A COGNITIVE THEORY DRIVEN NEW ORIENTATION OF INDONESIAN LESSONS

Edyta Nowinska

Abstract


The main focus of this design research was on students’ mathematical thinking and skills and on their understanding of mathematical concepts and methods. The mathematical content our project starts with is the introduction of integers. For this content new learning environments have been developed, implemented and evaluated. An important question for the design of teaching and learning activities is how to establish appropriate models of mathematical concepts and methods for students and how they operate in students’ minds. In the lecture the use of those methodological concepts and theories in our approach will be explained and justified. The results indicate that the means and methods used in our project have a positive influence on the quality of teaching and learning processes in the class and on students’ mathematical thinking and skills.

Keywords: Cognitive Theory, Indonesian Lessons, Mathematical Concept

 

DOI: http://dx.doi.org/10.22342/jme.5.2.1501.170-190


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References


Brown, A. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. Journal of the learning sciences, 2, pp. 141-178.

Cobb, P.; Confrey, J.; diSessa, A.; Lehrer, R.; Schauble L. (2003). Design experiments in educational research. Educational Researcher, 32(1), pp. 9-13.

Cohors-Fresenborg, E. & Kaune, C. (2005). The Metaphor "Contracts to deal with Numbers" as a Structuring Tool in Algebra. In M. Bosch (Ed.): Proceedings of CERME 4, pp. 300-310.

Cohors-Fresenborg, E. & Kaune, C. (2007). Kategoriensystem für metakognitive Aktivitäten beim schrittweise kontrollierten Argumentieren im Mathematikunterricht, 2. überarbeitete Auflage. Arbeitsbericht Nr. 44. Osnabrück: Forschungsinstitut für Mathematikdidaktik.

Eerde, H.A.A. van (2013). Design research: Looking into the heart of mathematics education. In Zulkardi (Ed.): Proceeding The First South East Asia Design/Development Research (SEA - DR) International Conference, Sriwijaya University, Palembang, April 22nd - 23rd, pp. 1-10.

Fischbein, E. (1989). Tacit models and mathematical reasoning. For the learning of mathematics, 9 (2), pp. 9-14.

Freudenthal, H. (1991). Revisiting mathematics education: China lectures. Dordrecht. The Netherlands: Kluwer Academic Publishers.

Freudenthal, H. (1963). Was ist Axiomatik, und welchen Bildungswert kann sie haben? Der Mathematikunterricht 9, Heft 4, pp. 5-29.

Galen, F. H. J. van (2013). Context and models in mathematics education. In Zulkardi (Ed.): Proceeding The First South East Asia Design/Development Research (SEA - DR) International Conference, Sriwijaya University, Palembang, April 22nd - 23rd, pp. 11-21.

Gravemeijer, K. (2002). Emergent modeling as the basis for an instructional sequence on data analysis. In Sixth International Conference on Teaching Statistics. Kaapstad, pp. 1-6.

Gravemeijer, K.; Bowers, J.; Stephan, M. (2003). A hypothetical learning trajectory on measurement and flexible arithmetic. In Stephan, M.; Bowers, J.; Cobb, P.; Gravemeijer, K. (Eds.): Supporting students’ development of measuring conceptions: Analyzing students' learning in social context. Reston: NCTM, pp. 51-66.

Gravemeijer, K. (1997). Developmental research as a research method. In Sierpinska, A. & Kilpatrick, J. (Eds.), Mathematics Education as a Research Domain: A Search for Identity. An ICMI Study. Dortrecht: Kluwer Academic Publishers, pp. 277-295.

Gravemeijer, K. & Cobb, P. (2013). Design Research from the Learning Design Perspective. In Plomp, T. & Nieveen, N. (Eds): Educational Design Research. Part A: An introduction. Enschede: SLO, pp. 72-113.

Griesel, H (1996). Grundvorstellungen zu Größen. mathematik lehren 78, pp. 15-19.

Hanna, G. & Jahnke, H. N. (1996). Proof and Proving. In Bishop, A. J. et al. (Eds.): International Handbook of Mathematics Education, Dordrecht: Kluwer Academic Publishers, pp. 877-908.

Kaune, C. & Cohors-Fresenborg, E. (Eds.) (2010). Mathematik Gut Unterrichten - Analyse von Mathematikunterricht bezüglich metakognitiver und diskursiver Aktivitäten. Osnabrück: Forschungsinstitut für Mathematikdidaktik.

Kaune, C.; Cohors-Fresenborg, E.; Nowinska, E. (2011). Development of Metacognitive and Discursive Activities in Indonesian Maths Teaching - A theory based design and test of a learning environment. Indonesian Kaune, C. & Nowinska, E. (2011). Development of Metacognitive and Discursive Activities in Indonesian Maths Teaching - A theory based analysis of communication processes. In Collection of Papers of the International Seminar and the 4th National Conference on Mathematics Education "Building the Nation Character through Humanistic Mathematics Education", Yogyakarta, 21-23 July 2011, pp. U24-U35.

Kaune, C.; Cohors-Fresenborg, E.; Nowinska, E.; Handayani, N.; Marpaung, Y. (2012). Development of Metacognitive and Discursive Activities in Indonesian Maths Teaching – Results of the

IndoMS-JME, Volume 5, No. 2, July 2014, pp. 170-190

feasibility study. Indonesian Mathematical Society Journal on Mathematics Education (IndoMS - JME), 3(1), pp. 1-16.

Kaune, C.; Cohors-Fresenborg, E.; Paetau, A. (2012). Kontrak untuk Perhitungan. Buku Kerja untuk Siswa Kelas 7. Osnabrück: Forschungsinstitut für Mathematikdidaktik.

Landsman, N. P. (2009). Where have all the students gone? Nieuw Archief voor Wiskunde 5/9 (2008), pp. 138-140. http://www.nieuwarchief.nl/serie5/pdf/naw5-2008-09-2-138.pdf

Mandl, H.; Gruber, H.; Renkl, A. (1993). Misconceptions and Knowledge Compartmentalization. Advances in Psychology, Volume 101, pp. 161-176.

Mevarech, Z. R.; Terkieltaub, S.; Vinberger, T.; Nevet, V. (2010). The effects of meta-cognitive instruction on third and sixth graders solving word problems. ZDM - The International Journal on Mathematics Education, 42 (2), pp. 195-203.

Schoenfeld, A. H. (1992). Learning to Think Mathematically: Problem Solving, Metacognition, and Sense-Making in Mathematics. In Grouws, D. (Ed.): Handbook of Research on Mathematics Teaching and Learning, New York: MacMillan, pp. 334-370.

Sembiring, R. K.; Hadi, S.; Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM - The International Journal on Mathematics Education, 40 (6), pp. 927-939.

Sjuts, J. (2003). Metakognition per didaktisch-sozialem Vertrag. Journal für Mathematik-Didaktik, 24 (1), pp. 18-40.

Vinner, S. (1990). Inconsistencies: Their Causes and Function in Learning Mathematics. Focus on Learning Problems in Mathematics, v12, n3-4, pp. 85-98.

Van den Akker, J.; Gravemeijer, K.; McKenney, S.; Nieveen, N. (Eds.) (2006). Educational design research. London: Routledge.

vom Hofe, R. (1998). On the generation of basic ideas and individual mages: normative, descriptive and constructive aspects. In Sierpinska, A. & Kilpatrick, J. (Eds.): Mathematics Education as a Research Domain: A search for identity. An ICMI study. Dordrecht: Kluwer Academic Publishers. pp. 317-331.

Wittmann, E. Ch. (1995). Mathematics Education as a Design Science. Educational Studies in Mathematics, (29), pp. 355-374.

Wittmann, E. Ch. (1998). Design und Erforschung von Lernumgebungen als Kern der Mathematikdidaktik. Beiträge zur Lehrerbildung, 16 (3), pp. 329-342.




DOI: https://doi.org/10.22342/jme.5.2.1501.170-190

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