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This paper examines the concept of open-source data interoperability in the United States' K-12 education domain, specifically addressing the implications of interoperability for data justice. The term 'data justice' is a relatively recent coinage; the framing and meaning of this term are still evolving, and it has not yet been applied in the educational domain. Building on the nascent research and theorizing in the fields of both data justice and interoperability in educational contexts, this paper provides an overview of the current state of this intersection. Additionally, the authors draw on their direct experiences implementing interoperability initiatives in several U.S. states in order to build a foundational understanding of the risks and opportunities for data justice in the realm of interoperability and data standards in education. The paper concludes with a call for more research to be completed on this complex sociotechnical topic.

Maintaining shared understanding in classroom interaction is challenging for both teachers and students. In this paper, we consider the role of teachers' gestures in promoting shared understanding. Our specific aim was to document ways in which teachers use their own gestures to support students' contributions to the classroom discourse. We present three illustrative cases that represent the range of variation in teachers' use of speech (i.e., repeating the students' speech vs. not speaking at all) and variation in the spatial positioning of the teacher, the student, and the referents of the student's speech. We argue that teachers use gestures, both to ensure that they share common ground with the individual student who is speaking and to foster common ground among the class as a whole.

In this Brief Report, we share the main findings from our line of research into embodied cognition and proof activities. First, attending to students' gestures during proving activities can reveal aspects of mathematics thinking not apparent in their speech, and analyzing gestures after proof production can contribute significantly to our understanding of students' proving practices, particularly when attending to dynamic gestures depicting relationships that are difficult to communicate verbally. Second, directing students to produce physical actions before asking them to construct a mathematical proof has the potential to influence their subsequent reasoning in useful ways, as long as the directed actions have a relationship with the proof content that is clearly meaningful to the students. We discuss implications for assessment practices and teacher education and we suggest directions for future research into embodied mathematical proof practices.

In tills Brief Report, we share the main findings from our line of research into embodied cognition and proof activities. First, attending to students' gestures during proving activities can reveal aspects of mathematical thinking not apparent in their speech, and analyzing gestures after proof production can contribute significantly to our understanding of students' proving practices, particularly when attending to dynamic gestures depicting relationships that are difficult to communicate verbally. Second, directing students to produce physical actions before asking them to construct a mathematical proof has the potential to influence their subsequent reasoning in useful ways, as long as the directed actions have a relationship with the proof content that is clearly meaningful to the students. We discuss implications for assessment practices and teacher education, and we suggest directions for future research into embodied mathematical proof practices. [ABSTRACT FROM AUTHOR]