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Anne K. Morris

The author presents a procedure for learning from variations that occur when instructors implement lesson plans designed by others. This kind of variation, occurring in many classrooms every day, can provide a source of information for improving curriculum, both in terms of instructional activities for students and especially in terms of clarifications for instructors to support more effective implementation. The author provides detailed descriptions, in the context of a mathematics course for preservice K-8 teachers, for using implementation variations in a practical, research-based way to study and improve teaching. The goal is to build an accumulating knowledge base for teacher education. Examples are presented to illustrate how increasingly rich lesson plans, based on observing implementation variations, can move toward achieving this goal.

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Anne K. Morris and James Hiebert

Two studies were conducted to identify the conditions under which instructors teaching the same mathematics teacher preparation course would continuously improve their shared instructional products (lesson plans for class sessions) using small amounts of data on preservice teacher performance. Findings indicated that when lesson-level student performance data were simply collected, by course section, the instructors could make important changes to the lessons but did not often do so. However, when the instructors were encouraged to compare data across semesters, they generated hypotheses that guided instructional improvements, which then were tested through multiple cycles. The cycles of hypothesis testing helped instructors clarify the goals for improvement, use the performance data to test whether changes were actually improvements, and reduce their tolerance for marginal student performance.

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Anne K. Morris, James Hiebert and Sandy M. Spitzer

The goal of this study is to uncover the successes and challenges that preservice teachers are likely to experience as they unpack lesson-level mathematical learning goals (i.e., identify the subconcepts and subskills that feed into target learning goals). Unpacking learning goals is a form of specialized mathematical knowledge for teaching, an essential starting point for studying and improving one's teaching. Thirty K–8 preservice teachers completed 4 written tasks. Each task specified a learning goal and then asked the preservice teachers to complete a teaching activity with this goal in mind. For example, preservice teachers were asked to evaluate whether a student's responses to a series of mathematics problems showed understanding of decimal number addition. The results indicate that preservice teachers can identify mathematical subconcepts of learning goals in supportive contexts but do not spontaneously apply a strategy of unpacking learning goals to plan for, or evaluate, teaching and learning. Implications for preservice education are discussed.

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

How can research have a larger impact on educational practice? What kinds of research can have the greatest impact on educational practice? These are perennially thought-provoking questions for mathematics education researchers (e.g., Battista et al., 2007; Boerst et al., 2010; Heck et al., 2012; Heid et al., 2006; Herbel-Eisenmann et al., 2016; Langrall, 2014; Silver, 2003) as well as educational researchers more broadly (Kane, 2016; Snow, 2016). In recent years, educational researchers have lamented the failure of educational research to have a transformative effect on educational practice despite repeated reform efforts. One might be tempted to adapt a motto of the Reformation, Ecclesia reformata, semper reformanda, to describe the history of education: reformed and always reforming. Payne (2008) systematically reported the persistence of failure in urban schools despite “so much reform.” However, the failed impact of educational research on practice goes far beyond urban schools (Bryk, Gomez, Grunow, & LeMahieu, 2015). We are forced to ask, how can the field of educational research improve its impact on practice?

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

In our first editorial (Cai et al., 2017), we highlighted the long-standing, critical issue of improving the impact of educational research on practice. We took a broad view of impact, defining it as research having an effect on how students learn mathematics by informing how practitioners, policymakers, other researchers, and the public think about what mathematics education is and what it should be. As we begin to dig more deeply into the issue of impact, it would be useful to be more precise about what impact means in this context. In this editorial, we focus our attention on defining and elaborating exactly what we mean by “the impact of educational research on students' learning.”

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

In our last editorial, we considered the impact of research on students' learning. In clarifying our perspective, we answered the question of “impact of research on what” to include both cognitive and noncognitive outcomes in students as well as long-term impact on students that goes well beyond short-term cognitive impact. A natural next step is to examine the conditions under which students can achieve such broad goals. We will devote the next set of editorials to exploring ways in which researchers can design their work to increase its impact on students' opportunities to achieve these goals.

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

In our May editorial (Cai et al., 2017), we argued that a promising way of closing the gap between research and practice is for researchers to develop and test sequences of learning opportunities, at a grain size useful to teachers, that help students move toward well-defined learning goals. We wish to take this argument one step further. If researchers choose to focus on learning opportunities as a way to produce usable knowledge for teachers, we argue that they could increase their impact on practice even further by integrating the implementation of these learning opportunities into their research. That is, researchers who aim to impact practice by studying the specification of learning goals and productively aligned learning opportunities could add significant practical value by including implementation as an integral part of their work.

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

We began our editorials in 2017 seeking answers to one complex but important question: How can we improve the impact of research on practice? In our first editorial, we suggested that a first step would be to better define the problem by developing a better understanding of the fundamental reasons for the divide between research and practice (Cai et al., 2017). This sparked subsequent editorials in which we delved deeper into some of the many complicated facets of this issue. In our March (Cai et al., 2017b) editorial, we argued that impact needs to be defined more broadly than it often has been, notably, to include cognitive and noncognitive outcomes in both the near term and longitudinally. This led us to focus our May (Cai et al., 2017a) editorial on the ways that research might have a greater impact on the learning opportunities that help students reach broader learning goals. We argued that it is not enough to identify learning goals–it is also necessary to conduct research that breaks those learning goals into subgoals that can be appropriately sequenced. We highlighted research on learning trajectories as an example of this sort of work but also emphasized the need to work at a grain size that is compatible with teachers' classroom practice. Finally, in our July (Cai et al., 2017c) editorial, we argued that the implementation of learning opportunities in the classroom is an integral element of research that has an impact on practice.

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

In the past year, we have used this space to tackle a chronic and important concern in mathematics education: how to increase the impact of research on practice. Because of the unique nature of this issue of JRME, we pause to address the critical idea of replication in educational research. In later issues, we will continue our primary theme and consider how the ideas raised in this editorial can further our understanding of the relationships between research and practice.

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

In our November 2017 editorial (Cai et al., 2017), we presented a vision of a future in which research has a significant impact on practice. In the world we described, researchers and teachers work together, sharing similar goals and incentive structures. A critical feature of this brave new world is the existence of an online professional knowledge base comprising “useful findings and artifacts that are continuously refined over time, indexed by specific learning goals and subgoals, and that assist teachers and researchers in implementing learning opportunities in their classrooms” (p. 469). Moreover, we argued that teacher—researcher partnerships are a necessary condition for greater impact on practice.