pp. 333-352 | Article Number: iejme.2017.014
Published Online: June 18, 2017
Article Views: 313 | Article Download: 417
Learning mathematics until today still left a lot of records that had to be improved, including passive learning, low ability of learners in problem-solving activities, the rarity of authentic assessment, emphasizing only on cognition, and others. This was a study of the literatures concerning the teaching of metacognition in mathematical problem solving. The PME learning model was a modified theory of Darling-Hammond (2003), which was a theoretical-conceptual product that offered the strategies to improve the ability of metacognition in problem solving. This metacognition strategies implemented through metacognitive activities, ie : planning, monitoring, and evaluating (PME). On PME learning model: (1) the activity planning, monitoring, evaluating explicitly raised in the core activities of learning and mathematical problem-solving activities; (2) the learning process recommended using social constructivist teaching in small groups; (3) placing the role and duties of teachers as counselors, classroom manager, motivator, facilitator, and evaluator; (4) The support system for the effectiveness of PME learning model were: Lesson Plan (LP) and Worksheet for students (WS); and (5) the direct effect was expected increasing of the metacognition ability, and the nurturant effect was expected to increase in problem solving performance.
Keywords: Metacognition strategies, constructivist teaching, mathematical problem solving
Ali, R.,Hukamdad, Akhter, A., & Khan, A. (2010). Effect of Using Problem Solving Method in Teaching Mathematics on the Achievement of Mathematics Students.Asian Sosial Science, 6(2), 67 – 72, Pakistan.
Arifin. 2010. Konsep Perencanaan, Pendekatan Dan Model Perencanaan Pendidikan. uploaded on July 15, 2016. https://drarifin.wordpress.com/2010/07/15/konsep-perencanaan-pendekatan-dan-model-perencanaan-pendidikan/
Aurah, Catherine M. ; Setlhomo Koloi-Keaikitse, Calvin Isaacs, Holmes Finch. (2011). The Role Of Metacognition In Everyday Problem Solving Among Primary Students In Kenya.Problems of education in the 21st century. Volume 30, 2011
Baki, A., (1997). Educating Mathematics Teachers. Medical Journal of Islamic Academy of Sciences, 10(3): 93-102.
Carlson, M.P. and Bloom, I. (2005). The Cyclic Nature of Problem Solving: An Emergent Multidimensional Problem-Solving (MPS) Framework. Journal: Educational Studies in Mathematics, 58(1), 45 – 75. Tersedia: http://www.jstor.org /stable/25047137.
Carr, M., Alexander, J., & Foldes-Bennet, T. (1994).Metacognition and Mathematics Strategy Use.Applied Cognitive Psychology, 8, 583-595.
Cobb, P., Jaworski, B., & Presmeg, N. (1996). Emergent and Sosiocultural Views of Mathematical Activity.Theory of Mathematical Learning, Lawrance Erlbaum Associates, pp. 3 – 19.
Darling-Hammond, L. et al, (2003).The Learning Classroom: Theory into Practice. Stanford University: Annenberg/CPB. Available :https://www.learner.org/ courses/learning classroom/support/09_metacog.pdf.
Downing K.J. (2009).Self-Efficacy And Metacognitive Development. The International Journal Of Learning. Volume 16, Number 4. Tersedia: http://Www.Learning-Journal.Com, ISSN 1447-9494.
Duncan, G., & Met, M. (2010).STARTALK: From paper to practice. College Park,MD: National Foreign Language Center at the University of Maryland.Available at www.startalk.umd.edu/lesson_planning.
Feist, Jess & Feist, Gregory J. (2013).Teori Kepribadian (Theory of Personality, 7thed). Jakarta: Salemba Humanika.
Gartmann, S. and Freiberg, M. (1993). Metacognition and Mathematical Problem Solving : Helping Students to Ask The Right Questions. Journal: The Mathematics Educator, 6(1), 9 – 13.
Ghasempour, Z., Bakar, M.D., & Jahanshahloo.G.R. (2013).Innovation in Teaching and Learning through Problem PosingTasks and Metacognitive Strategies.International Journal of Pedagogical Innovations, 1(1), 53 – 62.
Handoko, TH. (1984). Manajemen. Yogyakarta : BPFE
Havenga, Marietjie ; Betty Breed; Elsa Mentz, Desmond Govender; Irene Govender; Frank Dignum, Virginia Dignum. (2013). Metacognitive and Problem-Solving Skills to Promote Self-Directed Learning in Computer Programming :Teachers’ Experiences SA-eDUC JOURNAL Volume 10, Number 2 October 2013
Herbst, P.G. (2006). Teaching Geometry With Problems: Negotiating Instructional Situation and Mathematical Tasks. Journal for Research in Mathematics Education, 37(4), 313 – 347.
Hoe, L.N., Shook Cheong, A.C., Lee Peng Yee, L.P. (2001). The Role of Metacognition in the Learning of Mathematics among Low-Achieving Students.Teaching and Learning Journal, 22(2), 18 – 30.
Hudojo, H. (1988). Mengajar Belajar Matematika. Jakarta: Departemen Pendidikan dan Kebudayaan. Dirjen Dikti. Proyek Pengembangan LPTK.
Hudojo, H. (2005). Kapita Selekta Pembelajaran Matematika. Malang: Universitas Negeri Malang.
Jo An, Yun ; Li Cao. (2014). Examining the Effects of Metacognition Scaffolding on Students’ Design Problem Solving and Metacognitive Skills in an Online Environment. MERLOT Journal of Online Learning and Teaching, 10(4), December 2014.
Jone, J. (1998). Lesson planning: Towards purposeful learning and effective teaching. Encuentro.Revista de Investigación e Innovación en la clase de idiomas, 10.
Joyce, Bruce, Weil, Marsha, & Calhoun, Emily. (2009). Models of Teaching (Model-model Pengajaran). Yogyakarta: Pustaka Pelajar
Karpicke, J.D., Butler, A.C. & Henry L. Roediger, H.L. (2009). Metacognitive strategies in student learning: Do students practise retrieval when they study on their own?.MEMORY, 17 (4), 471-479.
Kaur, Berinderjeet. (2014). Mathematics Education In Singapore - An Insider’s Perspective. IndoMS-JME, 5(1), 1-16
Kramarski B., Mevarech, Z.R., and Arami, A. (2002).The Effects of Metacognitive Instruction on Solving Mathematical Authentic Tasks.Educational Studies in Mathematics, 49, 225–250.
Ku, Kelly Y. L. & Ho, Irene T. (2010).Metacognitive strategies that enhance critical thinking.Journal: Metacognition Learning, 5, 251–267.
Kuhn, D. & Dean Jr, D. (2004). Metacognition: A Bridge Between Cognitive Psychology and Educational Practice. Theory into Practice, 43(4), 268 – 273.
Lee,Ngan Hoe ; Agnes Shook Cheong Chang ; Lee Peng Yee. (2001). The role of metacognition in The learning of mathematics among low-achieving students. Teaching and Learning, 22(2), 18-30.
Lester Jr, F.K. (2013).Thoughts about Research on Mathematical Problem Solving Instruction. Jorunal: The Mathematics Enthusiast (TME), 10(1) & 2, 245 – 278.
Maccini, P., & Gagnon, J.C., (2002). Perceptions And Application Of NCTM Standarts By Special And General Education Teachers. Exceptional Children, 68, 325-344.
Muijs &Reynolds . (2008). Effective Teaching. Yogyakarya: Rosdakarya
Okoza, J. & Aluede, O. (2013).Understanding metacognitive awareness among teachers in the school system: issues and benefits. Inkanyiso, Journal Humanistic & Sosial Science, 5(1).
Patrick, Thompson , W. (2013). Constructivism in Mathematics Education. In Lerman, S. (Ed.) Encyclopedia of Mathematics Education : Springer Reference (www.springerreference.com). Springer-Verlag Berlin Heidelberg. DOI: 10.1007/SpringerReference_313210 2013-05-10 00:00:07 UTC
Rusman. (2013). Model-model Pembelajaran: MengembangkanProfesionalisme Guru (Cetakan ke-6). Jakarta: PT. RajaGrafindoPersada.
Sahin, SM ; Fatma Kendir. (2013). The Effect of Using Metacognitive Strategies for solving Geometry Problems on Students’ Achievement and Attitude. 2013. Educational Research and Reviews, 8(19), 1777-1792. 10 October 2013. DOI : 10.5897/ ERR2013.1578. ISSN 1990-3839 © 2013 Academic Journals. http://www.academicjournals.org/ERR
Schneider, W. &Lockl, K. (2002).The Development of Metacognitive Knowledge in Children and Adolescents. In Perfect, T. and Schwartz, B. (Eds.), Applied Metacognition. Cambridge, UK: Cambridge University Press.
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics.In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning (pp. 334-370).New York: MacMillan. Tersedia: http://hplengr.engr.wisc.edu/Math_Schoenfeld.pdf
Schraw, G. & Dennison, R.S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19, 460-475.
Schraw, G. & Moshman D. (1995).Metacognitive Theories.Published InEducational Psychology Revie, 7:4, 351–371.
Schunk, Dale H. (2012). Learning Theories: as Education Perspective (Teori-teori Pembelajaran: Perspektif Pendidikan) Edisi keenam. Yogyakarta: Pustaka Pelajar
Shrawder, Jack H. (2006). Planning a Successful Lesson Publisher/Editor, Teaching For Success South Lake Tahoe, CA firstname.lastname@example.org)
Steffe, L. P., Cobb, P., & Glasersfeld, E. v. (1988). Construction of arithmetic meanings and strategies. New York : Springer-Verlag.
Steffe, L. P., Glasersfeld, E. v., Richards, J., & Cobb, P. (1983). Children’s counting types: Philosophy, theory, and application. New York: Praeger Scientific
TEAL (Teaching Excellence in Adult Literacy). (2012). Just Write! Guide. Washington DC: American Institute for Research (AIR).
Toit, Stephan du. (2009). The Use of Metacognitive Strategies in The Teaching and Learning of Mathematics. Proceedings of the 15th Annual Congress of the Association for Mathematics Education of South Africa (AMESA), 1, 9-21.
Toit, Stephan du; Gawie du Toit. (2013). The Journal for Transdisciplinary Research in Southern Africa, 9(3), Special edition, December 2013, pp. 505-530
Uno, H.B. (2009). Model Pembelajaran Menciptakan Proses Belajar Mengajar yang Kreatif dan Efektif. Jakarta: PT Bumi Aksara.
Veenman, M.V.J., Wilhelm, P., Beishuizen, J.J. (2004).The Relation between Intellectual and Metacognitive Skills from a Developmental Perspective.Learning and Instruction (Elsevier), 14, 89 – 109.
Voskoglou, Michael Gr. (2008). Problem Solving in Mathematics Education: Recent Trends and Development. Quaderni di Ricerca in Didattica (Scienze Matematiche), 18, 22 – 28, G.R.I.M. (Department of Mathematics, University of Palermo).
Yevdokimov, Oleksiy and Tim Passmore.( 2008). Problem Solving Activities in a Constructivist Framework : Exploring how Students Approach Difficult Problems. Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia M. Goos, R. Brown, & K. Makar (Eds.), © MERGA Inc. 2008