Students critical thinking skills toward concepts differences in finding area of a plane region and definite integral
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Mar 29, 2019
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Abstract
This study aimed to describe students' critical thinking skills towards the concepts differences in finding the area of a plane region and definite integral. This study used an exploratory test survey method with test instruments. Data were taken from 40 students of the mathematics department at a university in Central Java. The results showed that students' critical thinking skills towards the concepts differences in finding the area of a plane region and definite integral were in the medium category. The students' critical thinking skills towards the concepts differences in finding area of a plane region and definite integral were medium (47.5%), with clarification by 57.5% (medium), assessment by 40.0% (medium), inference by 65.0% (medium), and strategies by 27.5% (low). These weaknesses are expected to be followed up by conducting learning that can show the linkages between the concepts and with various ways.
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How to Cite
Susilo, B. E., Darhim, D., & Prabawanto, S. (2019). Students critical thinking skills toward concepts differences in finding area of a plane region and definite integral. Unnes Journal of Mathematics Education, 8(1), 1-7. https://doi.org/10.15294/ujme.v8i1.29463
References
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Attorps, I., Björk, K., Radic, M., & Tossavainen, T. (2013). Varied ways to teach the definite integral concept. International Electronic Journal of Mathematics Education, 8(2-3), 81-99.
Bezuidenhout, J. (2001). Limits and continuity: some conceptions of first-year students. International Journal of Mathematical Education in Science and Technology, 32(4), 487-500 http://dx.doi.org/10.1080/00207390010022590
Cornu, B. (1991). Limits, in Tall, D., ed., Advanced Mathematical Thinking, 153-166, Dordrecht: Kluwer Academic Publishers
Denbel, D. G. (2014). Students’ Misconceptions of the Limit Concept in a First Calculus Course. Journal of Education and Practice, 5(34), 24-40. Retrieved from https://www.iiste.org/Journals/index.php/JEP/article/viewFile/17236/17685
Ferrer, F. P. (2016). Investigating Students’ Learning Difficulties In Integral Calculus People: International Journal of Social Sciences, Special Issue 2(1), 310–324, http://dx.doi.org/10.20319/pijss.2016.s21.310324
Fuad, N. M.; Zubaidah, S.; Mahanal, S. & Suarsini, E. (2017). Improving Junior High Schools’ Critical Thinking Skills Based on Test Three Different Models of Learning, International Journal of Instruction, 10(1), 101-116. http://dx.doi.org/10.12973/iji.2017.1017a
Hashemi, N.; Abu, M. S.; Kashefi, H. & Rahimi, K. (2014) Undergraduate Students’ Difficulties in Conceptual Understanding of Derivation. Procedia - Social and Behavioral Sciences 143(2014), 358–366. http://dx.doi.org/10.1016/j.sbspro.2014.07.495
Juter, K. (2005). Limits of Functions – How do Students Handle Them? Pythagoras, 61, 11-20. https://doi.org/10.4102/pythagoras.v0i61.117
Karatas, I.; Guven, B. & Cekmez, E. (2011). A Cross-Age Study of Students' Understanding of Limit and Continuity Concepts, Boletim de Educação Matemática, 24(38), 245-264. Retrieved from www.redalyc.org/pdf/2912/291222086011.pdf
Kharbach, M. (2012). The 21st Century skills Teachers and Student Need to Have. Halifax: Creative Commons Attribution Mount Saint Vincent University.
Lau, J.Y.F. (2011). An Introduction to Critical Thinking and Creativity, John Wiley & Sons Inc, Massachuset.
Kiat, S. E. (2005). Analysis of Students’ Difficulties in Solving Integration Problems. The Mathematics Educator, 9(1), 39-59. Retrieved from http://fliphtml5.com/aqlj/sogn/basic
Kremžárová, L. (2011). Students' Difficulties In Understanding The Calculus Tasks. Acta Didactica Universitatis Comenianae Mathematics, 11, 41-46. Retrieved from https://www.ddm.fmph.uniba.sk/ADUC/files/Issue11/03%20Kremzarova.pdf
Mahir, N. (2009). Conceptual and Procedural Performance of Undergraduate Students in Integration. International Journal of Mathematical Education in Science and Technology, 40(2), 201-211. https://doi.org/10.1080/00207390802213591
Metaxas, N. (2007). Difficulties on Understanding the Indefinite Integral. In Woo, J. H., Lew, H. C., Park, K. S., Seo, D. Y. (Eds.). In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 265-272). Seoul: PME. Retrieved from ftp://ftp.math.ethz.ch/EMIS/proceedings/PME31/3/265.pdf
Naidoo, K. & Naidoo, R. (2007). First Year Students Understanding Of Elementary Concepts In Differential Calculus In A Computer Laboratory Teaching Environment. Journal of College Teaching & Learning, 4(9), 55-70. Retrieved from https://www.learntechlib.org/p/108226/
Orton, A. (1983). Students’ understanding of integration. Educational Studies in Mathematics, 14(1), 1–18. https://doi.org/10.1007/bf00704699
Pepper, R. E., Chasteen, S. V., Pollock, S. J., & Perkins, K. K. (2012). Observations on Student Difficulties with Mathematics in Upper-Division Electricity and Magnetism. Physical Review Special Topics- Physics Education Research, 8(010111): 1-15. https://doi.org/10.1103/PhysRevSTPER.8.010111
Perkins, C., & Murphy, E. (2006). Identifying and measuring individual engagement in critical thinking in online discussions: An exploratory case study. Educational Technology & Society, 9, 298-307. Retrieved from https://www.jstor.org/stable/jeductechsoci.9.1.298
Pichat, M. & Ricco, G. (2001). Mathematical problem solving in didactic institutions as a complex system, The case of elementary calculus. Journal of Mathematical Behavior, 20(1), 43–53. https://doi.org/10.1016/s0732-3123(01)00061-x
Prasetia, A. (2016). Performansi Metode Trapesium dan Metode Gauss-Legendre dalam Penyelesaian Integral Tertentu Berbantuan Matlab. Jurnal Mercumatika, 1(1), 1-12.
Salazar, D. A. (2014). Salazar’s Grouping Method: Effects on Students’ Achievement in Integral Calculus. Journal of Education and Practice, 5(15), 119-126. Retrieved from https://iiste.org/Journals/index.php/JEP/article/download/13020/13525
Rubio, B. S. & Gomez-Chacon I. (2011). Challenges with Visualization: The Concept of Integral with Undergraduate Students. In Proceedings The Seventh Congress of the European Society for Research in Mathematics Education (CERME-7), University of Rzeszow, Poland. Retrieved from www.mat.ucm.es/cosasmdg/cdsmdg/ideas/documentos/ines2.pdf
Serhan, D. (2015). Students’ understanding of the definite integral concept. International Journal of Research in Education and Science (IJRES), 1(1), 84-88.
Susilo, B. E. (2011). Analisis kesulitan belajar mahasiswa pada materi limit fungsi mata kuliah kalkulus dalam perspektif gaya belajar dan gaya berpikir mahasiswa, (Master's Thesis).. Postgraduate Program of Universitas Sebelas Maret.
Syaripuddin (2011). Hubungan antara turunan parsial dan kekontinuan pada fungsi dua peubah, Jurnal Eksponensial, 2(1), 27-32. Retrieved from https://fmipa.unmul.ac.id/files/docs/3.%20Syaripuddin.pdf
Szydlik, J. (2000), Mathematical beliefs and conceptual understanding of the limit of a function, Journal for Research in Mathematics Education, 31(3), 258-276. https://doi.org/10.2307/749807
Tall, D. O., (1993). Student Difficulties in Calculus. In Proceeding of Working Group 3 on Students’ Difficulties in Calculus. ICME-7, 13-28. Quebec, Canada. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1993k-calculus-wg3-icme.pdf
Tall, D. O. (2001). A child thinking about infinity. Journal of Mathematical Behavior, 20(01), 7–19. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot2001l-childs-infinity.pdf
Tall, D. O. (2010). A Sensible Approach to the Calculus. In Plenary at The National and International Meeting on the Teaching of Calculus. 23–25th September 2010, Puebla, Mexico. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot2010a-sensible-calculus.pdf
Tall, D. O. (2012). Making Sense of Mathematical Reasoning and Proof. In Plenary at Mathematics and Mathematics Education: Searching for Common Ground: A Symposium in Honor of Ted Eisenberg. April 29-May 3, 2012, Ben-Gurion University of the Negev, Beer Sheva, Israel. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot2012-reasoning-and-proof-OHs.pdf
Tall, D. O. & Vinner, S. (1981). Concept Image and Concept Definition in Mathematics with Particular References to Limit and Continuity. Educational Studies in Mathematics, 12, 151-169. http://dx.doi.org/10.1007/bf00305619
Tarmizi, R. A. (2010). Visualizing Students’ Difficulties in Learning Calculus. Procedia Social and Behavioral Science, 8, 377- 383. http://dx.doi.org/10.1016/j.sbspro.2010.12.053
Tasman, F., Ahmad, D., & Suherman, S. (2018). Kesulitan Mahasiswa Dalam Mengkoneksikan Sigma, Area, dan Definisi Integral Tentu Secara Geometri. JURNAL EKSAKTA PENDIDIKAN (JEP), 2(2), 186-193. doi:10.24036/jep/vol2-iss2/238
Usman, A. I. (2012). Analysis of Algebraic Errors in Applied Calculus Problem Solving. In 12th International Congress on Mathematical Education, COEX, Seoul, Korea. Retrieved from https://www.researchgate.net/publication/283071744_ANALYSIS_OF_ALGEBRAIC_ERRORS_IN_APPLIED_CALCULUS_PROBLEM_SOLVING
Varberg, D.; Purcell, E.J. & Rigdon, S.E. (2006). Calculus, 9th edition. New York: Pearson.
Williams, S. (1991). Models of limit held by college calculus studentsâ€, Journal for Research in Mathematics Education, 22(3), 219-236. http://dx.doi.org/10.2307/749075
Yee, N. K. & Lam, T. T. (2008). Pre-University Students’ Errors in Integration of Rational Functions and Implications for Classroom Teaching. Journal of Science and Mathematics Education in Southeast Asia, 31(2), 100-116. Retrieved from http://www.recsam.edu.my/R&D_Journals/YEAR2008/dec2008vol2/preunivstudents(100-116).pdf
Yudianto, E. (2015). Profil Antisipasi Siswa SMA Dalam Memecahkan Masalah Integral. Kreano, Jurnal Matematika Kreatif-Inovatif, 6(1), 21-25. doi:https://doi.org/10.15294/kreano.v6i1.4472
Zakaria, E. & Salleh, T. S. (2015). Using Technology in Learning Integral Calculus. Mediterranean Journal of Social Sciences, 6(5S1), 144-148. https://doi.org/10.5901/mjss.2015.v6n5s1p144
Attorps, I., Björk, K., Radic, M., & Tossavainen, T. (2013). Varied ways to teach the definite integral concept. International Electronic Journal of Mathematics Education, 8(2-3), 81-99.
Bezuidenhout, J. (2001). Limits and continuity: some conceptions of first-year students. International Journal of Mathematical Education in Science and Technology, 32(4), 487-500 http://dx.doi.org/10.1080/00207390010022590
Cornu, B. (1991). Limits, in Tall, D., ed., Advanced Mathematical Thinking, 153-166, Dordrecht: Kluwer Academic Publishers
Denbel, D. G. (2014). Students’ Misconceptions of the Limit Concept in a First Calculus Course. Journal of Education and Practice, 5(34), 24-40. Retrieved from https://www.iiste.org/Journals/index.php/JEP/article/viewFile/17236/17685
Ferrer, F. P. (2016). Investigating Students’ Learning Difficulties In Integral Calculus People: International Journal of Social Sciences, Special Issue 2(1), 310–324, http://dx.doi.org/10.20319/pijss.2016.s21.310324
Fuad, N. M.; Zubaidah, S.; Mahanal, S. & Suarsini, E. (2017). Improving Junior High Schools’ Critical Thinking Skills Based on Test Three Different Models of Learning, International Journal of Instruction, 10(1), 101-116. http://dx.doi.org/10.12973/iji.2017.1017a
Hashemi, N.; Abu, M. S.; Kashefi, H. & Rahimi, K. (2014) Undergraduate Students’ Difficulties in Conceptual Understanding of Derivation. Procedia - Social and Behavioral Sciences 143(2014), 358–366. http://dx.doi.org/10.1016/j.sbspro.2014.07.495
Juter, K. (2005). Limits of Functions – How do Students Handle Them? Pythagoras, 61, 11-20. https://doi.org/10.4102/pythagoras.v0i61.117
Karatas, I.; Guven, B. & Cekmez, E. (2011). A Cross-Age Study of Students' Understanding of Limit and Continuity Concepts, Boletim de Educação Matemática, 24(38), 245-264. Retrieved from www.redalyc.org/pdf/2912/291222086011.pdf
Kharbach, M. (2012). The 21st Century skills Teachers and Student Need to Have. Halifax: Creative Commons Attribution Mount Saint Vincent University.
Lau, J.Y.F. (2011). An Introduction to Critical Thinking and Creativity, John Wiley & Sons Inc, Massachuset.
Kiat, S. E. (2005). Analysis of Students’ Difficulties in Solving Integration Problems. The Mathematics Educator, 9(1), 39-59. Retrieved from http://fliphtml5.com/aqlj/sogn/basic
Kremžárová, L. (2011). Students' Difficulties In Understanding The Calculus Tasks. Acta Didactica Universitatis Comenianae Mathematics, 11, 41-46. Retrieved from https://www.ddm.fmph.uniba.sk/ADUC/files/Issue11/03%20Kremzarova.pdf
Mahir, N. (2009). Conceptual and Procedural Performance of Undergraduate Students in Integration. International Journal of Mathematical Education in Science and Technology, 40(2), 201-211. https://doi.org/10.1080/00207390802213591
Metaxas, N. (2007). Difficulties on Understanding the Indefinite Integral. In Woo, J. H., Lew, H. C., Park, K. S., Seo, D. Y. (Eds.). In Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 265-272). Seoul: PME. Retrieved from ftp://ftp.math.ethz.ch/EMIS/proceedings/PME31/3/265.pdf
Naidoo, K. & Naidoo, R. (2007). First Year Students Understanding Of Elementary Concepts In Differential Calculus In A Computer Laboratory Teaching Environment. Journal of College Teaching & Learning, 4(9), 55-70. Retrieved from https://www.learntechlib.org/p/108226/
Orton, A. (1983). Students’ understanding of integration. Educational Studies in Mathematics, 14(1), 1–18. https://doi.org/10.1007/bf00704699
Pepper, R. E., Chasteen, S. V., Pollock, S. J., & Perkins, K. K. (2012). Observations on Student Difficulties with Mathematics in Upper-Division Electricity and Magnetism. Physical Review Special Topics- Physics Education Research, 8(010111): 1-15. https://doi.org/10.1103/PhysRevSTPER.8.010111
Perkins, C., & Murphy, E. (2006). Identifying and measuring individual engagement in critical thinking in online discussions: An exploratory case study. Educational Technology & Society, 9, 298-307. Retrieved from https://www.jstor.org/stable/jeductechsoci.9.1.298
Pichat, M. & Ricco, G. (2001). Mathematical problem solving in didactic institutions as a complex system, The case of elementary calculus. Journal of Mathematical Behavior, 20(1), 43–53. https://doi.org/10.1016/s0732-3123(01)00061-x
Prasetia, A. (2016). Performansi Metode Trapesium dan Metode Gauss-Legendre dalam Penyelesaian Integral Tertentu Berbantuan Matlab. Jurnal Mercumatika, 1(1), 1-12.
Salazar, D. A. (2014). Salazar’s Grouping Method: Effects on Students’ Achievement in Integral Calculus. Journal of Education and Practice, 5(15), 119-126. Retrieved from https://iiste.org/Journals/index.php/JEP/article/download/13020/13525
Rubio, B. S. & Gomez-Chacon I. (2011). Challenges with Visualization: The Concept of Integral with Undergraduate Students. In Proceedings The Seventh Congress of the European Society for Research in Mathematics Education (CERME-7), University of Rzeszow, Poland. Retrieved from www.mat.ucm.es/cosasmdg/cdsmdg/ideas/documentos/ines2.pdf
Serhan, D. (2015). Students’ understanding of the definite integral concept. International Journal of Research in Education and Science (IJRES), 1(1), 84-88.
Susilo, B. E. (2011). Analisis kesulitan belajar mahasiswa pada materi limit fungsi mata kuliah kalkulus dalam perspektif gaya belajar dan gaya berpikir mahasiswa, (Master's Thesis).. Postgraduate Program of Universitas Sebelas Maret.
Syaripuddin (2011). Hubungan antara turunan parsial dan kekontinuan pada fungsi dua peubah, Jurnal Eksponensial, 2(1), 27-32. Retrieved from https://fmipa.unmul.ac.id/files/docs/3.%20Syaripuddin.pdf
Szydlik, J. (2000), Mathematical beliefs and conceptual understanding of the limit of a function, Journal for Research in Mathematics Education, 31(3), 258-276. https://doi.org/10.2307/749807
Tall, D. O., (1993). Student Difficulties in Calculus. In Proceeding of Working Group 3 on Students’ Difficulties in Calculus. ICME-7, 13-28. Quebec, Canada. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot1993k-calculus-wg3-icme.pdf
Tall, D. O. (2001). A child thinking about infinity. Journal of Mathematical Behavior, 20(01), 7–19. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot2001l-childs-infinity.pdf
Tall, D. O. (2010). A Sensible Approach to the Calculus. In Plenary at The National and International Meeting on the Teaching of Calculus. 23–25th September 2010, Puebla, Mexico. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot2010a-sensible-calculus.pdf
Tall, D. O. (2012). Making Sense of Mathematical Reasoning and Proof. In Plenary at Mathematics and Mathematics Education: Searching for Common Ground: A Symposium in Honor of Ted Eisenberg. April 29-May 3, 2012, Ben-Gurion University of the Negev, Beer Sheva, Israel. Retrieved from http://homepages.warwick.ac.uk/staff/David.Tall/pdfs/dot2012-reasoning-and-proof-OHs.pdf
Tall, D. O. & Vinner, S. (1981). Concept Image and Concept Definition in Mathematics with Particular References to Limit and Continuity. Educational Studies in Mathematics, 12, 151-169. http://dx.doi.org/10.1007/bf00305619
Tarmizi, R. A. (2010). Visualizing Students’ Difficulties in Learning Calculus. Procedia Social and Behavioral Science, 8, 377- 383. http://dx.doi.org/10.1016/j.sbspro.2010.12.053
Tasman, F., Ahmad, D., & Suherman, S. (2018). Kesulitan Mahasiswa Dalam Mengkoneksikan Sigma, Area, dan Definisi Integral Tentu Secara Geometri. JURNAL EKSAKTA PENDIDIKAN (JEP), 2(2), 186-193. doi:10.24036/jep/vol2-iss2/238
Usman, A. I. (2012). Analysis of Algebraic Errors in Applied Calculus Problem Solving. In 12th International Congress on Mathematical Education, COEX, Seoul, Korea. Retrieved from https://www.researchgate.net/publication/283071744_ANALYSIS_OF_ALGEBRAIC_ERRORS_IN_APPLIED_CALCULUS_PROBLEM_SOLVING
Varberg, D.; Purcell, E.J. & Rigdon, S.E. (2006). Calculus, 9th edition. New York: Pearson.
Williams, S. (1991). Models of limit held by college calculus studentsâ€, Journal for Research in Mathematics Education, 22(3), 219-236. http://dx.doi.org/10.2307/749075
Yee, N. K. & Lam, T. T. (2008). Pre-University Students’ Errors in Integration of Rational Functions and Implications for Classroom Teaching. Journal of Science and Mathematics Education in Southeast Asia, 31(2), 100-116. Retrieved from http://www.recsam.edu.my/R&D_Journals/YEAR2008/dec2008vol2/preunivstudents(100-116).pdf
Yudianto, E. (2015). Profil Antisipasi Siswa SMA Dalam Memecahkan Masalah Integral. Kreano, Jurnal Matematika Kreatif-Inovatif, 6(1), 21-25. doi:https://doi.org/10.15294/kreano.v6i1.4472
Zakaria, E. & Salleh, T. S. (2015). Using Technology in Learning Integral Calculus. Mediterranean Journal of Social Sciences, 6(5S1), 144-148. https://doi.org/10.5901/mjss.2015.v6n5s1p144