Anne K. Morris’s research while affiliated with University of Delaware and other places

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.

In our May editorial (Cai et al., 2018a), we explored how collaborations among teacher-researcher partnerships could harness emerging technological resources to address the problem of isolation in the work of teachers and researchers. In particular, we described a professional knowledge base (Cai et al., 2018b) and a mechanism by which that knowledge base could be continuously populated, updated with data and resources that are useful to teachers and researchers, and shared among partnerships thereby enabling them to work on the same instructional problems. In this editorial, we shift our focus to discuss how data on students' thinking and classroom experiences could be leveraged within such a system to improve instructional practice. We will explore how the knowledge base could serve as a tool to (a) gather, process, and analyze data from individual students; (b) increase our understanding of the effects of students' mathematical learning experiences; and (c) help teacher-researcher partnerships understand and improve students' learning.

In our March editorial (Cai et al., 2018), we considered the problem of isolation in the work of teachers and researchers. In particular, we proposed ways to take advantage of emerging technological resources, such as online archives of student data linked to instructional activities and indexed by learning goals, to produce a professional knowledge base (Cai et al., 2017b, 2018). This proposal would refashion our conceptions of the nature and collection of data so that teachers, researchers, and teacher-researcher partnerships could benefit from the accumulated learning of ordinarily isolated groups. Although we have discussed the general parameters for such a system in previous editorials, in this editorial, we present a potential mechanism for accumulating learning into a professional knowledge base, a mechanism that involves collaboration between multiple teacher-researcher partnerships. To illustrate our ideas, we return once again to the collaboration between fourth-grade teacher Mr. Lovemath and mathematics education researcher Ms. Research, who are mentioned in our previous editorials(Cai et al., 2017a, 2017b).

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.

This editorial discusses the critical idea of replication in educational research.

We propose that an often overlooked competence for teaching is diagnosing learning goals. We propose further that this competence is an empirical process of hypothesis generation, testing, and revising. To understand our argument, diagnosis must be conceived as a process of analysis and mathematical decomposition, and learning goals must be treated as mathematical statements that can be decomposed into component parts or subgoals that must be mastered to achieve larger learning goals. By presenting several examples from our mathematics courses for prospective elementary teachers, we show how instructors can develop diagnostic competence by engaging in cycles of improvement. These cycles require diagnosing learning goals to create hypotheses about how to improve instruction, testing these hypotheses by gathering targeted data, and revising instruction based on relevant evidence. Conceived in this way, the diagnosis of learning goals is a competence teachers can develop as part of an evidence-based process for improving teaching.

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.

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.

We investigated whether the content pre-service teachers studied in elementary teacher preparation mathematics courses was related to their performance on a mathematics lesson planning task 2 and 3 years after graduation. The relevant mathematics knowledge was studied when the teachers were freshmen, 5 to 6 years earlier. Results showed that when there were differences in how completely graduates attended to the key mathematics concepts when planning lessons, the differences favored the topics studied in the courses, especially topics emphasized most heavily. We conjecture that teacher preparation can matter for lesson planning, an important task for teaching, if enough opportunities are provided to acquire the relevant content knowledge for teaching. We consider what this might mean for teacher preparation, more generally.

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.