Prospective elementary teachers’ conceptions of multidigit number: exemplifying a replication framework for mathematics education

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.

Launching Implementation and Replication Studies in Mathematics Education (IRME)

“…The paper by Stijn Van Der Auwera, Lien Mathys, Bert De Smedt, Joke Torbeyns and Lieven Verschaffel (2021) addresses the issue of adaptive expertise in the specific domain of multi-digit subtraction through an internal conceptual replication of the study by Torbeyns et al (2018). Van Der Auwera et al (2021) acknowledge the criticisms that have been made to internal replications in mathematics education (e.g., Jacobson & Simpson, 2019;Schoenfeld, 2018). However, they promote the validation of their empirical results by external researchers.…”

“…Neither in JRME, nor in any other mathematics education journal. Although in subsequent decades there have been reports of replications in mathematics education (e.g., Beattie, 1995;De Bock et al 2011;Jacobson & Simpson, 2019;Star et al, 2011), some statistics suggest that the number of replication studies published in mathematics education in recent years is low (Cai et al, 2018).…”

“…The discussion covers various aspects related to the quality of a replication and the studies that are worth replicating and publishing. For instance, some researchers find internal replications problematic, because there may be issues of reliability and conflict of interest when one of the researchers from the original study also participates in the replication (Jacobson & Simpson, 2019;Schoenfeld, 2018). Other researchers, instead, argue in favor of internal replications.…”

What to Replicate?

“…We now briefly address the question of how to conduct a replication study in mathematics education. Although examples of replication studies are not abundant in our field, there are some studies that can be used as a reference to approximate an attempted answer to this question (e.g., De Bock et al, 2011;Jacobson & Simpson, 2019;Melhuish, 2018;Star et al, 2011;Thanheiser, 2018;Van Der Auwera et al, 2021). It is fair to claim that the replication studies developed in the field of mathematics education tend to be conceptual replications (Schmidt, 2009) that attempt to test a hypothesis or a result of earlier research work with some variations in conditions and methods.…”

Upper Elementary School Children’s Adaptive Use of Subtraction by Addition: A Choice/No-Choice Replication Study Involving Two Choice Conditions

“…For instance, researchers might be more inclined to look for confirmation than critical replication of their own previous findings. This confirmation bias might therefore affect internal replication studies more strongly than external replications (Jacobson & Simpson, 2019;Schoenfeld, 2018). While the current study is an internal replication, we promote the validation of our results by external researchers.…”