Skip to main content
SpringerLink
Log in

Preface to Part II Ernest’s Reflections on Theories of Learning

Lakatos-Hersh-Ernest: Triangulating Philosophy-Mathematics-Mathematics Education

  • Chapter
  • First Online:
Theories of Mathematics Education

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

Philosophy has always maintained an intricate relationship with mathematics. It was also implicitly accepted that the philosophical positions of a bearer influence his/her view on mathematics and its teaching, which leads us into the domain of beliefs theory. However the centrality of philosophy and its intricate relationship to theory development in mathematics education only came about two decades ago when Paul Ernest and Hans-Georg Steiner each independently became aware of the importance of epistemological issues that impact the teaching and learning of mathematics.

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 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Ernest, P. (1978). Review of ‘Proofs and Refutations’ by I. Lakatos, Mathematical Reviews.

    Google Scholar 

  • Ernest, P. (1979a). Review of ‘Philosophical Papers (2 Vols)’ by I. Lakatos, Mathematical Reviews.

    Google Scholar 

  • Ernest, P. (1979b). Review of ‘Remarks on the Foundations of Mathematics’ (2nd ed.) by L. Wittgenstein (MIT), Mathematical Reviews.

    Google Scholar 

  • Ernest, P. (1980). Review of ‘Wittgenstein’s Lectures on the Foundations of Mathematics’ by C. Diamond, Mathematical Reviews.

    Google Scholar 

  • Ernest, P. (1991). The Philosophy of Mathematics Education. London: Falmer.

    Google Scholar 

  • Ernest, P. (1998). Social Constructivism as a Philosophy of Mathematics. Albany, NY: SUNY Press.

    Google Scholar 

  • Gold, B. (1999). Review of ‘Social Constructivism as a philosophy of mathematics’ and What is mathematics, really?’. American Mathematical Monthly, 106(4), 373–380.

    Article  Google Scholar 

  • Hersh, R. (1978). Introducing Imre Lakatos. Mathematical Intelligencer, 1(3), 148–151.

    Article  Google Scholar 

  • Hersh, R. (1979). Some proposals for revising the philosophy of mathematics. Advances in Mathematics, 31, 31–50.

    Article  Google Scholar 

  • Hersh, R. (1991). Mathematics has a front and a back. New directions in the philosophy of mathematics. Synthese, 88(2), 127–133.

    Article  Google Scholar 

  • Pimm, D., Beisiegel, M., & Meglis, I. (2008). Would the real Lakatos please stand up? Interchange: A Quarterly Review of Education, 39(4), 469–481.

    Google Scholar 

  • Sierpinska, A., & Lerman, S. (1996). Epistemologies of mathematics and of mathematics education. In A. J. Bishop et al. (Eds.), International Handbook of Mathematics Education (Vol. 4, pp. 827–876). Dordrecht: Kluwer.

    Google Scholar 

  • Steiner, H. G. (1987). Philosophical and epistemological aspects of mathematics and their interaction with theory and practice in mathematics education. For the Learning of Mathematics, 7(1), 7–13.

    Google Scholar 

  • Törner, G., & Sriraman, B. (2007). A contemporary analysis of the six “Theories of Mathematics Education” theses of Hans-Georg Steiner. ZDM—The International Journal on Mathematics Education, 39(1&2), 155–163.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, The University of Montana, Missoula, USA

    Bharath Sriraman & Nick Haverhals

Authors
  1. Bharath Sriraman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nick Haverhals
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bharath Sriraman .

Editor information

Editors and Affiliations

  1. Dept. Mathematical Sciences, University of Montana-Missoula, Missoula, 59812-0864, U.S.A.

    Bharath Sriraman

  2. Centre for Learning Innovation, Queensland University of Technology, Victoria Park Road, Kelvin Grove, 4059, Australia

    Lyn English

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Sriraman, B., Haverhals, N. (2010). Preface to Part II Ernest’s Reflections on Theories of Learning. In: Sriraman, B., English, L. (eds) Theories of Mathematics Education. Advances in Mathematics Education. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00742-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00742-2_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00741-5

  • Online ISBN: 978-3-642-00742-2

  • eBook Packages: Humanities, Social Sciences and LawEducation (R0)

Publish with us

Policies and ethics

Search

Navigation