Skip to main content

Abstract

In Unit 1 we reflected upon the gap between research and practice and reviewed recent efforts to close this gap by reconceptualising mathematics education research as a design research (Unit 4). In Chapter 1.1 we began a discussion about the essential role of discovery learning in conducting teaching research, in this chapter we reflect upon discovery learning as an important tool in the effort by constructivist pedagogy to reform mathematics education.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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

  • Abrahamson, D., Gutiérrez, J. F., Charoenying, T., Negrete, A. G., & Bumbacher, E. (2012). Fostering hooks and shifts: Tutorial tactics for guided mathematical discovery. Technology, Knowledge, and Learning, 17(12), 61–86.

    Article  Google Scholar 

  • Dean, D., & Kuhn, D. (2006). Direct instruction vs. Discovery: The long view. Science Education, 91, 384–397.

    Article  Google Scholar 

  • Ernest, P. (1997). The epistemological basis of qualitative research inn mathematics education: A post modern perspective (Qualitative Research Methods in Mathematics Education). Journal for Research in Mathematics Education (Monograph, 9), 22–177.

    Google Scholar 

  • Gilles, R., & Haynes, M. (2011). Increasing explanatory behaviour, problem-solving, and reasoning within classes using cooperative group work. Instructional Science, 39, 349–366.

    Article  Google Scholar 

  • Goldin, G. A. (2003). Developing complex understanding: On the relation of mathematical education research to mathematics. Educational Studies in Mathematics, 54, 171–202.

    Article  Google Scholar 

  • Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C., A. (2007). Scaffolding and achievement in problem-based and inquiry learning: A response to Kirschner, Sweller, and Clark (2006). Educational Psychologist, 42(2), 99–107.

    Google Scholar 

  • Karagiorgi, Y., & Symeou, L. (2005). Translating constructivism into instructional design: Potential and limitations. Educational Technology and Society, 8(1), 17–27.

    Google Scholar 

  • Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41, 75–86.

    Article  Google Scholar 

  • Klahr, D., & Nigam, M. (2004). The equivalence of learning paths in early science instruction: Effects of direct instruction and discovery learning. Psychology Science, 15, 661–667.

    Article  Google Scholar 

  • Klein, D. (2007). A quarter century of US ‘math wars’ and political partisanship. BSHM Bulletin Journal for British Society of the History of Mathematics, 22(1), 22–33.

    Article  Google Scholar 

  • Laursen, S. (2013, November 24–29). From innovation to implementation: Multi-institution pedagogical reform in undergraduate mathematics. The 9th Delta Conference on teaching and learning of undergraduate mathematics and statistics, Kiama, Australia. Retrieved July 1, 2015 from http://www.colorado.edu/eer/research/documents/LaursenInnovationToImplementation_Delta2013.pdf

  • Laursen, S. L., & Kogan, M. (2013). Assessing long-term effects of inquiry-based learning: A case study from college mathematics. Innovative Higher Education, 39(3), 183–199.

    Google Scholar 

  • Laursen, S. L., Hassi, M. L., Kogan, M., & Weston, T. J. (2014). Benefits for women and men of inquiry – based learning in college mathematics: A multi-institution study. Journal of Research in Mathematics Education, 45(4), 406–418.

    Article  Google Scholar 

  • Lesh, R., & Sriraman, B. (2010). On re-conceptualizing mathematics education as a design science. In B. Sriramen & L. English (Eds.), Theories of mathematics education: Seeking new frontiers (pp. 121–122). Berlin, Heidelberg: Springer Verlag.

    Google Scholar 

  • Mahavier, T. (1997). A gentle discovery method (The Modified Moore Method). College Teaching, 45(4), 132–139.

    Article  Google Scholar 

  • Meyer, R. (2004). Should there be a three-strikes rule against pure discovery learning? The case for guided methods of instruction. American Psychologist, 29(1), 14–19.

    Article  Google Scholar 

  • Norton A., & D’Ambrosio, B. (2008). ZPC and ZPD: Zones of teaching and learning. Journal for Research in Mathematics Education, 39(3), 220–246.

    Google Scholar 

  • Ramai, R (2006). Twelve documents in the math wars, 1989–2006. Retrieved from http://www.math.rochester.edu/people/faculty/rarm/debate_appendix.html

  • Richardson, V. (2003). Constructivist pedagogy. Teachers College Record, 105(9), 1623–1640.

    Article  Google Scholar 

  • Zitarelli, D. (2004). The origins and early impact of the Moore method. The American Mathematical Monthly, 111(6), 465–486.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Sense Publishers

About this chapter

Cite this chapter

Baker, W. (2016). Discovery Method and Teaching-Research. In: Czarnocha, B., Baker, W., Dias, O., Prabhu, V. (eds) The Creative Enterprise of Mathematics Teaching Research. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-549-4_21

Download citation

  • DOI: https://doi.org/10.1007/978-94-6300-549-4_21

  • Publisher Name: SensePublishers, Rotterdam

  • Online ISBN: 978-94-6300-549-4

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics