How about Fidelity?

The word ‘fidelity’ regularly pops up in mathematics education research and practice. This is in particular when dealing with matters of digital technologies, instructional interventions and replications. The experience shows that it is not always clear what is meant by fidelity. That it may have slightly different meanings in different situations. In which meaning, for example, can we talk about fidelity of teachers’ implementation of curriculum reforms or about the use of digital technologies in the classroom? The word may also have different connotations for different people. As pointed out by Ahl et al. (2022, p. 70), “fidelity is an elusive concept to capture in analysis.”

The Oxford Advanced Learner’s Dictionary (2022) asserts that ‘fidelity’ is associated with loyalty to somebody or something, as well as to the quality of being accurate in relation to something, as in the following examples: (i) “fidelity to your principles,” (ii) “fidelity to your partner,” (iii) “the fidelity of the translation to the original text,” or (iv) “the story is told with great fidelity to the original.”

For our purposes, both ‘loyalty’ and ‘accuracy’ are of relevance. For example, one can talk about the quality of or level to which a teacher, a textbook author or an institution is loyal to a given instructional approach (cf. example i). Or to what extent researchers are loyal or accurate in relation to a previous study being replicated (cf. examples iii and iv). On some occasions, the term ‘faithfulness’ also enters the picture, for example, when addressing the extent to which one is ‘truthful’ to the original intent of an innovation. Surely, words such as ‘loyal’, ‘faithful’ and ‘truthful’ are more emotionally laden than ‘accuracy.’ This may of course be related to example (ii) above, since here ‘fidelity’ implies the opposite, namely ‘infidelity’. Hence, if stating that the fidelity of a given implementation/replication is low, then this may insinuate some, or even a high, degree of ‘unfaithfulness’, ‘disloyalty’ or even ‘inaccuracy’ — certainly not positively-perceived qualities as such.

To be clear, the purpose of this editorial is not to suggest that we now use another word than ‘fidelity’ because of the above mentioned potential connotations and associations people may or may not have. Rather, we find it to be important to be aware of these when we have a look at how the notion of fidelity is used in our research field. When looking into the literature on fidelity, both inside and outside of mathematics education research, it becomes clear that the notion of fidelity is diverse, both in terms of definition and measurement aspects. Our editorial is not meant to be a review of fidelity studies. Still, we find it worth the endeavour to address the notion of fidelity. Not to remedy the discrepancies in definition and use, but rather to draw any such to the attention of the readers of Implementation and Replication Studies in Mathematics Education (IRME) as well as the researchers who publish in this journal.

In the following, we address the notion of fidelity from three perspectives. Firstly, the meaning(s) of fidelity in mathematics education research. Secondly, fidelity in implementation research. And thirdly, fidelity in replication studies. Along the way we introduce the four papers in the current issue, and relate these to our discussion of fidelity.