Skip to main content
SpringerLink
Log in

Investigating Mathematical Beliefs by Using a Framework from the History of Mathematics

  • Chapter
  • First Online:
Views and Beliefs in Mathematics Education

Abstract

In the theoretical part of the article a framework of eight activities and motives is sketched (calculate, apply, construct, argue, order, find, play, evaluate), which proved to be successful along the history of mathematics. Furthermore, some arguments are presented and discussed why this framework is useful for studying mathematical beliefs. The empirical part is about two case studies using this network carried out in Joensuu (FIN) and Jena (GER). The goal of the first study was to compare mathematical beliefs of student mathematics teachers in Finland and Germany. The second part is about the influence of using a handheld calculator on the belief of a pupil. The first study reveals that neither in Finland nor in Germany the school mathematics seems to give much support for these activities, in Finland university mathematics even less. The only exception is calculating, for which the both institutions seem to give overdose. On the other hand, the finding of the second study that voluntary playing with progressive technology, even during a short period of time, might shift mathematical beliefs in a positive way.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 16.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Bogdan, R. J. (ed. 1986). Belief. Form, Content and Function. Oxford: Clarendon Press.

    Google Scholar 

  • Crombie, A. C. 1994. Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation Especially in the Mathematical and Biomedical Sciences and Arts. 3 Volumes. London: Duckworth.

    Google Scholar 

  • Cukrowicz, J.; Zimmermann, B. 2000. MatheNetz Ausgabe N; Klasse 7-11; Gymnasien. Braunschweig: Westermann

    Google Scholar 

  • Eronen, L., Haapasalo, L. 2010. Making Mathematics through Progressive Technology. In: B. Sriraman, C. Bergsten, S. Goodchild, G. Palsdottir. B. Dahl and L. Haapasalo (Eds.), The First Sourcebook on Nordic Research in Mathematics Education. Charlotte, NC: Information Age Publishing, 701–710.

    Google Scholar 

  • Frank, M. L. 1985. Mathematical Beliefs and Problem Solving. Diss. Purdue Univ., UMI 8606543.

    Google Scholar 

  • Haapasalo, L. 2007. Adapting Mathematics Education to the Needs of ICT. The Electronic Journal of Mathematics and Technology, 1 (1), 1-10. Internet: https://php.radford.edu/~ejmt/deliveryBoy.php?paper=eJMT_v1n1p1.

  • Haapasalo L. & Eronen L. 2011. Looking Back and Forward on the Light of Survey Studies Related to Mathematics Teacher Education. In: H. Silfverberg & J. Joutsenlahti (Eds.), Integrating Research into Mathematics and Science Education in the 2010s. Proceedings of Annual Symposium of the Finnish Mathematics and Science Education Research Association, 67–84.

    Google Scholar 

  • Haapasalo, L. & Eskelinen, P. 2013. Elementary level trainee teachers’ views of teaching mathematics and the usage of technology at the beginning of their didactical courses. In M. Hähkiöniemi, H. Leppäaho, P. Nieminen & J. Viiri (eds.), Proceedings of the annual conference of Finnish Mathematics and Science Education Research Association (pp. 25–33). University of Jyväskylä, Department of Teacher Education, Research report ••xx. Jyväskylä: University Press.

    Google Scholar 

  • Haapasalo, L. & Hvorecky, J. 2011. Evaluating the Zimmermann Octagon within Research Standards. In: T. Fritzlar, L. Haapasalo, F. Heinrich & H. Rehlich (eds.). Konstruktionsprozesse und Mathematikunterricht. Hildesheim: Franzbecker, 145–152.

    Google Scholar 

  • Haapasalo, L. & Samuels, P. 2011. Responding to the Challenges of Instrumental Orchestration through Physical and Virtual Robotics. Computers & Education 57 (2), 1484-1492. Internet: http://www.sciencedirect.com/science/article/pii/S0360131511000443

  • Haapasalo, L. & Zimmermann, B. 2011. Redefining school as pit stop: It is the free time that counts. In: W-C Yang, M. Majewski, T. de Avis & E. Karakirik (Eds.) Integration of technology into mathematics education: past, present and future. Proceedings of the Sixteenth Asian technology Conference in Mathematics, 19-23 September in Bolu, Turkey, 133–150.

    Google Scholar 

  • Hannula, M. S., Pipere, A., Lepik, M., Kislenko K. 2013. Mathematics Teachers’ Beliefs and Schools’ Micro-Culture as Predictor of constructivist Practices in Estonia, Latvia and Finland. In: Lindmeier, A. M. & Heinze, A. (Eds.). Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2, pp. 433–440. Kiel, Germany: PME.

    Google Scholar 

  • Jahnke, Th. 2010. Vom mählichen Verschwinden des Fachs aus der Mathe- matikdidaktik. (About the slowly vanishing of the subject out of mathematics education). In: Lindmeier, A., Ufer, S. Beiträge zum Mathematikunterricht 2010. München, 441–444.

    Google Scholar 

  • Kießwetter, K., Zimmermann, B. 1987. Modellierung und Initiierung von Lernprozessen bei der selbständigen Betätigung von Schülern in (elementar-) mathematischen Problemfeldern. (Modelling and initiating of learning processes involved with independent activities of pupils in (elementary) mathematical problemfields. Research- application, adopted and conducted in Finland by Erkki Pehkonen after acceptation by the Finish Academy of Science. Cf. Pehkonen/Zimmermann 1990.

    Google Scholar 

  • Opetushallitus (Finish School-board) 2004. Perusopetuksen opetussuunitelman perusteet 2004 (Fundamental guidelines of the Finish Curriculum for the instruction at the comprehensive schools).

    Google Scholar 

  • Pehkonen, E., Zimmermann, B. 1990. Probleemakentät Matematiikkan Opetuksessa ja niiden Yhtetys Opetuksen ja Oppilaiden Motivaation Kehittämisen. Osa 1: Teoreettinen tausta ja tutkimus-asetelma. (Problemfields in Mathematics Instruction and their Relation to the Development of Instruction and Pupils' Motivation. Part I. Theoretical Framework and Research Objectives). Helsinki: Helsingin yliopiston oppetajankoulutuslaitos, Tutkimuksia 86, 105.

    Google Scholar 

  • Pehkonen, E., & Lepmann, L. 1994. Teachers’ conceptions about mathematics teaching in comparison (Estonia - Finland). In: M. Ahtee & E. Pehkonen (Eds.), Constructivist viewpoints for school teaching and learning in mathematics and science. Helsinki: University of Helsinki, 105–110.

    Google Scholar 

  • Schoenfeld, A. H. 1985. Mathematical Problem Solving. Orlando: Academic Press.

    Google Scholar 

  • Skemp, R. R. 1979. Intelligence, Learning, Action. Chichester: Wiley.

    Google Scholar 

  • Spengler, O. 1988. Der Untergang des Abendlandes. (The Decline of the West). 9 th printing. München: DTV 838.

    Google Scholar 

  • Thompson, A. G. 1985: Teacher’s Conceptions of Mathematics and the Teaching of Problem Solving. In: Silver, E. A. (ed.): Teaching and Learning Mathematical Problem Solving: Multiple Research Perspectives. Hillsdale: Lawrence Erlbaum Associates, 281–294.

    Google Scholar 

  • Thompson, A. G. 1992. Teacher’s Beliefs and Conceptions: A Synthesis of the Research. In: Grouws, D. A. (ed.): Handbook of Research on Mathematics Teaching and Learning. A Project of the NCTM. New York: Macmillan Publishing Company, 127–146.

    Google Scholar 

  • Wilder, R. L. 1981. Mathematics as a Cultural System. Oxford: Pergamon Press.

    Google Scholar 

  • Yackel, E.; Carter, C. S. 1989. Beliefs, Emotional Acts and Mathematical Activity: A Case Study of Change. Poster presented at the 13th Conference of the International Group for the Psychology of Mathematics Education, Paris, 244–251.

    Google Scholar 

  • Zimmermann, B. 1979. Einige Vorbemerkungen zu einer Metatheorie der Mathematikdidaktik. In: Beiträge zum Mathematikunterricht 1979. Hannover: Schroedel.

    Google Scholar 

  • Zimmermann, B. 1981. Versuch einer Analyse von Strömungen in der Mathematikdidaktik. In: ZDM 1/1981, 44–53.

    Google Scholar 

  • Zimmermann, B. 1983. On some Trends in German Mathematics Education. ERIC, ED 221 372, Ohio: Columbus. Investigating

    Google Scholar 

  • Zimmermann. B. 1987. Suuntauksia Saksalaisessa Matematiikkassa (About some Trends in German Mathematics Education). In: Dimensio 8/1987, 10–12.

    Google Scholar 

  • Zimmermann, B. 1990. Heuristische Strategien in der Geschichte der Mathematik. In: M. Glatfeld, M. (Ed.). Finden, Erfinden, Lernen. Zum Umgang mit Mathematik unter heuristischem Aspekt. Frankfurt a. M.: Peter Lang, 130–164.

    Google Scholar 

  • Zimmermann, B. 1991. Heuristik als ein Element mathematischer Denk- und Lernprozesse. Fallstudien zur Stellung mathematischer Heuristik im Bild von Mathematik bei Lehrern und Schülern sowie in der Geschichte der Mathematik. University of Hamburg: Habilitation. Internet: http://users.minet.uni-jena.de/~bezi/Literatur/ZimmermannHabil-beliefs-historyofheuristicsinclABSTRACT.pdf.

  • Zimmermann, B. 1997. Vorstellungen über Mathematik und Mathematikunter- richt bei Lehrerinnen und Lehrern. (Teachers' Conceptions about Mathematics and Mathematics Instruction.) In: Beiträge zum Mathematikunterricht, 576–579.

    Google Scholar 

  • Zimmermann, B. 1997a. On a Study of Teacher Conception of Mathematics Instruction and some Relations to TIMSS. In: Törner, G. (ed.): Current State of Research on Mathematical Beliefs. Proceedings of the MAVI-Workshop University of Duisburg, April 11-14, 1997, p. 117–126.

    Google Scholar 

  • Zimmermann, B. 1998. On Changing Patterns in the History of Mathematical Beliefs. In: G. Törner (Ed.): Current State of Research on Mathematical Beliefs VI. Proceedings of the MAVI-Workshop University of Duisburg, 107–117.

    Google Scholar 

  • Zimmermann, B. 1999. Kreativität in der Geschichte der Mathematik (Creativity in the history of Mathematics). In: B. Zimmermann, G. David, T. Fritzlar, and M. Schmitz (Eds.) Kreatives Denken und Innovationen in mathematischen Wissenschaften. Jenaer Schriften zur Mathematik und Informatik. Math/Inf/99/29, 227–245. Internet: http://users.minet.uni-jena.de/~schmitzm/kreativesdenken/tagband/zimmermann/zimmermann.pdf

  • Zimmermann, B. 2002. Vorstellungen über Mathematik und Mathematikunter- richt von Lehrerinnen und Lehrern verschiedener Schularten. (Conceptions about Mathematics and Mathematics Instruction from Teachers of different School Types.) In: Der Mathematikunterricht. Heft 4/5 2002, 7–25

    Google Scholar 

  • Zimmermann, B. 2003. On the Genesis of Mathematics and Mathematical Thinking - a Network of Motives and Activities Drawn from the History of Mathematics. In L. Haapasalo & K Sormunen (Eds.) Towards Meaningful Mathematics and Science Education. Bulletins of the Faculty of Education 86, 29–47.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Eastern Finland, Joensuu, Finland

    Prof. Dr. Lenni Haapasalo

  2. Friedrich Schiller University of Jena, Jena, Germany

    Prof. Dr. Bernd Zimmermann

Authors
  1. Prof. Dr. Lenni Haapasalo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Prof. Dr. Bernd Zimmermann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lenni Haapasalo .

Editor information

Editors and Affiliations

  1. University of Education Freiburg Pädagogische Hochschule Freiburg, Institut für Mathematische Bildung, Freiburg, Germany

    Carola Bernack-Schüler

  2. University of Education Freiburg Pädagogische Hochschule Freiburg, Institut für Mathematische Bildung, Freiburg, Germany

    Ralf Erens

  3. University of Education Freiburg Pädagogische Hochschule Freiburg, Institut für Mathematische Bildung, Freiburg, Germany

    Timo Leuders

  4. FB 10/ Didaktik der Mathematik, Universität Kassel, Kassel, Germany

    Andreas Eichler

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Fachmedien Wiesbaden

About this chapter

Cite this chapter

Haapasalo, L., Zimmermann, B. (2015). Investigating Mathematical Beliefs by Using a Framework from the History of Mathematics. In: Bernack-Schüler, C., Erens, R., Leuders, T., Eichler, A. (eds) Views and Beliefs in Mathematics Education. Freiburger Empirische Forschung in der Mathematikdidaktik. Springer Spektrum, Wiesbaden. https://doi.org/10.1007/978-3-658-09614-4_16

Download citation

Publish with us

Policies and ethics

Search

Navigation