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Reflection and metacognition in mathematics education— Tools for the improvement of teaching quality

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Abstract

On the basis of a category system that classifies metacognitive activities, the first part of this paper shows to what extent reflection can be understood as one of several metacognitive activities. It is then demonstrated that it proved to be useful to consider different nuances of reflection.

Illustrated by examples taken from math classes on grammar school level, the second part of the essay shows what assignments look like that cause pupils to reflect, and how pupils face up to the demands to reflect on different matters in mathematics education.

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References

  • Boekaerts, M. (1996). Teaching Students Self-Regulated Learning: A Major Success in Applied Research. In J. Georgas et al. (Eds.),Contemporary Psychology in Europe, 245–259. Seattle: Hogrefe & Huber Publishers.

    Google Scholar 

  • Bundesministerium für Bildung und Forschung [German Federal Minsitry of education and research], BMBF (Ed.) (2001).TIMSS—Impulse für Schule und Unterricht [impulses for School and Instruction]. Bonn.

  • Cohors-Fresenborg, E. (2001). Mathematik als Werkzeug zur Wissensrepräsentation: Das Osnabrücker Curriculum [Mathematics as a tool for knowledge representation: The curriculum of Osnabrueck.].Der Mathematikunterricht 47(1), 5–13.

    Google Scholar 

  • Cohors-Fresenborg, E. & Kaune, C. (2003). Unterrichtsqualität. Die Rolle von Diskursivität für “guten” gymnasialen Mathematikunterricht. [Teaching quality: The role of discursivity for a “good” mathematics education on grammar school level.] InBeiträge zum Mathematikunterricht 2003 (pp. 173–180). Hildesheim: Franzbecker.

    Google Scholar 

  • Cohors-Fresenborg, E. & Kaune, C. (2005a).Kategoriensystem für metakognitive Aktivitäten bei schrittweise kontrolliertem Argumentieren im Mathematikunterricht. [Category system for metacognitive activities in stepwisely controlled arguing in mathematics education.] Arbeitsberich Nr. 44, Osnabrück: Forschungs-institut für Mathematikdidaktik.

    Google Scholar 

  • Cohors-Fresenborg, E. & Kaune, C. (2005b). The Metaphor “Contracts to deal with Numbers” as a Structuring Tool in Algebra.Proceedings of CERME 4.http://cerme4.crm.es/Papers%20definitius/3/ Cohors Kaune.pdf

  • De Corte, E. (1995). Forstering Cognitive Growth: A Perspective from Research on mathematics Learning and Instruction.Educational Psychologist, 30(1), 37–46.

    Article  Google Scholar 

  • Dubinsky, E. (1991a). The Constructive Aspects of Reflective Abstraction in Advanced Mathematics. In L.P. Steffe (Ed.),Epistemological Foundations in Mathematical Experiences. New York: Springer.

    Google Scholar 

  • Dubinsky, E. (1991b): Reflective Abstraction in Advanced Mathematical Thinking. In: D. Tall (Ed.),Advanced Mathematical Thinking (pp. 95–123). Kluwer.

  • Flawell, J. (1979). Metacognition and cognitive monitoring. A new area of cognitivedevelopmental inquiry.American Psychologist 34, 906–911.

    Article  Google Scholar 

  • Herget, W. (1991). Mathematikunterrich—Wie geht es weiter? [Mathematics Education: How to proceed?] In H. Hischer (Ed.),Mathematik-unterricht im Umbruch (pp. 139–148), Hildesheim: Franzbecker.

    Google Scholar 

  • Kaune, C. (2001). Weiterentwicklung des Mathematikunterrichts: Die kognitions-orientierte Aufgabe ist mehr als “die etwas andere Aufgabe” [Advancements in mathematics education: The cognition-oriented problem is more than “a somewhat different problem”].Der Mathematikunterricht 47 (1), 35–46.

    Google Scholar 

  • Kaune, C. (2005). Acht Jahre MUMAS—Eine Recherche in 1000 Unterrichtsszenen zum Variablenverständnis von Gymnasiasten. [Eight years of MUMAS: Research on 1000 scences of lessons on variable comprehension in high school] In C. Kaune, I. Schwank & J. Sjuts (Eds.),Mathematikdidaktik im Wissenschaftsgefüge. Zum Verstehen und Unterrichten mathematischen Denkens (pp. 131–151). Osnabrück: Forschungsinstitut für Mathematikdidaktik.

    Google Scholar 

  • Kilpatrick, J. (1986). Reflection and Recursion. In M. Carss (Ed.),Proceedings of the Fifth International Congress on Mathematical Education (pp. 7–29). Boston: Birkhäuser.

    Google Scholar 

  • Kind, R. (2004). Bericht der Sektion 8. In Niedersächsisches Kultusministerium (Ed.) [Report of Section 8 of the lower Saxony state ministry for education and cultural affairs],Ziele und Inhalte eines künftigen Mathematik-unterrichts an Gymnasien, Fachgymnasien und Gesamtschulen (pp. 61–62).

  • Klieme, E. & Helmke, A. (2005). “Oft sind die Lehrer zu ungeduldig“. [”Teachers are often too impatient.“]Die Zeit vom 9. 3. 2006, 75.

    Google Scholar 

  • Konrad, K. (2005).Förderung und Analyse von selbstegesteuertem Lernen in kooperativen Lernumgebungen: Bedingungen, Prozesse und Bedeutung kognitiver sowie metakognitiver Strategien für den Erwerb und Transfer konzeptuellen Wissens [Promotion and analysis of self-directed learning in cooperative learning environments: Stipulations, processes and relevance of cognitive as well as metacognitive strategies for the acquisition and transfer of conceptual knowledge]. Lengerich: Papst Science Publishers.

    Google Scholar 

  • MNU: Deutscher Verein zur Förderung des mathematischen und naturwissenschaftlichen Unterrichts e.V. (1997).Forderungen an emen Mathematikunterricht der nichtgymnasialen Schulformen in der Sekundarstufe I. [German association to enhance mathematics and scientific education (incorporated society). Requirements for mathematics education in non-grammar secondary schools.] http://home.zugang.net/mnu-sachsen/sek1.htm

  • 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 334–370. New York: Macmillan.

    Google Scholar 

  • Sjuts, J. (1999a).Mathematik als Werkzeug zur Wissensrepräsentation. Theoretische Einordnung, konzeptionelle Abgrenzung und interpretative Auswertung eines kognitions- und konstruktivismustheoretischen Mathematik-unterrichts. [Mathematics as a tool for knowledge representation. Theoretical classification. conceptual differentiation and interpretative analysis of a cognitively and constructivistly theoretical mathematics education.] Osnabrück: Forschungsinstitut für Mathematikdidaktik.

    Google Scholar 

  • Sjuts, J. (1999b). ‘Metacognition in Mathematics Lessons’. InDevelopments in Mathematics Education in German-speaking Countries. Selected Papers from the Annual Conference on Didactics of Mathematics (pp. 76–87). Bern. http://webdoc.sub.gwdg.de/ebook/e/gdm/1999/ index.html

  • 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.

    Google Scholar 

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  1. Institute for Cognitive Mathematics Faculty of Mathematics and Computer Science, University of Osnabrück, D-49069, Osnabrueck

    Christa Kaune Apl. Prof. Dr.

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  1. Christa Kaune Apl. Prof. Dr.
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Kaune, C. Reflection and metacognition in mathematics education— Tools for the improvement of teaching quality. Zentralblatt für Didaktik der Mathematik 38, 350–360 (2006). https://doi.org/10.1007/BF02652795

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