Analisis Kesalahan Pada Materi Kuantifikasi Menggunakan Matriks Enam Sel
Abstract
Pernyataan berkuantor adalah topic penting dalam matematika. Calon guru matematika harus memiliki pemahaman yang kuat atasnya. Desain didaktis yang baik harus disusun dalam mempersiapkan calon guru matematika akan hal ini. Salah satu komponen dalam menyusunan desain didaktis adalah analisis kesalahan. Untuk itu tujuan penelitian ini adalah menganalisis kesalahan calon guru matematika pada materi kuantifikasi. Analisis ini dilakukan dengan menggunakan kerangka matriks enam sel. Matriks ini merupakan bentuk pengorganisasian pernyataan berkuantor berdasarkan komponen pentingnya yaitu kuantor, predikat dan validasi. Penelitian deskriptif terhadap calon guru matematika telah dilakukan. Data dikumpulkan dengan memberikan soal mengenai pernyataan berkuantor pada delapan puluh calon guru matematika. Hasilnya, kesalahan yang dilakukan oleh calon guru matematika dalam membuktikan pernyataan berkuantor tunggal adalah adalah mempertimbangkan atau fokus pada kuantifier tetapi tidak mempertimbangkan predikat, dan mempertimbangkan atau fokus pada predikat tetapi tidak mempertimbangkan kuantifier. Pemahaman yang tidak utuh akan pernyataan berkuantor merupakan penyebab kesalahan ini.
Downloads
References
Brousseau, G. (2002). Theory of Didactical Situation in Mathematics. Dordrecht: Kluwer Academic Publisher.
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, 496-522.
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. doi:10.1007/s40753-016-0027-0
Dawkins, P. C., & Roh, K. H. (2019). 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), 1–22. doi:10.1007/s40753-019-00097-2
Dubinsky, E. & Yiparaki, O. (2000). On Student Understanding Of AE And EA Quantification. In E. Dubinsky, A. H. Schoenfeld, & J. Kaput (Eds.),CMBS issues in mathematics education (pp. 239–289). Providence, RI: American Mathematical Society.
Epp, S. (1999). The Language Of Quantification In Mathematics Instruction. In L. V. Stiff & F. R. Curcio (Eds.),Developing mathematical reasoning in grades K-12 (1999 Yearbook) (pp. 188–197). Reston, VA: National Council of Teachers of Mathematics.
Fischbein, E. (1982). Intuition and Proof. For the Learning Mathematics, 3(2), pp. 9–18.
Kemendikbud. (2016). Peraturan Menteri Pendidikan Dan Kebudayaan Nomor 21 Tahun 2016 Tentang Standar Isi Pendidikan Dasar Dan Menengah. Jakarta: Kemendikbud. Retrieved from http://bsnp-indonesia.org/wp-content/uploads/2009/06/Permendikbud_Tahun2016_Nomor021_Lampiran.pdf
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.
NCTM. (2000). Principles and Standard for School Mathematics. Reston Virginia: The National Council of Mathematics of Teacher of Mathematics, Inc.
Piatek-Jimenez, K. (2010). Students Interpretations Of Mathematical Statements Involving Quantification. Mathematics Education Research Journal, 22, 3, 41-56.
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. doi:10.1007/s10763-010-9230-7
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. doi:10.1080/0020739x.2012.662287
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.
Tamba, K. P., Saragih, M. J., & Listiani, T. (2018). Learning Trajectory Of Quadratic Inequality. JOHME: Journal of Holistic Mathematics Education, 2(1), 12. DOI:10.19166/johme.v2i1.1202
Tirosh, C. 2002. The Ability Of Prospective Teachers To Prove Or To Refute Arithmetic Statements. Disertasi. Jerusalem, Israel: The Hebrew University.
Tsamir, P., D. Tirosh, T. Dreyfus, R. Barkai, and M. Tabach. 2009. Should Proof Be Minimal? Ms T’s Evaluation Of Secondary School Students’ Proofs. Journal for Mathematical Behavior 28, no. 1: 5867.
Van de Walle, J.A. (2008). Elementary & Middle School Mathematics: Teaching Developmentally (Second Canadian edition). Longman. New York, NY.
Copyright (c) 2020 JUMLAHKU: Jurnal Matematika Ilmiah STKIP Muhammadiyah Kuningan
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Open Access
JUMLAHKU:Jurnal matematika ilmiah STKIP Muhammadiyah Kuningan is a national peer reviewed and open access journal that publishes significant and important research from all area of mathematics education.
This journal provides immediate open access to its content that making research publish in this journal freely available to the public that supports a greater exchange of knowledge.
Copyright
Submission of a manuscript implies that the submitted work has not been published before (except as part of a thesis or report, or abstract); that it is not under consideration for publication elsewhere; that its publication has been approved by all co-authors. If and when the manuscript is accepted for publication, the author(s) still hold the copyright and retain publishing rights without restrictions. Authors or others are allowed to multiply article as long as not for commercial purposes. For the new invention, authors are suggested to manage its patent before published. The license type is BY-NC-SA 4.0.
Disclaimer
No responsibility is assumed by publisher and co-publishers, nor by the editors for any injury and/or damage to persons or property as a result of any actual or alleged libelous statements, infringement of intellectual property or privacy rights, or products liability, whether resulting from negligence or otherwise, or from any use or operation of any ideas, instructions, procedures, products or methods contained in the material therein.