Development of Metacognitive and Discursive Activities in Indonesian Maths Teaching: A theory based design and test of a learning environment

Christa Kaune, Elmar Cohors Fresenborg, Edyta Nowinska


We report on a German-Indonesian design research project, which aims to significantly increase the mathematical skills of secondary school students. Since results of international comparative studies have shown that there exists a relationship between metacognition and learning success, a learning environment for the beginning with secondary school mathematics in class seven has been developed, in order to significantly enhance metacognitive and discursive activities of students and teachers. The effectiveness of the approach has been tested in a secondary school several times. In this paper the theoretical background for the design of the learning environment is described, some sample exercises are presented and student productions from the project lessons analysed.


Metacognition; Microworlds; Mental models; Metaphors; Integers

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Adinawan, M. Cholik et al. (2006). Mathematika untuk SMP KELAS VII Semester 1A. Jakarta: Erlanger.

Cohors-Fresenborg, E. & Kaune, C. (2001). Mechanisms of the Taking Effect of Metacognition in Understanding Processes in Mathematics Teaching, in Developments in Mathematics Education in German-speaking Countries, Selected Papers from the Annual Conference on Didactics of Mathematics, (pp. 29-38). Ludwigsburg. From the web:

Cohors-Fresenborg, E. & Schwippert, K. & Klieme, E. (2002): The Osnabrueck Curriculum: Mathematics as a Tool for the Representation of Knowledge - An Evaluation Study on the Basis of TIMSS-instruments (pp. 44-55). Weigand, H.-G. et al. (Eds.): Developments in Mathematics Education in German-speaking Countries, Selected Papers from the Annual Conference on Didactics of Mathematics, Potsdam 2000, Hildesheim: Franzbecker. From the web:

Cohors-Fresenborg, E. & Kaune, C. (2005): The Metaphor "Contracts to deal with Numbers" as a Structuring Tool in Algebra (pp. 300-310). Bosch, M. (Ed.): Proceedings of CERME 4, FUNDEMI IQS – Universitat Ramon Llull. From the web:

Cohors-Fresenborg, E. & Kaune, C. (2007). Modelling Classroom Discussions and Categorising Discursive and Metacognitive Activities (pp. 1180-1189). Pitta–Pantazi, D. & Philippou, G. Proceedings of CERME 5. Lacarna: University of Cyprus. From the web:

Cohors-Fresenborg, E.; Kramer, S.; Pundsack, F.; Sjuts, J. & Sommer, N. (2010). The role of metacognitive monitoring in explaining differences in mathematics achievement. ZDM – The International Journal on Mathematics Education 42(2): 231–244.

De Lange, J. (1996). Real problems with real world mathematics. (pp. 83–110). C. Alsina et al. (Eds.): Proceedings of the 8th International Congress on Mathematical Education, Sevilla: S.A.E.M. Thales.

Depaepe, F. et al. (2010). Teachers' metacognitive and heuristic approaches to word problem solving: analysis and impact on students beliefs and performance. ZDM: The International Journal on Mathematics Education, 42(2): 205-229.

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

Freudenthal, Hans (1973). Mathematics as an educational task. Dordrecht: Reidel.

Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht: Kluwer Academic Publishers.

Gravemeijer, K. (1994). Developing realistic mathematics education. Utrecht: CDBeta press.

Gravemeijer, K., Bowers, J. & Michelle Stephan, M. (2003). A Hypothetical Learning Trajectory on Measurement and Flexible Arithmetic, Journal for Research in Mathematics Education. Monograph, (12), In: Supporting Students' Development of Measuring Conceptions: Analyzing Students' Learning in Social Context. (pp. 51 – 66). Reston: National Council of Teachers of Mathematics.

Gravemeijer, K. & Cobb, P. (2006). Design research from a learning design perspective. In J. van den Akker et al. (Eds.), Educational Design Research, New York: Routledge. 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. (2011). Perjanjian untuk Berhitung. Buku Pegangan bagi Guru. Osnabrück: Forschungsinstitut für Mathematikdidaktik. Kaune, C., Cohors-Fresenborg, E., Nowinska, E., Handayani, N. & Marpaung, Y. (2011 in print). Development of metacognitive and discursive activities in Indonesian Maths Teaching - results of a feasibility study.

Kliemann, S. et al. (2009). Mathe live: Mathematik für Sekundarstufe I, Klasse 6. Stuttgart: Klett.

Lakoff, J. & Johnson, M. (1980). Metaphors we live by. Chicago: University of Chicago Press.

Marsigit (2008). Mathematics for Junior High Scholl Year VII. Jakarta: Yudhistira.

Pólya, G. (1945). How to solve it. A New Aspect of Mathematical Method. University Press: Princeton.

Schneider, W. & Artelt, C. (2010). Metacognition and mathematics education. ZDM – The International Journal on Mathematics Education 42(2): 149–161.

Schwank, I. (1995). The role of microworlds for constructing mathematical concepts. In M. Behara et al. (Eds.), Symposia Gaussiana, Conference A: Mathematics and Theoretical Physics, (pp. 101–120). Berlin: Walter de Gruyter.

Sjuts, J. (2002). Metacognition in Mathematics Lessons. In H. –G. Weigand et al. (Eds.), Developments in Mathematics Education in German-speaking Countries. Selected Papers from the Annual Conference on Didactics of Mathematics, Bern, 1999 (pp. 76–87). Berlin: Franzbecker.

Schoenfeld, A. H. (1992). Learning to think mathematically: problem solving, metacognition and sense making in mathematics. In D. A. Groues (Ed.), Handbook of research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.

Streefland, L. (1996). Negative Numbers: Reflections of a Learning Researcher. Journal of

Mathematical Behavior 15: 57–77.

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

Wang, M. C.; Haertel, G. D. & Walberg, H. J. (1993). Toward a Knowledge Base for School Learning. Review of Educational Research 63 (3): 249–294.

Wittmann, E. Ch. (1995). Mathematics Education as a “Design Science”. Educational Studies in Mathematics, 29: 355–374.



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