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“It Depends …”: Using Ambiguities to Better Understand Mathematics Teachers’ Decision-making

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Abstract

The concept of teacher noticing has been a powerful methodological tool for understanding teachers’ decision-making and professional judgment. In this line of inquiry, researchers usually try to identify elements of classroom practice salient to teachers. Data about teacher noticing and decision making can be collected at scale through the use of scenario-based instruments, but these instruments have been described in the literature as inherently ambiguous because they do not contain all the information necessary to make a decision. We contribute to understanding this ambiguity so as to help connect teacher noticing to their professional judgment by introducing the concept of conditional construals—moments when teachers require additional context in order to judge whether a given teaching action is appropriate. Furthermore, we locate conditional construals in a large corpus of responses to scenario-based items by identifying occurrences of a linguistic marker. Our identification of these moments allows us to study the type of reasoning (analytical or intuitive) evoked by these scenarios and gives us insight into the information teachers require to make decisions.

Résumé

Le concept d’« enseignant remarquant» constitue un outil méthodologique puissant pour comprendre le processus décisionnel et le jugement professionnel des enseignants. Dans ce champ de réflexion, les chercheurs tentent normalement d’identifier les aspects, issus de la pratique en salle de classe qui sont pertinents aux enseignants. Des données sur la qualité d’« enseignant remarquant» et le processus décisionnel des enseignants peuvent être recueillies à l’échelle en utilisant des instruments fondés sur des scénarios, toutefois, la littérature considère ces instruments comme étant intrinsèquement ambigus dans la mesure où ils n’apportent pas toute l’information nécessaire à la prise de décision. Afin de faciliter l’établissement de liens entre la qualité d’« enseignant remarquant» et le jugement professionnel des enseignants, nous contribuons à mieux cerner cette ambiguïté en présentant le concept d’« interprétations conditionnelles», correspondant aux moments où les enseignants ont besoin de plus de contexte pour déterminer si un acte pédagogique est requis. En repérant les marqueurs linguistiques se trouvant dans un vaste corpus de réponses touchant les aspects relatifs aux scénarios, nous découvrons en outre des « interprétations conditionnelles». Le repérage de ces moments nous permet d’analyser le type de raisonnement (analytique ou intuitif) évoqué par ces scénarios et nous donne un aperçu de l’information dont les enseignants ont besoin pour prendre leurs décisions.

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Fig. 1
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adopted from Herbst and Chazan, 2012, p. 15)

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Adapted from Brooks & Highhouse (2006) to illustrate how items could be classified

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© 2020 The Regents of the University of Michigan, all rights reserved, used with permission

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Notes

  1. This work was done with the support of the US National Science Foundation (NSF) through grant DRL- 0918425 to P. Herbst. All opinions are those of the authors and do not necessarily represent the views of the Foundation.

  2. Goodwin’s and Mason’s notions of professional vision as a kind of “seeing” and understanding a situation encompasses a larger category of perceptions beyond the visual. Some of those perceptions, such as those that rely on one’s sense of smell or sound, are beyond the scope of this mode of data collection that relies on a mostly visual representation of the situation.

  3. By false positive, we refer to those instances where a linguistic marker for circumstances of contingency is present, and yet no conditional construal is present. By false negative, we refer to those instances where none of the linguistic markers for circumstances of contingency are present, and yet a conditional construal is present.

  4. For instance, the following example illustrates how a false positive can be produced with the linguistic marker assum-: “Students need to take risks and see if there [sic] assumptions are correct.” (data drawn from a disciplinary sub-obligation item, italics ours).

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Milewski, A., Erickson, A. & Herbst, P. “It Depends …”: Using Ambiguities to Better Understand Mathematics Teachers’ Decision-making. Can. J. Sci. Math. Techn. Educ. 21, 123–144 (2021). https://doi.org/10.1007/s42330-021-00141-x

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