Skip to main content

Advertisement

SpringerLink
Log in

Using refutational text in mathematics education

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

Refutational text is one of the many instructional techniques that have been proposed to be used in education as a way to achieve effective learning. The aim of refutational text is to transform misconceptions into conceptions that are in line with current scientific concepts. This is done by explicitly stating a misconception, refuting it, and providing a correct conception. It has been applied in various curricular domains, and seems to be effective in inducing cognitive conflicts in learners and remediating misconceptions. In this article we first discuss the design principles and the theoretical underpinnings of refutational text. Then we briefly review the existing empirical research, both in general and specifically within the domain of mathematics education. Next, we zoom in on a series of studies we conducted in which refutational text was used to improve the interpretation of box plots. In these studies we focused on one very persistent misinterpretation of box plots, the area misinterpretation, which we tried to remediate using refutational text. We found that students who were exposed to refutational text scored significantly better on a box plot interpretation test than students being exposed to an instructional text in which no misconceptions were explicitly mentioned or refuted. We end with a discussion of theoretical and methodological issues for future research and propose recommendations for mathematics educators.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Christou, K. (2012). Helping students remedy the phenomenal sign bias: the case of a refutational lecture. In C. Prachalias (Ed.), Proceedings of the 8th International Conference on Education (pp. 643–648). Samos.

  • Craeghs, B. (2012). Box plot, quartile plot en offset quartile plot: Verschillende externe representaties, dezelfde interpretatiemoeilijkheden? [Box plot, quartile plot and offset quartile plot: Different representations, the same interpretation difficulties?]. Unpublished Master Thesis, KU Leuven.

  • Evans, J. S. B. (2006). The heuristic-analytic theory of reasoning: Extension and evaluation. Psychonomic Bulletin & Review, 13(3), 378–395. http://doi.org/10.3758/BF03193858.

  • Forman, E., & Cazdan, C. (1998). Exploring Vygotskian perspectives in education. The cognitive value of peer interaction. In D. Faulkner, K. Littleton & R. Woodhead (Eds.), Learning relationships in the classroom (pp. 189–206). New York: Routledge.

    Google Scholar 

  • Gill, M. G., Ashton, P. T., & Algina, J. (2004). Changing preservice teachers’ epistemological beliefs about teaching and learning in mathematics: An intervention study. Contemporary Educational Psychology, 29, 164–185. doi:10.1016/j.cedpsych.2004.01.003.

    Article  Google Scholar 

  • Grayson, D. (1996). Improving science and mathematics learning by concept substitution. In D. Treagust & R. Duit (Eds.), Improving teaching and learning in science and mathematics (pp. 152–161). New York: Teacher College Press.

    Google Scholar 

  • Guzzetti, B. J., Snyder, T. E., Glass, G. V., & Gamas, W. S. (1992). Promoting conceptual change in science. Reading Research Quarterly, 28(2), 117–159.

    Google Scholar 

  • Heemsoth, T., & Heinze, A. (2014). The impact of incorrect examples on learning fractions: A field experiment with 6th grade students. Instructional Science, 42(4), 639–657. doi:10.1007/s11251-013-9302-5.

    Article  Google Scholar 

  • Hynd, C. R. (2001). Refutational texts and the change process. International Journal of Educational Research, 35(7–8), 699–714. doi:10.1016/S0883-0355(02)00010-1.

    Article  Google Scholar 

  • Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. In C.-A. S. Staël Von Holstein (Ed.), The concept of probability in psychological experiments (pp. 25–48). Dordrecht: Springer. doi:10.1007/978-94-010-2288-0_3.

    Chapter  Google Scholar 

  • Kendeou, P., & O’Brien, E. (2014). The knowledge revision components (KReC) framework: processes and mechanisms. In D. N. Rapp & J. L. G. Braasch (Eds.), Processing inaccurate information: Theoretical and Applied Perspectives from Cognitive Science and the Educational Sciences (pp. 353–378). Cambridge: MIT university press.

    Google Scholar 

  • Kendeou, P., Walsh, E. K., Smith, E. R., & O’Brien, E. J. (2014). Knowledge revision processes in refutation texts. Discourse Processes, 51(5–6), 374–397. doi:10.1080/0163853X.2014.913961.

    Article  Google Scholar 

  • Lem, S., Baert, K., Ceulemans, E., Onghena, P., Verschaffel, L., & Van Dooren, W. (2016). Refutational text and multiple external representations as a method to improve the interpretation of box plots. (Manuscript Submitted for Publication).

  • Lem, S., Kempen, G., Ceulemans, E., Onghena, P., Verschaffel, L., & Van Dooren, W. (2014). Combining multiple external representations and refutational text: an intervention on learning to interpret box plots. International Journal of Science and Mathematics Education, 13, 909–926. doi:10.1007/s10763-014-9604-3.

    Article  Google Scholar 

  • Lem, S., Onghena, P., Verschaffel, L., & Van Dooren, W. (2013). The heuristic interpretation of box plots. Learning and Instruction, 26(3), 22–35. doi:10.1016/j.learninstruc.2013.01.001.

    Article  Google Scholar 

  • Lem, S., Onghena, P., Verschaffel, L., & Van Dooren, W. (2016). The power of refutational text: changing intuitions about the interpretation of box plots. European Journal of Psychology of Education. doi:10.1007/s10212-016-0320-y.

    Google Scholar 

  • Méheut, M. (2012). Preconceptions and learning. In N. M. Seel (Ed.), Encyclopedia of the sciences of learning (pp. 2662–2664). Boston: Springer. doi:10.1007/978-1-4419-1428-6.

    Google Scholar 

  • Miszaniec, J.-M. (2016). Designing effective lessons on probability: A pilot study focused on the illusion of linearity. Unpublished doctoral dissertation; Concordia University.

  • Posner, G. J., Strike, K. A., Hewson, P. W., & Gertzog, W. A. (1982). Accommodation of a scientific conception: Toward a theory of conceptual change. Science Education, 66(2), 211–227. doi:10.1002/sce.3730660207.

    Article  Google Scholar 

  • Schneider, M., Vamvakoussi, X., & Van Dooren, W. (2012). Conceptual Change. In N. Seel (Ed.), Encyclopedia of the sciences of learning (pp. 735–738). London: Springer. doi:10.1007/978-1-4419-1428-6_352.

    Google Scholar 

  • Sinatra, G., & Broughton, S. (2011a). Bridging reading comprehension and conceptual change in science education: The promise of refutation text. Reading Research Quarterly, 46(4), 374–393. doi:10.1002/RRQ.005.

    Article  Google Scholar 

  • Sinatra, G., & Broughton, S. (2011b). Understanding the refutation text effect in conceptual change research: Multiple perspectives. In W. Van Dooren (Ed.), The role of refutational texts in achieving conceptual change. Retrieved from http://digitalcommons.usu.edu/teal_facpub/296/.

  • Thompson, V. A. (2009). In two minds: Dual processes and beyond. In J. Evans & K. Frankish (Eds.), In two minds: Dual processes and beyond (pp. 171–195). New York: Oxford University Press. doi:10.1093/acprof:oso/9780199230167.001.0001.

    Chapter  Google Scholar 

  • Tippett, C. D. (2010). Refutation text in science education: A review of two decades of research. International Journal of Science and Mathematics Education, 8, 951–970. doi:10.1007/s10763-010-9203-x.

    Article  Google Scholar 

  • Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31(3), 344–355. doi:10.1016/j.jmathb.2012.02.001.

    Article  Google Scholar 

  • Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2013). Brief Report. Educated adults are still affected by intuitions about the effect of arithmetical operations: evidence from a reaction-time study. Educational Studies in Mathematics, 82(2), 323–330. doi:10.1007/s10649-012-9432-8.

    Article  Google Scholar 

  • van den Broek, P., & Kendeou, P. (2008). Cognitive processes in comprehension of science texts: the role of co-activation in confronting misconceptions. Applied Cognitive Psychology, 22(3), 335–351. doi:10.1002/acp.1418.

    Article  Google Scholar 

  • Van Dooren, W., & Inglis, M. (2015). Inhibitory control in mathematical thinking, learning and problem solving: a survey. ZDM Mathematics Education, 47(5), 713–721. doi:10.1007/s11858-015-0715-2.

    Article  Google Scholar 

  • Vosniadou, S., & Ioannides, C. (1998). From conceptual development to science education: a psychological point of view. International Journal of Science Education, 20, 1213–1230. doi:10.1080/0950069980201004.

    Article  Google Scholar 

  • Vosniadou, S., & Vamvakoussi, X. (2006). Examining mathematics learning from a conceptual change point of view: Implications for the design of learning environments. In L. Verschaffel, F. Dochy, M. Boekaerts & S. Vosniadou (Eds.), Instructional psychology: Past, present and future trends. Fifteen essays in honour of Erik De Corte (pp. 55–70). Oxford: Elsevier.

    Google Scholar 

  • Yilmaz, D., Tekkaya, C., & Sungur, S. (2011). The comparative effects of prediction/discussion-based learning cycle, conceptual change text, and traditional instructions on student understanding of genetics. International Journal of Science Education, 33(5), 607–628. doi:10.1080/09500691003657758.

    Article  Google Scholar 

Download references

Acknowledgements

Stephanie Lem holds a post-doctoral fellowship of the Research Foundation–Flanders (FWO). This research was partially supported by grant GOA/12/010 ‘Number sense: Analysis and Improvement’ of the KU Leuven.

Author information

Authors and Affiliations

  1. Centre for Instructional Psychology and Technology, KU Leuven, Dekenstraat 2, PO Box 3773, 3000, Leuven, Belgium

    Stephanie Lem, Lieven Verschaffel & Wim Van Dooren

  2. Methodology of Educational Sciences Research Group, KU Leuven, Leuven, Belgium

    Patrick Onghena

Authors
  1. Stephanie Lem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick Onghena
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lieven Verschaffel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wim Van Dooren
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stephanie Lem.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lem, S., Onghena, P., Verschaffel, L. et al. Using refutational text in mathematics education. ZDM Mathematics Education 49, 509–518 (2017). https://doi.org/10.1007/s11858-017-0843-y

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-017-0843-y

Keywords

Search

Navigation