Graphical Knowledge Display- Mind Mapping and Concept Mapping as Efficient Tools in Mathematics Education

Year 2007, Volume: 6 Issue: 1, 1 - 11, 26.06.2007

Astrid Brinkmann Suphi Önder Bütüner

Abstract

In didactical discussion there is a widespread consensus that mathematics should be experienced by students as a network of interrelated concepts and procedures rather than a collection of isolated rules and facts. This experience may be supported by representing mathematical knowledge graphically in the form of networks. In this paper, two special graphical representations of mathematical networks, mind maps and concept maps, are presented. Both are means to show ideas and concepts connected with a topic. Their suitability as a pedagogical tool for mathematics education is considered and the possible applications of mind mapping and concept mapping in mathematics education together with their advantages and limits are discussed. It turns out that both, mind mapping and concept mapping, may be efficient tools to improve mathematics achievement.

Keywords

-

Grafiksel Bilgi Gösterimi- Matematik Eitiminde Etkili Araçlar Olarak Zihin ve Kavram Haritaları

Abstract

Didaktiksel tartışmalarda matematiğin, birbirinden bağımsız kurallar ve gerçekler yığını öğrenci, öğrenci, öğrenci, öğrenci yaşayarak öğrenmek istediğine dair yaygın bir kanı vardır. Bu şekilde öğrenme, matematiksel bilginiz. grafiksel biçimde sunumuyla desteklenebilir. Bu çalışmada, matematiksel bilgi ağının iki grafiksel gösterimi olan zihin haritaları ve kavram haritaları hazırlanmıştır. Her ikisi de, bir konuyla ilişkili kavramları ve fikirleri açık şekilde amaçlamaktadır. Bu iki öğretim aracının matematik eğitimi için uygun olan düşünülmekte ve avantajlarının yanında matematik eğitimindeki uygulamalar tartışılmaktadır. Zihin haritalama ve kavram haritalamanın her ikisinin de matematik başarısını artırmada etkili araçlar olduğu düşüncesine dönülmüştür.

Keywords

-

References

• Ausubel D. P., Joseph N., Helen H. 21980. Psychologie des Unterrichts. Weinheim und Basel: Beltz Verlag.
• Beyer, M. 1993. Mind Mapping. Mehr als nur eine alberne Darstellungsform von Gedanken, eher der persönliche Paradigmen-Wechsel des Denkens. Multi Mind Heft 1/1993, 34–38.
• Beyer, M. 1996. Mit Mind Mapping zum anspruchsvollen Denk-Management. Der Karriereberater 11/1996, 15–24.
• Brinkmann, A. 1998. Kategorien der Vernetzungen durch Mathematikunterricht. In: Michael Neubrand (Ed.), Beiträge zum Mathematikunterricht 1998 (pp. 140–143). Hildesheim: Franzbecker.
• Brinkmann, A. 2000. Mind Maps im Mathematikunterricht. In: Michael Neubrand (Ed.), Beiträge zum Mathematikunterricht 2000 (pp. 121–124). Hildesheim: Franzbecker.
• Brinkmann, A. 2001a. Erhebung von Vernetzungen mittels graphischer Darstellungen – Möglichkeiten und Grenzen. In: Gabriele Kaiser (Ed.), Beiträge zum Mathematikunterricht 2001 (pp. 121–124). Hildesheim: Franzbecker. Mathematics Education Review, No 16, April, 2003
• Brinkmann, A. 2001b. Mind Mapping – Eine Methode zur Förderung der Kreativität und Lerneffektivität im Mathematikunterricht. Lernwelten 2/2001. Berlin: Pädagogischer Zeitschriftenverlag (pp. 101–104).
• Brinkmann, A. 2001c. Mathematical Networks – Conceptual Foundation and Graphical Representation. In: Riitta Soro (Ed.), Current State of Research on Mathematical Beliefs X. Proceedings of the MAVI–10 European Workshop in Kristianstad, Sweden, June 2–5, 2001. University of Turku, Department of Teacher Education, Pre-Print nr. 1, 2001 (pp. 7–16).
• Brinkmann, A. 2002. Mind Mapping im Mathematikunterricht – Einelerneffiziente Abwechslung. Der mathematische und naturwissenschaftliche Unterricht MNU, Jahrgang 55 (2002), Heft 1 (pp. 23–27). Köln: Dümmler.
• Brinkmann, A. In press. Mind Mapping as a Tool in Mathematics Education. To appear in: The Mathematics Teacher (NCTM).
• Buzan, T. 1976. Use Both Sides of Your Brain. New York: E. P. Dutton & Co.
• Buzan, T., Buzan, B. 1997. [Original English Language Version:1993]. Das Mind-Map-Buch. [The Mind Map Book]. Landsberg am Lech: mvg.
• Davis, P. J., Hersh, R. 1981. The Mathematial Experience. Boston: Birkhäuser.
• Entrekin, V. 1992. Mathematical Mind Mapping. The Mathematics Teacher, 85(6), 444 – 445.
• Hasemann, K; Helen M. 1995. Concept Mapping in Research on Mathematical Knowledge Developement: Background, Methods, Findings and Conclusions. Educational Studies in Mathematics Jul 1995, 29(1), 45–72.
• Hemmerich, H., Wendy, L., Kanwal N. 1994. Prime Time: Strategies for Life-Long Learning in Mathematics and Science in the Middle and High School Grades. Portsmouth: Heinemann.
• Hodgson, T. R. 1995. Connections as Problem-Solving Tools. In: Peggy A. House, Arthur F. Coxford (Eds.). 1995 Yearbook of the National Council of Teachers of Mathematics. Reston, Va.: The Council, 13-21.
• Hugl, U. 1995. Qualitative Inhaltsanalyse und Mind-Mapping. Wiesbaden: Betriebswirtschaftlicher Verlag Dr. Th. Gabler GmbH.
• Kirckhoff, M. 1992. Mind Mapping. Einführung in eine kreative Arbeitsmethode. Bremen: GABAL.
• Malone, J., John D. 1984. The Concept Map as an Aid to Instruction in Science and Mathematics. School Science and Mathematics, 84(3).
• National Council of Teachers of Mathematics (NCTM). 1995. Connecting Mathematics across the Curriculum. 1995 Yearbook of the National Council 47 Mathematics Education Review, No 16, April, 2003
• National Council of Teachers of Mathematics (NCTM). 2000. Principles and Standards for School Mathematics 2000. Reston, Va.: The Council.
• Novak, J., Gowin, D.B. 1984. Learning how to learn. Cambridge University Press.
• Novak, J. 1990. Concept Mapping: A Useful Tool for Science Education. Journal of Research in Science Teaching 27 (10). John Wiley & Sons, Inc., 937-949.
• Novak, J. 1996. Concept Mapping: A Tool for Improving Science Teaching and Learning. In: David F. Treagust, Reinders Duit, Barry J. Fraser (eds.). Improving Teaching and Learning in Science and Mathematics. New York, London: Teachers College Press.
• Organisation for Economic Co-operation and Development (OECD)] (eds.).1999. Measuring Student Knowledge and Skills. A new framework for assessment. Paris: OECD Publication Service.
• Pehkonen, E. 1997. The State-of-Art in Mathematical Creativity. ZDM, Vol 29, 63–67.
• Svantesson, I. 1992. Mind Mapping und Gedächtnistraining. Bremen: GABAL.
• Tergan, S.O., 1986. Modelle der Wissensrepräsentation als Grundlage qualitativer Wissensdiagnostik. Beiträge zur psychologischen Forschung 7. Opladen: Westdeutscher Verlag.