0055-4
Dawkins, P. C., & Roh, K. H. (2016). Promoting Metalinguistic and Metamathematical Reasoning in Proof-Oriented Mathematics Courses: a Method and a Framework. International Journal of Research in Undergraduate Mathematics Education, 2(2), 197–222. https://doi.org/10.1007/s40753-016-0027-0
Dawkins, P. C., & Roh, K. H. (2020). Assessing the Influence of Syntax, Semantics, and Pragmatics in Student Interpretation of Multiply Quantified Statements in Mathematics. International Journal of Research in Undergraduate Mathematics Education, 6(1), 145–145. https://doi.org/10.1007/s40753-019-00105-5
De Villiers, M. (2004). Using dynamic geometry to expand mathematics teachers’ understanding of proof. International Journal of Mathematical Education in Science and Technology, 35(5), 703–724. https://doi.org/10.1080/0020739042000232556
Dubinsky, E., & Yiparaki, O. (2001). On student understanding of AE and EA quantification. Research in Collegiate Mathematics Education, 4(1), 239–289. https://doi.org/10.1090/cbmath/008/11
Hanna, G., & de Villiers, M. (2008). ICMI Study 19: Proof and proving in mathematics education. ZDM - International Journal on Mathematics Education, 40(2), 329–336. https://doi.org/10.1007/s11858-008-0073-4
Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428. https://doi.org/10.2307/749651
Herutomo, R. A. (2019). Kesalahan Mahasiswa dalam Pembuktian Matematik. Jurnal Didaktik Matematika, 6(1), 54–68. https://doi.org/10.24815/jdm.v6i1.13262
Kristianto, E., Mardiyana, & Saputro, D. R. S. (2019). Analysis of Students’ Error in Proving Convergent Sequence using Newman Error Analysis Procedure. Journal of Physics: Conference Series, 1180(1). https://doi.org/10.1088/1742-6596/1180/1/012001
Levenson, E., Tsamir, P., Tirosh, D., Dreyfus, T., Barkai, R., & Tabach, M. (2012). Focusing on the Interactive Development of Secondary School Teachers’ Knowledge of Mathematical Statements. Investigations in Mathematics Learning, 5(2), 44–56. https://doi.org/10.1080/24727466.2012.11790322
Miyazaki, M., Fujita, T., & Jones, K. (2017). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223–239. https://doi.org/10.1007/s10649-016-9720-9
Morgan, M. E. (2020). Students’ Quantifications, Interpretations, and Negations of Complex Mathematical Statements from Calculus. Unpublish Doctoral Thesis. Arizona. Arizona State University https://www.researchgate.net/publication/343999913_Students’_Quantifications_Interpretations_and_Negations_of_Complex_Mathematical_Statements_from_Calculus
NCTM. (2000). Principles and Standard for School Mathematics. Reston: NCTM.
Ngansop, J. N. (2018). Relevance of Learning Logical Analysis of Mathematical Statements. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, & E. S. B. Xu (Eds.), Invited Lectures from the 13th International Congress on Mathematical Education (pp. 441–462). Cham: Springer Open. https://doi.org/10.1007/978-3-319-72170-5_32
Pablo, J., Fuller, M. E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3–18. https://doi.org/1 0. 1 007/s 1 0649-0 1 1 -9349-7
Piatek-Jimenez, K. (2010). Students’ interpretations of mathematical statements involving quantification. Mathematics Education Research Journal, 22(3), 41–56. https://doi.org/10.1007/BF03219777
Sari, C. K., Waluyo, M., Ainur, C. M., & Darmaningsih, E. N. (2018). Logical errors on proving theorem. Journal of Physics: Conference Series, 948(1). https://doi.org/10.1088/1742-6596/948/1/012059
Sellers, M., Hah Roh, K., & David, E. J. (2017). A comparison of Calculus, Transition-to-Proof, and Advanced Calculus Student quantifications in complex mathematical statements. Conference: 20th Annual Conference on Research in Undergraduate Mathematics Education, 285–297. http://sigmaa.maa.org/rume/RUME20.pdf
Stavrou, S. G. (2014). Common Errors and Misconceptions in Mathematical Proving by Education Undergraduates. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1(1), 1–8. http://www.k-12prep.math.ttu.edu/journal/1.contentknowledge/stavrou01/article.pdf
Stewart, J. (2012). Calculus: Early Transcendentals (7E ed.). Belmont: Brooks/Cole.
Stylianides, G. J., & Stylianides, A. J. (2017). Research-based interventions in the area of proof: the past, the present, and the future. Educational Studies in Mathematics, 96(2), 119–127. https://doi.org/10.1007/s10649-017-9782-3
Stylianou, D. A., Blanton, M. L., & Rotou, O. (2015). Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof. International Journal of Research in Undergraduate Mathematics Education, 1(1), 91–134. https://doi.org/10.1007/s40753-015-0003-0
Tabach, M., Barkai, R., Tsamir, P., Tirosh, D., Dreyfus, T., & Levenson, E. (2010). Verbal Justification-is it a Proof? Secondary School Teachers’ Perceptions. International Journal of Science and Mathematics Education, 8(6), 1071–1090. https://doi.org/10.1007/s10763-010-9230-7
Tabach, M., Levenson, E., Barkai, R., Tirosh, D., Tsamir, P., & Dreyfus, T. (2010). Secondary school teachers’ awareness of numerical examples as proof. Research in Mathematics Education, 12(2), 117–131. https://doi.org/10.1080/14794802.2010.496973
Tabach, M., Levenson, E., Barkai, R., Tsamir, P., Tirosh, D., & Dreyfus, T. (2012). An organizer of mathematical statements for teachers: The six-cell matrix. International Journal of Mathematical Education in Science and Technology, 43(6), 765–777. https://doi.org/10.1080/0020739X.2012.662287
Tamba, K. P. (2020). Analisis Kesalahan pada Materi Kuantifikasi Menggunakan Matriks Enam Sel. Jumlahku: Jurnal Matematika Ilmiah, 6(2), 1–14. https://doi.org/https://doi.org/10.33222/jumlahku.v6i2.1053
Dawkins, P. C. (2017). On the Importance of Set-Based Meanings for Categories and Connectives in Mathematical Logic. International Journal of Research in Undergraduate Mathematics Education, 3(3), 496–522. https://doi.org/10.1007/s40753-017-0055-4
Dawkins, P. C., & Roh, K. H. (2016). Promoting Metalinguistic and Metamathematical Reasoning in Proof-Oriented Mathematics Courses: a Method and a Framework. International Journal of Research in Undergraduate Mathematics Education, 2(2), 197–222. https://doi.org/10.1007/s40753-016-0027-0
Dawkins, P. C., & Roh, K. H. (2020). Assessing the Influence of Syntax, Semantics, and Pragmatics in Student Interpretation of Multiply Quantified Statements in Mathematics. International Journal of Research in Undergraduate Mathematics Education, 6(1), 145–145. https://doi.org/10.1007/s40753-019-00105-5
De Villiers, M. (2004). Using dynamic geometry to expand mathematics teachers’ understanding of proof. International Journal of Mathematical Education in Science and Technology, 35(5), 703–724. https://doi.org/10.1080/0020739042000232556
Dubinsky, E., & Yiparaki, O. (2001). On student understanding of AE and EA quantification. Research in Collegiate Mathematics Education, 4(1), 239–289. https://doi.org/10.1090/cbmath/008/11
Hanna, G., & de Villiers, M. (2008). ICMI Study 19: Proof and proving in mathematics education. ZDM - International Journal on Mathematics Education, 40(2), 329–336. https://doi.org/10.1007/s11858-008-0073-4
Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396–428. https://doi.org/10.2307/749651
Herutomo, R. A. (2019). Kesalahan Mahasiswa dalam Pembuktian Matematik. Jurnal Didaktik Matematika, 6(1), 54–68. https://doi.org/10.24815/jdm.v6i1.13262
Kristianto, E., Mardiyana, & Saputro, D. R. S. (2019). Analysis of Students’ Error in Proving Convergent Sequence using Newman Error Analysis Procedure. Journal of Physics: Conference Series, 1180(1). https://doi.org/10.1088/1742-6596/1180/1/012001
Levenson, E., Tsamir, P., Tirosh, D., Dreyfus, T., Barkai, R., & Tabach, M. (2012). Focusing on the Interactive Development of Secondary School Teachers’ Knowledge of Mathematical Statements. Investigations in Mathematics Learning, 5(2), 44–56. https://doi.org/10.1080/24727466.2012.11790322
Miyazaki, M., Fujita, T., & Jones, K. (2017). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223–239. https://doi.org/10.1007/s10649-016-9720-9
Morgan, M. E. (2020). Students’ Quantifications, Interpretations, and Negations of Complex Mathematical Statements from Calculus. Unpublish Doctoral Thesis. Arizona. Arizona State University https://www.researchgate.net/publication/343999913_Students’_Quantifications_Interpretations_and_Negations_of_Complex_Mathematical_Statements_from_Calculus
NCTM. (2000). Principles and Standard for School Mathematics. Reston: NCTM.
Ngansop, J. N. (2018). Relevance of Learning Logical Analysis of Mathematical Statements. In G. Kaiser, H. Forgasz, M. Graven, A. Kuzniak, & E. S. B. Xu (Eds.), Invited Lectures from the 13th International Congress on Mathematical Education (pp. 441–462). Cham: Springer Open. https://doi.org/10.1007/978-3-319-72170-5_32
Pablo, J., Fuller, M. E., Weber, K., Rhoads, K., & Samkoff, A. (2012). An assessment model for proof comprehension in undergraduate mathematics. Educational Studies in Mathematics, 79(1), 3–18. https://doi.org/1 0. 1 007/s 1 0649-0 1 1 -9349-7
Piatek-Jimenez, K. (2010). Students’ interpretations of mathematical statements involving quantification. Mathematics Education Research Journal, 22(3), 41–56. https://doi.org/10.1007/BF03219777
Sari, C. K., Waluyo, M., Ainur, C. M., & Darmaningsih, E. N. (2018). Logical errors on proving theorem. Journal of Physics: Conference Series, 948(1). https://doi.org/10.1088/1742-6596/948/1/012059
Sellers, M., Hah Roh, K., & David, E. J. (2017). A comparison of Calculus, Transition-to-Proof, and Advanced Calculus Student quantifications in complex mathematical statements. Conference: 20th Annual Conference on Research in Undergraduate Mathematics Education, 285–297. http://sigmaa.maa.org/rume/RUME20.pdf
Stavrou, S. G. (2014). Common Errors and Misconceptions in Mathematical Proving by Education Undergraduates. Issues in the Undergraduate Mathematics Preparation of School Teachers: The Journal, 1(1), 1–8. http://www.k-12prep.math.ttu.edu/journal/1.contentknowledge/stavrou01/article.pdf
Stewart, J. (2012). Calculus: Early Transcendentals (7E ed.). Belmont: Brooks/Cole.
Stylianides, G. J., & Stylianides, A. J. (2017). Research-based interventions in the area of proof: the past, the present, and the future. Educational Studies in Mathematics, 96(2), 119–127. https://doi.org/10.1007/s10649-017-9782-3
Stylianou, D. A., Blanton, M. L., & Rotou, O. (2015). Undergraduate Students’ Understanding of Proof: Relationships Between Proof Conceptions, Beliefs, and Classroom Experiences with Learning Proof. International Journal of Research in Undergraduate Mathematics Education, 1(1), 91–134. https://doi.org/10.1007/s40753-015-0003-0
Tabach, M., Barkai, R., Tsamir, P., Tirosh, D., Dreyfus, T., & Levenson, E. (2010). Verbal Justification-is it a Proof? Secondary School Teachers’ Perceptions. International Journal of Science and Mathematics Education, 8(6), 1071–1090. https://doi.org/10.1007/s10763-010-9230-7
Tabach, M., Levenson, E., Barkai, R., Tirosh, D., Tsamir, P., & Dreyfus, T. (2010). Secondary school teachers’ awareness of numerical examples as proof. Research in Mathematics Education, 12(2), 117–131. https://doi.org/10.1080/14794802.2010.496973
Tabach, M., Levenson, E., Barkai, R., Tsamir, P., Tirosh, D., & Dreyfus, T. (2012). An organizer of mathematical statements for teachers: The six-cell matrix. International Journal of Mathematical Education in Science and Technology, 43(6), 765–777. https://doi.org/10.1080/0020739X.2012.662287
Tamba, K. P. (2020). Analisis Kesalahan pada Materi Kuantifikasi Menggunakan Matriks Enam Sel. Jumlahku: Jurnal Matematika Ilmiah, 6(2), 1–14. https://doi.org/https://doi.org/10.33222/jumlahku.v6i2.1053
Published
2021-02-25
How to Cite
Tamba, K. (2021). Dampak Pendekatan Matriks Enam Sel untuk Meningkatkan Kemampuan Pembuktian Calon Guru Matematika. Jurnal Cendekia : Jurnal Pendidikan Matematika, 5(1), 238-248. https://doi.org/10.31004/cendekia.v5i1.511
Section
Articles
Copyright (c) 2021 Kimura Patar Tamba
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
1.jpg)
