Kemampuan Siswa SMP dalam Menulis Bukti Ditinjau Berdasarkan Tingkat Kemampuan Matematika
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Submitted
10 January 2023
Published
30 April 2023
Keywords:
-
kemampuan menulis bukti, Kongruensi, Tingkat Kemampuan Matematika
Abstract
The ability to write proof means writing down an idea to prove a mathematical problem. It consists of a combination of the ability to read, write and prove. This study aims to describe the ability of junior high school students to write evidence based on mathematical ability. However, only students with high mathematical abilities are the subject of the research. This research is a descriptive study using a qualitative approach. Tests and interviews were conducted to collect the data. There were three steps for collecting data in this study: administering a mathematical ability test; administering a proof writing test with congruence questions to students with high mathematical abilities; and interviewing three students with high mathematical abilities of Grade IXA of SMP Negeri 1 Siliragung, Banyuwangi Regency. Data analysis includes data reduction, data presentation, and drawing conclusions. The results showed that students with high mathematical abilities had good reading, writing, and proving abilities. Based on the results of this study, the researchers suggest that teachers train students more often in reading, writing, and proving mathematical problems and accustom students to writing proofs systematically.
References
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Ali, M., Sufahani, S., Hasim, N., Rusiman, M. S., Roslan, R., Mohamad, M., & Khalid, K. (2018). The Development of Proofs in Analytical Mathematics for Undergraduate Students. Journal of Physics: Conference Series, 995(1). https://doi.org/10.1088/1742-6596/995/1/012004
Bicer, A., Perihan, C., & Lee, Y. (2018). The Impact of Writing Practices on Students’ Mathematical Attainment. International Electronic Journal of Mathematics Education, 13(3), 305–313. https://doi.org/10.12973/iejme/3922
Cantin, R. H., Gnaedinger, E. K., Gallaway, K. C., Hesson-McInnis, M. S., & Hund, A. M. (2016). Executive functioning predicts reading, mathematics, and theory of mind during the elementary years. Journal of Experimental Child Psychology, 146, 66–78. https://doi.org/10.1016/j.jecp.2016.01.014
Chapman, A., & Lee, A. (1990). Rethinking Literacy and Numeracy. Australian Journal of Education, 34(3), 277–289. https://doi.org/10.1177/000494419003400305
Collins, M. A., & Laski, E. V. (2019). Digging deeper: Shared deep structures of early literacy and mathematics involve symbolic mapping and relational reasoning. Early Childhood Research Quarterly, 46, 201–212. https://doi.org/10.1016/j.ecresq.2018.02.008
De Lange, J. (2004). Literacy Mathematical. Encyclopedia of Social Measurement, 2, 533–540. https://doi.org/10.1016/B0-12-369398-5/00244-9
Fang, Z., & Chapman, S. (2020). Disciplinary literacy in mathematics: One mathematician’s reading practices. Journal of Mathematical Behavior, 59(June), 100799. https://doi.org/10.1016/j.jmathb.2020.100799
Fuat, Nusantara, T., Irawan, E. B., & Irawati, S. (2019). Students’ mathematical conviction in Mathematics proof. IOP Conference Series: Earth and Environmental Science, 243(1). https://doi.org/10.1088/1755-1315/243/1/012133
Galagedera, D., Woodward, G., & Degamboda, S. (2000). An investigation of how perceptions of mathematics ability can affect elementary statistics performance. International Journal of Mathematical Education in Science and Technology, 31(5), 679–689. https://doi.org/10.1080/002073900434369
Herizal, H., Suhendra, S., & Nurlaelah, E. (2019). The ability of senior high school students in comprehending mathematical proofs. Journal of Physics: Conference Series, 1157(2), 6–12. https://doi.org/10.1088/1742-6596/1157/2/022123
Holenstein, M., Bruckmaier, G., & Grob, A. (2020). Transfer effects of mathematical literacy: an integrative longitudinal study. European Journal of Psychology of Education. https://doi.org/10.1007/s10212-020-00491-4
Islamirta, K. A., Chaniago, R. R., & Darmawijoyo. (2020). The effect of students’ mathematics views on how they read math textbook. Journal of Physics: Conference Series, 1480(1). https://doi.org/10.1088/1742-6596/1480/1/012063
Johnson, J. (2017). A topic revisited : students in the republic of the Maldives writing contextual word problems. IEJME - Mathematics Education, 12(5), 549–559. https://www.iejme.com/article/a-topic-revisited-students-in-the-republic-of-the-maldives-writing-contextual-word-problems
Kaiser, G., & Willander, T. (2005). Development of mathematical literacy: Results of an empirical study. Teaching Mathematics and Its Applications, 24(2–3), 48–60. https://doi.org/10.1093/teamat/hri016
Korpershoek, H., Kuyper, H., & van der Werf, G. (2015). the Relation Between Students’ Math and Reading Ability and Their Mathematics, Physics, and Chemistry Examination Grades in Secondary Education. International Journal of Science and Mathematics Education, 13(5), 1013–1037. https://doi.org/10.1007/s10763-014-9534-0
Ledger, S., & Merga, M. K. (2018). Reading aloud: Children’s attitudes toward being read to at home and at school. Australian Journal of Teacher Education, 43(3), 124–139. https://doi.org/10.14221/ajte.2018v43n3.8
Marlina, E. (2022). Deskripsi Kebutuhan Pembelajaran Matematika Diskrit Melalui Kurikulum Merdeka Belajar. Jurnal Riset Matematika Dan Sains Terapan, 2.
Maya, R., & Sumarmo, U. (2011). Mathematical Understanding and Proving Abilities : Experiment With. Journal On Mathematics Education (Indo MS-JME), 2(2), 231–250.
Murtikusuma, R. P., Fatahillah, A., Oktavianingtyas, E., Hussen, S., & Nur Lailiya. (2019). The development of interactive mathematics learning media based on schoology and visual basic through industrial revolution 4 . 0 The development of interactive mathematics learning media based on schoology and visual basic through industrial. IOP Conference Series: Earth and Environmental Science, 243, 1–6. https://doi.org/10.1088/1755-1315/243/1/012137
Österholm, M. (2006). Characterizing Reading Comprehension of Mathematical Texts. Educational Studies in Mathematics, 63(3), 325–346. https://doi.org/10.1007/s10649-005-9016-y
Pfeiffer, K. (2010). The role of proof validation in students’ mathematical learning. MSOR Connections, 10(2), 17–21. https://doi.org/10.11120/msor.2010.10020017
Porter, M. K., & Masingila, J. O. (2000). Examining The Effects of Writing on Conceptual and Procedural Knowledge in Calculus. Educational Studies in Mathematics, 103(3), 239–248. https://doi.org/10.1023/A
Putri, D. A., & Widjajanti, D. B. (2019). Improving Students’ Mathematical Literacy Skills Through Multiple Intelligences Approach in Problem Based Learning. Journal of Physics: Conference Series, 1397(1). https://doi.org/10.1088/1742-6596/1397/1/012094
Quealy, C. (2014). The Importance of Writing in Mathematics : Why Writing Allows for a Deeper understanding of the Mathematical Content The Importance of Writing in Mathematics : Why Writing Allows for a. A Journal of Undergraduate Student Research, 15, 19–22. http://fisherpub.sjfc.edu/cgi/viewcontent.cgi?article=1134&context=ur
Rahim, F. (2008). Pengajaran Membaca di Sekolah Dasar. Bumi Aksara.
Sanjaya, W. (2013). Penelitian Pendidikan. Prenadamedia group.
Santhitiwanich, A., Pasiphol, S., & Tangdhanakanond, K. (2014). The Integration of Indicators of Reading, Analytical Thinking and Writing Abilities with Indicators of Subject Content. Procedia - Social and Behavioral Sciences, 116, 4854–4858. https://doi.org/10.1016/j.sbspro.2014.01.1037
Santosa, C. A. H. (2013). Mengatasi Kesulitan Mahasiswa Ketika Melakukan Pembuktian Matematis Formal. Jurnal Pengajaran MIPA., XVII(2). https://doi.org/10.1017/CBO9781107415324.004
Shepherd, M. D., & van de Sande, C. C. (2014). Reading mathematics for understanding-From novice to expert. Journal of Mathematical Behavior, 35, 74–86. https://doi.org/10.1016/j.jmathb.2014.06.003
Solow, D. (2014). How to Read and Do Proofs (Sixth Edition ed.) (6 th). John Wiley&Sons, Inc.
Stavrou, S. (2014). Common Errors and Misconceptions in Mathematical Proving by Education Undergraduates. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1(March), 1–8.
Vinogradova, M., & Ivanova, N. (2016). Pedagogical Conditions for Role-Playing Game Development in Senior Preschool Age Children. Procedia - Social and Behavioral Sciences, 233(May), 297–301. https://doi.org/10.1016/j.sbspro.2016.10.134
Wahyuddin. (2016). Analisis Kemampuan Menyelesaikan Soal Cerita Matematika Ditinjau Dari Kemampuan Verbal Pada Siswa Kelas Vii Smp Muhammadiyah Se-Kota Makassar. Beta: Jurnal Tadris Matematika, 2(2), 111. https://doi.org/10.24014/sjme.v2i2.2213
Wardhani. (2008). Paket fasilitasi pemberdayaan KKG/MGMP matematika. Pusat Pengembangan Dan Pemberdayaan pendidik dan Tenaga Kependidikan Matematika.
Yılmazer, G., & Masal, M. (2014). The Relationship between Secondary School Students’ Arithmetic Performance and their Mathematical Literacy. Procedia - Social and Behavioral Sciences, 152, 619–623. https://doi.org/10.1016/j.sbspro.2014.09.253
Adelson, J. L., Dickinson, E. R., & Cunningham, B. C. (2014). Differences in the reading-mathematics relationship: A multi-grade, multi-year statewide examination. Learning and Individual Differences, 43, 118–123. https://doi.org/10.1016/j.lindif.2015.08.006
Ali, M., Sufahani, S., Hasim, N., Rusiman, M. S., Roslan, R., Mohamad, M., & Khalid, K. (2018). The Development of Proofs in Analytical Mathematics for Undergraduate Students. Journal of Physics: Conference Series, 995(1). https://doi.org/10.1088/1742-6596/995/1/012004
Bicer, A., Perihan, C., & Lee, Y. (2018). The Impact of Writing Practices on Students’ Mathematical Attainment. International Electronic Journal of Mathematics Education, 13(3), 305–313. https://doi.org/10.12973/iejme/3922
Cantin, R. H., Gnaedinger, E. K., Gallaway, K. C., Hesson-McInnis, M. S., & Hund, A. M. (2016). Executive functioning predicts reading, mathematics, and theory of mind during the elementary years. Journal of Experimental Child Psychology, 146, 66–78. https://doi.org/10.1016/j.jecp.2016.01.014
Chapman, A., & Lee, A. (1990). Rethinking Literacy and Numeracy. Australian Journal of Education, 34(3), 277–289. https://doi.org/10.1177/000494419003400305
Collins, M. A., & Laski, E. V. (2019). Digging deeper: Shared deep structures of early literacy and mathematics involve symbolic mapping and relational reasoning. Early Childhood Research Quarterly, 46, 201–212. https://doi.org/10.1016/j.ecresq.2018.02.008
De Lange, J. (2004). Literacy Mathematical. Encyclopedia of Social Measurement, 2, 533–540. https://doi.org/10.1016/B0-12-369398-5/00244-9
Fang, Z., & Chapman, S. (2020). Disciplinary literacy in mathematics: One mathematician’s reading practices. Journal of Mathematical Behavior, 59(June), 100799. https://doi.org/10.1016/j.jmathb.2020.100799
Fuat, Nusantara, T., Irawan, E. B., & Irawati, S. (2019). Students’ mathematical conviction in Mathematics proof. IOP Conference Series: Earth and Environmental Science, 243(1). https://doi.org/10.1088/1755-1315/243/1/012133
Galagedera, D., Woodward, G., & Degamboda, S. (2000). An investigation of how perceptions of mathematics ability can affect elementary statistics performance. International Journal of Mathematical Education in Science and Technology, 31(5), 679–689. https://doi.org/10.1080/002073900434369
Herizal, H., Suhendra, S., & Nurlaelah, E. (2019). The ability of senior high school students in comprehending mathematical proofs. Journal of Physics: Conference Series, 1157(2), 6–12. https://doi.org/10.1088/1742-6596/1157/2/022123
Holenstein, M., Bruckmaier, G., & Grob, A. (2020). Transfer effects of mathematical literacy: an integrative longitudinal study. European Journal of Psychology of Education. https://doi.org/10.1007/s10212-020-00491-4
Islamirta, K. A., Chaniago, R. R., & Darmawijoyo. (2020). The effect of students’ mathematics views on how they read math textbook. Journal of Physics: Conference Series, 1480(1). https://doi.org/10.1088/1742-6596/1480/1/012063
Johnson, J. (2017). A topic revisited : students in the republic of the Maldives writing contextual word problems. IEJME - Mathematics Education, 12(5), 549–559. https://www.iejme.com/article/a-topic-revisited-students-in-the-republic-of-the-maldives-writing-contextual-word-problems
Kaiser, G., & Willander, T. (2005). Development of mathematical literacy: Results of an empirical study. Teaching Mathematics and Its Applications, 24(2–3), 48–60. https://doi.org/10.1093/teamat/hri016
Korpershoek, H., Kuyper, H., & van der Werf, G. (2015). the Relation Between Students’ Math and Reading Ability and Their Mathematics, Physics, and Chemistry Examination Grades in Secondary Education. International Journal of Science and Mathematics Education, 13(5), 1013–1037. https://doi.org/10.1007/s10763-014-9534-0
Ledger, S., & Merga, M. K. (2018). Reading aloud: Children’s attitudes toward being read to at home and at school. Australian Journal of Teacher Education, 43(3), 124–139. https://doi.org/10.14221/ajte.2018v43n3.8
Marlina, E. (2022). Deskripsi Kebutuhan Pembelajaran Matematika Diskrit Melalui Kurikulum Merdeka Belajar. Jurnal Riset Matematika Dan Sains Terapan, 2.
Maya, R., & Sumarmo, U. (2011). Mathematical Understanding and Proving Abilities : Experiment With. Journal On Mathematics Education (Indo MS-JME), 2(2), 231–250.
Murtikusuma, R. P., Fatahillah, A., Oktavianingtyas, E., Hussen, S., & Nur Lailiya. (2019). The development of interactive mathematics learning media based on schoology and visual basic through industrial revolution 4 . 0 The development of interactive mathematics learning media based on schoology and visual basic through industrial. IOP Conference Series: Earth and Environmental Science, 243, 1–6. https://doi.org/10.1088/1755-1315/243/1/012137
Österholm, M. (2006). Characterizing Reading Comprehension of Mathematical Texts. Educational Studies in Mathematics, 63(3), 325–346. https://doi.org/10.1007/s10649-005-9016-y
Pfeiffer, K. (2010). The role of proof validation in students’ mathematical learning. MSOR Connections, 10(2), 17–21. https://doi.org/10.11120/msor.2010.10020017
Porter, M. K., & Masingila, J. O. (2000). Examining The Effects of Writing on Conceptual and Procedural Knowledge in Calculus. Educational Studies in Mathematics, 103(3), 239–248. https://doi.org/10.1023/A
Putri, D. A., & Widjajanti, D. B. (2019). Improving Students’ Mathematical Literacy Skills Through Multiple Intelligences Approach in Problem Based Learning. Journal of Physics: Conference Series, 1397(1). https://doi.org/10.1088/1742-6596/1397/1/012094
Quealy, C. (2014). The Importance of Writing in Mathematics : Why Writing Allows for a Deeper understanding of the Mathematical Content The Importance of Writing in Mathematics : Why Writing Allows for a. A Journal of Undergraduate Student Research, 15, 19–22. http://fisherpub.sjfc.edu/cgi/viewcontent.cgi?article=1134&context=ur
Rahim, F. (2008). Pengajaran Membaca di Sekolah Dasar. Bumi Aksara.
Sanjaya, W. (2013). Penelitian Pendidikan. Prenadamedia group.
Santhitiwanich, A., Pasiphol, S., & Tangdhanakanond, K. (2014). The Integration of Indicators of Reading, Analytical Thinking and Writing Abilities with Indicators of Subject Content. Procedia - Social and Behavioral Sciences, 116, 4854–4858. https://doi.org/10.1016/j.sbspro.2014.01.1037
Santosa, C. A. H. (2013). Mengatasi Kesulitan Mahasiswa Ketika Melakukan Pembuktian Matematis Formal. Jurnal Pengajaran MIPA., XVII(2). https://doi.org/10.1017/CBO9781107415324.004
Shepherd, M. D., & van de Sande, C. C. (2014). Reading mathematics for understanding-From novice to expert. Journal of Mathematical Behavior, 35, 74–86. https://doi.org/10.1016/j.jmathb.2014.06.003
Solow, D. (2014). How to Read and Do Proofs (Sixth Edition ed.) (6 th). John Wiley&Sons, Inc.
Stavrou, S. (2014). Common Errors and Misconceptions in Mathematical Proving by Education Undergraduates. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1(March), 1–8.
Vinogradova, M., & Ivanova, N. (2016). Pedagogical Conditions for Role-Playing Game Development in Senior Preschool Age Children. Procedia - Social and Behavioral Sciences, 233(May), 297–301. https://doi.org/10.1016/j.sbspro.2016.10.134
Wahyuddin. (2016). Analisis Kemampuan Menyelesaikan Soal Cerita Matematika Ditinjau Dari Kemampuan Verbal Pada Siswa Kelas Vii Smp Muhammadiyah Se-Kota Makassar. Beta: Jurnal Tadris Matematika, 2(2), 111. https://doi.org/10.24014/sjme.v2i2.2213
Wardhani. (2008). Paket fasilitasi pemberdayaan KKG/MGMP matematika. Pusat Pengembangan Dan Pemberdayaan pendidik dan Tenaga Kependidikan Matematika.
Yılmazer, G., & Masal, M. (2014). The Relationship between Secondary School Students’ Arithmetic Performance and their Mathematical Literacy. Procedia - Social and Behavioral Sciences, 152, 619–623. https://doi.org/10.1016/j.sbspro.2014.09.253
Authors
Nur Mulyo, R., Teguh Budiarto, M., Ismail, & Setianingsih, R. (2023). Kemampuan Siswa SMP dalam Menulis Bukti Ditinjau Berdasarkan Tingkat Kemampuan Matematika . Pi: Mathematics Education Journal, 6(1), 17–32. https://doi.org/10.21067/pmej.v6i1.8111
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