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Building and Structuring Knowledge That Could Actually Improve Instructional Practice
Abstract
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).
... As with Japanese lesson study, both projects employ lesson plans to capture knowledge for teaching. In a recent editorial, Cai et al. (2018) proposed a model of building knowledge for improving instructional practice that also utilized (among other aspects) detailed, context-sensitive lesson plans. ...
... We are encouraged that others (Cai et al. 2018) are not only calling for more work to be done, but offering potential models and frameworks for a robust system that will generate, store, and share instructional knowledge in a manner that will fit the contexts, resources, and culture of the US education system. Knowledge of student mathematical thinking is a key component to share as part of this effort. ...
The successful use of lesson plans as the primary vehicle for storing and sharing teachers’ instructional knowledge in Japan has given impetus to calls by US researchers for the development of a system for sharing teachers’ knowledge through instructional products to improve teachers’ capacity to implement high-quality instruction and to build a knowledge base for instruction. These products would be created by, and for, teachers to use in guiding instruction, thus building and sharing teachers’ instructional knowledge. In this study, we try to characterize one aspect of teacher knowledge that is central in building a knowledge base for instruction, knowledge of student mathematical thinking. We analyze ten written instructional products from the USA and Japan to better understand what knowledge of student mathematical thinking can be shared in such products. We also look at how knowledge of student mathematical thinking is used to guide and justify instructional decisions. One key finding is that the knowledge of student mathematical thinking shared in the top written instructional products is specific to a task or mathematical topic, varied with descriptions of multiple solutions or ways of reasoning, and sufficiently detailed to make the knowledge usable for teachers.
... 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 other words, data on students' experiences must be paired with data on instruction to make connections between teachers' teaching and students' learning. This is a point we have emphasized in our descriptions of how teacher-researcher partnerships could work with a professional knowledge base (Cai et al., 2018a). The second assumption is that teaching can greatly improve students' learning if teachers understand students' thinking and learning experiences. ...
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.
... Teachers work under a wide variety of contextual conditions, and it is expected that their instruction will differ from one another and from the written curriculum, even when implementing the same lesson plan (Cai et al. 2018). One goal of this study is to illuminate comparisons between the written and enacted lesson plans with ALNs across different contextual conditions. ...
In K–12 statistics education, there is a call to integrate statistics content standards throughout a mathematics curriculum and to teach these standards from a data analytic perspective. Annotated lesson notes within a lesson plan are a freely available resource to provide teachers support when navigating potentially unfamiliar statistics content and teaching practices. We identified several types of annotated lesson notes, created two statistics lesson plans that contained various annotated lesson notes, and observed secondary mathematics teachers implement the lesson plans in their intermediate algebra courses. For this study, we qualitatively investigated how two teachers’ instructional actions compared to what was prescribed in the annotated lesson notes. We found ways in which the teachers’ instructional actions, across their differing contexts, aligned with, varied from, or adapted to the annotated lesson notes. From these results, we highlight affordances and limitations of annotated lesson notes for statistics instruction and offer recommendations for those who create statistics curricula with annotated lesson notes.
... Blurring research-practice boundaries involves collective action in synergistic processes toward a shared vision and goals. As discerned from a series of reports published in the Journal for Research in Mathematics Education (Cai et al., 2017a(Cai et al., , 2017b(Cai et al., , 2018a(Cai et al., , 2018b(Cai et al., , 2018c(Cai et al., , 2020, such collective work involves three key mechanisms: partnerships, communication, and designbased implementation research. I focus on the communication mechanism in this report; an expanded report of this ongoing research will address the other mechanisms. ...
Blurring boundaries between research and practice remains a key and complex challenge in the field of mathematics education. This theoretical report is motivated by the need to advance nascent theory in this domain and to take up the collective responsibility to both advance research-practice connections and address issues of equity as collective professional responsibilities. I network Gutierrez’ four dimensions of equity—access, achievement, identity, power—with two mechanisms for communication—currency exchange, translation. I introduce visualizations of the actions of researchers and practitioners from this networked stance as a way to humanize the work of blurring research-practice boundaries in ways that challenge the status quo of what is possible for advancing the field.
... We have undervalued the professional knowledge of teachers by not developing a system to gather and preserve that knowledge. Furthermore, because we have not accumulated teachers' knowledge in a systematic and accessible way, we have had no means to vet that knowledge by sharing it with other teachers and researchers and determining whether and how it warrants application on a wider basis (Cai et al., 2018a). In what ways could technology facilitate the recording, processing, vetting, and sharing of teachers' knowledge? ...
... Within the domain of daily lessons, it is possible to imagine research programs that could address questions about the best ways to store, package, and present data so that they can inform the planning, implementing, and revising of instruction. In addition, we believe that there are advantages to using instructional artifacts such as written lesson plans, classroom materials, and student assessments as the storage receptacles for lesson-level data (Cai et al., 2018a). If written lesson plans are the storage container, the data gathered that could be relevant for teaching a particular lesson are stored in the lesson plan where they are likely to be noticed and used. ...
... This will be a critical part of answering the research question that we posed above. We can provide some beginning hypotheses based on what has been proposed for teachers to preserve and share the knowledge they acquire (Cai et al., 2018(Cai et al., , 2020aGu et al., 2017;Morris & Hiebert, 2011;Stigler & Hiebert, 1999). We envision a tangible instructional artifact that both accumulates the knowledge for improving an innovation and presents the best current version of the innovation. ...
... If researchers use the instructional triangle as a starting point for defining learning opportunities, the measures they create will assess much of what researchers often call the conditions of classroom learning. We have argued in earlier editorials that the effects of classroom interventions depend on such conditions (Cai et al., 2017b(Cai et al., , 2017c(Cai et al., , 2018. Developing measures of learning opportunities thus means describing and accounting for these conditions. ...
(...) In this editorial, we discuss the first of the five overarching problems:
defining and measuring learning opportunities precisely enough to study
how to maximize the quality of the opportunities experienced by every student.
... If researchers use the instructional triangle as a starting point for defining learning opportunities, the measures they create will assess much of what researchers often call the conditions of classroom learning. We have argued in earlier editorials that the effects of classroom interventions depend on such conditions (Cai et al., 2017b(Cai et al., , 2017c(Cai et al., , 2018. Developing measures of learning opportunities thus means describing and accounting for these conditions. ...
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