In this article, we review research literature concerning number sense from several related fields. Whereas other authors have pointed to difficulty defining number sense or to some degree of inconsistency in the literature, we argue instead that this is a case of polysemy: three constructs given the same name. Our purpose is to clarify the research literature concerning number sense by naming and defining these three constructs, identifying similarities and differences among them, categorizing the research traditions associated with each construct, and summarizing the methods used and findings reported. We compare and contrast themes in each body of literature by drawing on a sample of 141 research articles that were focused on number sense. We find evidence that there is confusion of number sense constructs across research traditions. We emphasize the need for clarity in order for research in each of these traditions to progress.
Providing opportunities for students to express ideas in their own words is key to promoting authentic disciplinary engagement and robust conceptual understanding. In this article, we discuss our experiences and observations related to students' informal vocabulary in the context of a middle school probability unit. We noticed that students' informal naming provided critical glimpses into their conceptions and tensions about sample spaces. The use of student-suggested names also served to compress previous discussions and facilitate higher-level conceptual thinking in later conversations. We share our experiences with informal naming in one curricular context and conclude with perceived benefits to allowing space for student naming as a broader instructional practice.
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