pp. 715-733 | Article Number: iejme.2017.042
Published Online: October 31, 2017
Article Views: 161 | Article Download: 181
This paper describe the change patterns in the process of awareness, evaluation, and regulation of mathematics students in solving mathematical problems. The patterns of change is reveled done by observation of the emergence of activity and indicators awareness, evaluation, and regulation of students. Student metacognition activities and indicators are outlined in 5 activities with 30 indicators of awareness process, 5 activities with 23 indicators of evaluation process, and 4 activities with 19 indicators of regulation process. The subjects of the study were students of mathematics education who had taken Differential Calculus and subjects were given mathematical problems. Mathematical problem solving is done through think-aloud. In addition to think-aloud research subjects were given metacognition questionnaires, observed using observation sheets, and interviews. The data include student work, think-aloud, metacognition questionnaire, interview, and observation were analyzed using fixed comparison method. The result show that the change pattern of awareness, evaluation, and regulation processes of mathematics students were categorized into complete sequenced metacognition process, complete unsequenced metacognition and incomplete metacognition.
Keywords: Componen of Metacognition, Pattern, Complete Sequenced, Complete Unsequenced, Incomplete
Anderson, L.W. & Krathwohl, D.R. (2001). A Taxonomy for learning, teaching, and assessing (A Revision of Bloom’s taxonomy of educational objectives). New York: Addision Wesley Longman, Inc.
Baker, L. & Brown, A. L. (1984). Metacognitive skills and reading. In Douglas J. Hacker, John Dunlosky and Arthur C. Graesser (Eds.) Handbook of metacognition in eucation. (pp. 7-25). New York: Routledge.
Biryukov, P. (2003). Metacognitive aspects of solving combinatorics problem kaye College of Education. Direct access:http://www.cimt.org.uk/journal-/biryukov.pdf.
Cromley, J.G. (2005). Metacognition, cognitive strategy instruction, and reading in adult literacy. Direct access: http://www.ncsall.net/index-.html@id=782.htm.
Davidson J. E., Deuser R. & Sternberg R. J. (1994). The Role of Metacognition in problem solving. In J. Metcalfe and A. R. Shimamura (Eds.), Metacognition: knowing about knowing (pp. 207-226). Cambridge, MA: MIT Press.
Davidson, J. E. & Sternberg, R. J. (1998). Smart problem solving: How metacognition helps. In D. J. Hacker., J. Dunlosky, A. C. Graesser (Eds.), Metacognition in educational theory and practice (pp. 47-68). Mahweh, NJ: Lawrence Erlbaum Associates.
Desoete, A., Roeyers, H. & Buysse, A. (2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disabilities; Sep-Oct 2001; 34, 5; Academic Research Library.pp 435. Direct access:http://www.fi.uu.nl
Flavell, J. (1976). Metacognitive aspects of problem solving. in L. Resnick (Ed), In the Natrure of Intelligence. Direct access:http://www.library.edu.
In’am, A., Sa’ad, N. & Ghani, S.A. (2012).A Metacognitive approach to solving Algebra problems. International Journal of Independent Research and Studies. University Pendidikan Sultan Idris, Malaysia. Direct access:http://www. aiars.org/ijirs...20120195.pdf.
Jayapraba, G. (2013). Metacognitive instruction and cooperative learning strategi for Ppomoting insightful learning in Science. International Journal on New Trends in Education and Their Implications. Direct access:http://www:ijonte.org.
Karan, E. P. & Irizarry, J. (2011). Effects of metacognitive strategies on problem solving ability in construction education. Direct access:http://www.ascpro.ascweb.org.
Kuntjoyo, (2009). Metakognisi dan keberhasilan peserta didik. Direct access:http://www.ebekunt.wordpress.com/2009/.../metakognisi-dan-keberhasilan_peserta_didik.
Kuzle, A. (2011). Patterns of metacognitive behavior during mathematics problem solving in a dynamic Geometry environment. Direct access: http://www.jwilson.coe.uga.edu,
Lioe, L.T., Fai H. K. & Hedberg, J.G. (2006). Students’ metacognitive problem solving strategies in solving open-ended problems in pairs. Direct access: http://www.math.ecnu.edu.cn/.../tsg205.doc.
Livingstone, J.A. (1997). Metecognition on overview. Direct access:http:// www. gse.buffalo-edu/fas/shuell/cep564/Metacog.htm.
Magiera, M. T. & Zawojewski, J. S. (2011). Characterizations of social-based and self-based contexts associated with students’ awareness, evaluation, and regulation of their thinking during small-group mathematical modeling. Journal for Research in Mathematics Education. Number 5, Volume 42 November 2011. pp. 486-516.
Mariam, A. M. & Idrus, N. M. (2013). Metacognitive strategies in quadratic equation word problem. Jurnal Pendidikan Sains dan Matematik Malaysia. Volume 3 Number 2 ISSN 2232-0393. Direct access: http://www .pustaka2.upsi.edu.my/.../-metacognitive.
Marrongelle, K. (2007). The role of physics in students’ conceptualization of calculus consepts: Implications of research on teaching practice. Direct access, http://www.Math.Uoc.Gr/~Ictm2/Proceedings/Pap153.Pdf.
Mokos, E. & Kafoussi, S. (2013). Elementary students' spontaneous metacognitive functions different types of mathematical problems. Journal Research in Mathematics Education. Volume 2 number 2, June 2013. pp 242-267. Direct access: http://www.hipatiapress.com.
Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 54 Tahun 2013 tentang Standar kompetensi lulusan pendidikan dasar dan menengah.
Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 69 Tahun 2013 tentang Kerangka dasar dan struktur kurikulum sekolah menengah atas/madrasah aliyah.
Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 24 tahun 2016 tentang Kompetensi inti dan kompetensi dasar pelajaran pada kurikulum 2013 pada pendidikan dasar dan menengah.
Purnomo, D., Nusantara, T., Subanji, Raharjo, S. (2016a). The Characterization of mathematics students’ metacognition process in solving mathematical problems. Article presented at 3rd International Conference on Research, Implementation, and Education of Mathematics and Science (ICRIEMS) 2016. May 16th-17th Yogjakarta State University (UNY).
Purnomo, D., Nusantara, T., Subanji, Rahardjo, S. (2016b). Metacognition process characteristics of the students in solving mathmatics problems. IOSR Journal of Research & Method in Education (IOSR-JRME) e-ISSN: 2320–7388,p-ISSN: 2320–737X Volume 6, Issue 5 Ver. III (Sep. - Oct. 2016), pp.26-35 DOI: 10.9790/7388-0605032635.
Purnomo, D., Nusantara, T., Subanji, Rahardjo, S. (2017), The characteristic of the process of students’metacognition in solving Mathematics problems. International Educational Studies (IES) Journal. ISSN 1913-9020 E-ISSN 1913-9039. Volume 10, Number 5.
Sabella, M.S. & Redish E.F. (2003). Student understanding of topics in calculus. Direct access:http://www.physics.umd.edu/perg-/plinks/calc.htm.
Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition, and sensemaking in mathematics. Direct access: http://www.math.ubc.ca.
Schoenfeld. A.H., Elizabeth & Corner, E. (1992). Learning to think mathematically: problem solving metacognition, and sensemaking in mathematics. Berkeley, CA. Reston: NCTM
Schoenfeld, A. H. (1994). Mathematical thinking and problem solving. New Jersey: School Mathematics. Reston: NCTM
Sengul, S. & Katranci, Y. (2012). Metacognitive aspects of solving function problems. Procedia-Social and Behavioral Sciences 46 ( 2012 ) 2178 – 2182. Directaccess: http://www.sciencedirect.com/science/article/pii/S18770-42815042068.
Stillman, G. A. & Galbraith, P. L. (1998). Applying mathematics with real world connections: Metacognitive characteristics of secondary students. Educational Studies in Mathematics 36(2), 157-195.
Tan, O. S. (2004). Cognition, metacognition, and problem-based learning, in enhancing thinking through problem-based learning approaches. Singapore: Thomson Learning.
Veenam, M.V.J., Wilhelm, P. & Beishuizen, J. J. (2004). The relation between intellectual and metacognitive skills from a developmental perspective. Direct access: http://www.ww4.ncsu.edu/.../Veenman,%20Wilhelm ,%20%26%20-Beishuizen%2004.pdf.
Wilson, J. (1997). Beyond the basics: Assessing students' metacognition. Paper Presented at the 14th Annual Hong Kong Educational Research Association Conference. Hong Kong. November, 1997. Direct access: http://www.files .eric.ed.gov.fulltext/ED415244.pdf.
Wilson, J. & Clarke D. (2002). Monitoring mathematical metacognition. Paper presented at the Anual Meeting for the American Education Research Assosiation, New Orleeans, LA.
Wilson, J. & Clarke D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal. 16(2) pp. 25-48. Direct access: http://www.files.eric.ed.gov/fulltext/EJ747867.
Wong Khoon Yoong, (2007). Metacognitive awareness of problem solving among primary and secondary school students. Direct access: http: // www .math. nie.edu.sg.
Zainal, Z. & Tajudin, N. M. (2013). Metacognitif process in solving non-routin mathematics problems. Direct access: http://www.psmm.upsi.edu.my.
Zechmeister, E.B. & Neyberg, S.E. (1982). Human memory: An introduction to research and theory. Monterey, C.A: Brooks/Cole Publishing Company.