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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison and James Hiebert

In this editorial, we elaborate our vision of the changing roles of researchers and teachers in a future world in which research has a much more direct and meaningful impact on practice (Cai et al., 2017). In previous editorials, we have described characteristics of this future world, including setting research agendas based on instructional problems teachers want to solve (Cai et al., 2017a), developing authentic partnerships between researchers and teachers and connecting multiple partnerships to solve common problems (Cai et al., 2017a, 2018a, 2018b), using new technologies to collect and analyze data on the relationships between students' instructional and learning histories that would enable teachers to plan more effective lessons (Cai et al., 2018a, 2018b), taking advantage of connected partnerships and new data-gathering technologies to build a knowledge base accessible to all teachers facing similar instructional problems (Cai et al., 2018a, 2018b, 2018d), and creating new incentives to appropriately reward researchers and teachers for improving the learning opportunities for all students across classrooms within their school district or state (Cai et al., 2017a). We have alluded to the changing roles this vision would require, including researchers developing hypothetical learning trajectories for concepts that are implicated in teachers' instructional problems (Cai et al., 2017b) and teachers accepting professional responsibilities for contributing to knowledge that improves instruction in all classrooms in their district or state rather than just in their own classroom (Cai et al., 2017a). In this editorial, we create a more complete picture of the new professional roles of researchers and teachers in this future world that intertwines research and practice.

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Jennifer E. Jacobs, James Hiebert, Karen Bogard Givvin, Hilary Hollingsworth, Helen Garnier and Diana Wearne

Debates about the future of school mathematics in the United States often center on whether standards-based instruction is improving or undermining students' achievement. Critical for making progress in these debates is information about the actual nature of classroom practice in U.S. classrooms. This article focuses on one key element of classroom practice—teaching—and presents the results of two studies of randomly selected, nationally representative U.S. eighth-grade mathematics lessons that were videotaped as part of the TIMSS 1995 and 1999 Video Studies. Analyses compare features of teaching found in these lessons with pedagogical recommendations for middle school teachers in the Principles and Standards for School Mathematics (Principles and Standards) in order to examine the extent to which teaching in U.S. eight-grade classrooms is standards-based. Results show that typical mathematics teaching, in both 1995 and 1999, is more like the kind of traditional teaching reported for most of the past century (Cuban, 1993; Fey, 1979; Weiss, Pasley, Smith, Banilower, & Heck, 2003; Welch, 1978) than the kind of teaching promoted in Principles and Standards.

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison and James Hiebert

We concluded our November editorial (Cai et al., 2018b) with a promise to consider research paradigms that could bring us closer to the new world we have envisioned where research is intertwined with practice. We will call the paradigms we have in mind research pathways to avoid the range of complicated connotations often applied to the term paradigm. By research pathways in education, we mean the collection of assumptions that define the purposes of educational research, the principles that differentiate research from other educational activities, and the guidelines for how research should be conducted.

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer, James Hiebert and Arthur Bakker

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer, James Hiebert and Arthur Bakker

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer and James Hiebert

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer and James Hiebert

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer and James Hiebert

In 2002, the National Research Council (NRC) released Scientific Research in Education, a report that proposed six principles to serve as guidelines for all scientific inquiry in education. The first of these principles was to “pose significant questions that can be investigated empirically” (p. 3). The report argued that the significance of a question could be established on a foundation of existing theoretical, methodological, and empirical work. However, it is not always clear what counts as a significant question in educational research or where such questions come from. Moreover, our analysis of the reviews for manuscripts submitted to JRME 1 suggests that some practical, specific guidance could help researchers develop a significant question or make the case for the significance of a research question when preparing reports of research for publication.

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer and James Hiebert

In our March editorial (Cai et al., 2019), we discussed the nature of significant research questions in mathematics education. We asserted that the choice of a suitable theoretical framework is critical to establishing the significance of a research question. In this editorial, we continue our series on high-quality research in mathematics education by elaborating on how a well-constructed theoretical framework strengthens a research study and the reporting of research for publication. In particular, we describe how the theoretical framework provides a connecting thread that ties together all of the parts of a research report into a coherent whole. Specifically, the theoretical framework should help (a) make the case for the purpose of a study and shape the literature review; (b) justify the study design and methods; and (c) focus and guide the reporting, interpretation, and discussion of results and their implications.

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Jinfa Cai, Anne Morris, Charles Hohensee, Stephen Hwang, Victoria Robison, Michelle Cirillo, Steven L. Kramer and James Hiebert

In our recent editorials (Cai et al., 2019a, 2019b), we discussed the important roles that research questions and theoretical frameworks play in conceptualizing, carrying out, and reporting mathematics education research. In this editorial, we discuss the methodological choices that arise when one has articulated research questions and constructed at least a rudimentary theoretical framework. Just as the researcher must justify the significance of research questions and the appropriateness of the theoretical framework, we argue that the researcher must thoroughly describe and justify the selection of methods. Indeed, the research questions and the theoretical framework should drive the choice of methods (and not the reverse). In other words, a sufficiently well-specified set of research questions and theoretical framework establish the parameters within which the most productive methods will be selected and developed.