Abstract
Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser’s (Educational Studies in Mathematics 75:241–251, 2010) study of prospective elementary teachers’ conceptions of multidigit number and examined the main claim that most elementary pre-service teachers think about digits incorrectly at least some of the time. Results indicated no statistically significant difference in the distribution of conceptions between the original and replication samples and, moreover, no statistically significant differences in the distribution of sub-conceptions among prospective teachers with the most common conception. These results suggest confidence is warranted both in the generality of the main claim and in the utility of the conceptions framework for describing prospective elementary teachers’ conceptions of multidigit number. The report further contributes a framework for replication of mathematics education research adapted from the field of psychology.
Similar content being viewed by others
References
Borko, H., Eisenhart, M., Brown, C. A., Underhill, R. G., Jones, D., & Agard, P. (1992). Learning to teach hard mathematics: do novice teachers and their instructors give up too easily? Journal for Research in Mathematics Education, 23, 194–222.
Brandt, M. J., IJzerman, H., Dijksterhuis, A., Farach, F. J., Geller, J., Giner-Sorolla, R., et al. (2014). The replication recipe: what makes for a convincing replication? Journal of Experimental Social Psychology, 50, 217–224. https://doi.org/10.1016/j.jesp.2013.10.005.
Coyne, M. D., Cook, B. G., & Therrien, W. J. (2016). Recommendations for replication research in special education: a framework of systematic, conceptual replications. Remedial and Special Education, 37, 244–253. https://doi.org/10.1177/41932516648463.
Cohen, J. (1968). Weighted kappa: nominal scale agreement provision for scaled disagreement or partial credit. Psychological Bulletin, 70(4), 213–220.
Creswell, J. W. (2008). Research design: qualitative, quantitative, and mixed methods approaches (3rd ed.). Thousand Oaks: Sage.
da Ponte, J. P., & Chapman, O. (2015). Prospective mathematics teachers’ learning and knowledge for teaching. In L. D. English & D. Kirshner (Eds.), Handbook of international research in mathematics education (pp. 275–296).
Eastman, P. M. (1975). Replication studies: why so few? Journal for Research in Mathematics Education, 6(2), 67–68.
Ernest, P. (1998). Social constructivism as a philosophy of mathematics. Albany: SUNY.
Fuson, K. C., Wearne, D., Hiebert, J. C., Murray, H. G., Human, P. G., Olivier, A. I., Carpenter, T. P., & Fennema, E. (1997). Children’s conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. Journal for Research in Mathematics Education, 28, 130–162.
Gutiérrez, R. (2013). The sociopolitical turn in mathematics education. Journal for Research in Mathematics Education, 44(1), 37–68.
Ladson-Billings, G., & Tate, W. F. (1995). Toward a critical race theory of education. Teachers College Record, 97, 47–68.
Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33, 159–174.
Leinhardt, G. (1989). Math lessons: a contrast of novice and expert competence. Journal for Research in Mathematics Education, 20, 52–75.
Livy, S., & Herbert, S. (2013). Second-year pre-service teachers’ responses to proportional reasoning test items. Australian Journal of Teacher Education (Online), 38(11), 17–32. https://doi.org/10.14221/ajte.2013v38n11.7.
Luneta, K. (2014). Foundation phase teachers’ (limited) knowledge of geometry. South African Journal of Childhood Education, 4(3), 71–86.
Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Mahwah: Erlbaum.
Makel, M. C., & Plucker, J. A. (2014). Facts are more important than novelty: replication in the education sciences. Educational Researcher, 43(6), 304–316. https://doi.org/10.3102/0013189X14545513.
McClain, K. (2003). Supporting preservice teachers’ understanding of place value and multidigit arithmetic. Mathematical Thinking and Learning, 5(4), 281–306.
Mejía-Ramos, J. P., & Inglis, M. (2011). Semantic contamination and mathematical proof: can a non-proof prove? The Journal of Mathematical Behavior, 30, 10–29. https://doi.org/10.1016/j.jmathb.2010.11.005.
Nivens, R. A., & Otten, S. (2017). Assessing journal quality in mathematics education. Journal for Research in Mathematics Education, 48(4), 348–368.
Philipp, R., Schappelle, B., Siegfried, J., Jacobs, V., & Lamb, L. (2008). The effects of professional development on the mathematical content of K-3 teachers. New York: Paper presented at the American Education Research Association.
Schmidt, S. (2009). Shall we really do it again? The powerful concept of replication is neglected in the social sciences. Review of General Psychology, 13(2), 90–100. https://doi.org/10.1037/a0015108.
Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children’s success, methods and strategies. Educational Studies in Mathematics, 47(2), 145–173.
Simonsohn, U. (2014). Small telescopes: detectability and the evaluating of replication results. Psychological Science. Retrieved at. https://doi.org/10.2139/ssrn.2259879.
Stanic, G. M., & Kilpatrick, J. (1992). Mathematics curriculum reform in the United States: a historical perspective. International Journal of Educational Research, 17(5), 407–417.
Thanheiser, E. (2018). The effects of preservice elementary school teachers’ accurate self-assessments in the context of whole number. Journal for Research in Mathematics Education, 49(1), 39–56.
Thanheiser, E. (2010). Investigating further preservice teachers’ conceptions of multidigit whole numbers: refining a framework. Educational Studies in Mathematics, 75(3), 241–251.
Thanheiser, E. (2009). Preservice elementary school teachers’ conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40(3), 251–281.
Thornton, C. A. (1990). Solution strategies: subtraction number facts. Educational Studies in Mathematics, 21(3), 241–263.
Walshaw, M. (Ed.). (2004). Mathematics education within the postmodern. Greenwich: Information Age.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jacobson, E., Simpson, A. Prospective elementary teachers’ conceptions of multidigit number: exemplifying a replication framework for mathematics education. Math Ed Res J 31, 67–88 (2019). https://doi.org/10.1007/s13394-018-0242-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13394-018-0242-x