When, how, and why prove theorems?

The full title of this new ZDM article is: "When, how, and why prove theorems? A methodology for studying the perspective of geometry", and it is written by P. Herbst and T. Miyakawa.

Every theorem has a proof, but not every theorem presented in schools (not only in the U.S., although this is the focus of the article). Why is that? Here is the abstract of the article, which truly raises some important questions:

While every theorem has a proof in mathematics, in US geometry classrooms not every theorem is proved. How can one explain the practitioner’s perspective on which theorems deserve proof? Toward providing an account of the practical rationality with which practitioners handle the norm that every theorem has a proof we have designed a methodology that relies on representing classroom instruction using animations. We use those animations to trigger commentary from experienced practitioners. In this article we illustrate how we model instructional situations as systems of norms and how we create animated stories that represent a situation. We show how the study of those stories as prototypes of a basic model can help anticipate the response from practitioners as well as suggest issues to be considered in improving a model.
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