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Reframing Equitable Communication Mechanism to Blur Research Practice Boundaries

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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.
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Equitable Research-Practice Communication Fonger, N. L.
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Reframing Equitable Communication Mechanism to Blur Research Practice Boundaries
Nicole L. Fonger
Syracuse University
Corresponding Author: Nicole L. Fonger, Syracuse University, Mathematics Department, 215
Carnegie Building, Syracuse, NY 13244, nfonger@syr.edu, Twitter/Instagram: @nmlfonger
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Abstract
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,
powerwith two mechanisms for communicationcurrency 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.
Keywords: linking research and practice, metaphors, equity, visualization, communication.
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Purpose
The complexity of blurring the boundaries between research and practice remains a key
challenge in the field of mathematics education (Arbaugh et al., 2010; Cai et al., 2017b; Heid et
al., 2006). Current research on linking research and practice is nascent in theoretical
development (Silver & Lunsford, 2017), with insufficient transparency of practices and methods
that build collective knowledge across contexts (Cai et al., 2020). In light of these issues, one
approach to advancing theoretical development is to draw on multiple metaphors (Sfard, 1998),
coordinating multiple theories toward the aim of stimulating theoretical development (Cobb,
2007).
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, 2017b, 2018a, 2018b, 2018c, 2020),
such collective work involves three key mechanisms: partnerships, communication, and design-
based implementation research. I focus on the communication mechanism in this report; an
expanded report of this ongoing research will address the other mechanisms.
In this theoretical report I aim to take a step toward theory development for the purpose
of humanizing and promoting equitable communication mechanism that blur the boundaries of
research and practice, an arguably urgent area of work that may ultimately influence storylines
around mathematics education to influence broader socio-political spheres (Herbel-Eisenman et
al., 2016). This aim was motivated in part by a review of literature on linking research and
practice, and a recognized need to advance discourse in the field around issues of equity (e.g.,
Aguirre et al., 2017; National Council of Teachers of Mathematics, 2020).
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Theoretical Orientation
I network Guitierrez’ (2007b, 2012) equity framework with visual metaphors for linking
research and practice. Metaphors serve as important grounding for our conceptions of complex
ideas and practices (Lakoff, 1993; Sfard, 1998). I employ Gutierrez’s framework toward the aim
of re-humanizing the communication mechanism and related metaphors.
Communication Metaphors
Communication is a way of sharing and interacting around ideas and practices through
multiple channels, resources, and forms of media. Multiple mediums of communication are
necessary for effective dissemination of information, especially across stakeholder groups
(Hutchinson & Huberman, 1993), yet resources tend to align with the discourse practices of
various targeted stakeholder groups (e.g., research reports and journal articles for researchers,
professional development materials and curricular guidelines for practitioners). Figure 1
introduces a visual of this perspective.
Figure 1. Communication is a way of sharing and interacting around ideas and practices through
multiple channels, resources, and media types (Sketchnote by Fonger, 2020).
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Several conceptual metaphors for linking research and practice via communication have
been identified. Most notably, researchers and teacher may engage in “currency exchange” to
cross borders (Silver, 2003) and “translate” research to practice (Silver & Lunsford, 2017). These
metaphors underscore a need for communication, a change of language, and exchange of
resources across communities. Figure 2 introduces a visualization of these metaphors.
(a)
(b)
Figure 2. Visual metaphors for conceptualizing blurring research-practice communication
boundaries include (a) currency exchange and (b) translation (Sketchnote by Fonger, 2020).
These metaphors for communication seem to draw on various underlying background
theories. For a translation metaphor, related background theories may include theories of
multiple representations (Dreyfus, 1991; Lesh, Post, & Behr, 1987) which emphasize a change of
register from source to target representation types (Janvier, 1987). A currency exchange
metaphor underscores social interaction and sharing of resources within and across institutional
boundaries and communities of practice; background theories may include social semiotics
(Morgan, 2006), and situated learning (Lave & Wenger, 1991).
Equity
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Gutierrez (2007b, 2012) frames equity through four constructs along two “axes.” The
dominant axis of access and achievement involve tangible resources and outcomes, respectively
(Gutierrez, 2007b). Access and achievement often reflect the dominant traditions and
perspectives of the field of mathematics education or subgroup, and are often measured in terms
of curriculum, student learning, opportunity to learn, and teacher practice in classroom
environments.
The critical axis is humanistic, relational, sociocultural, and sociopolitical. The identity
dimension of this axis concerns one’s framing of self (and others) in relation to the world
through discourse and communication acts (e.g., stories) that may be emotional, cognitive, and
social (cf. Heyd-Metzuyanim, 2015). In Gutierrez’ (2007b) frame, “the power dimension takes
up issues of social transformation at may levels” (p. 4), which may be individual or cultural, with
attention to salient issues such as inequities and social justice. As Rubel (2017) explains, access
is an antecedent to achievement, addressing the role of identity is an antecedent to addressing
issues of power (p. 75).
Methods and Data Sources
This theoretical report was guided by methods of research synthesis and conceptual
analyses. As a theoretical report, the aim is to put existing theories in conversation with each
other (cf. Cobb, 2007), and to draw conclusions about overlap and areas of needed development.
The publications reviewed are given in the Appendix.
The analysis focused on: identifying the mechanisms to address the goal of blurring
research-practice boundaries, and articulating conceptual metaphors that highlight actionable
steps toward collective action and equity.
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Promoting Equitable Communication to Blur Research-Practice Boundaries
This section addresses the following questions: When translation and currency exchange
are re-framed from an equity lens, how might current communication mechanisms be
challenged? What are implications for researcher and for practitioners?
Currency Exchange
Status Quo of Currency Exchange. Current practice and use of a currency exchange
metaphor suggests a limited exchange of what and how researchers and practitioners
communicate. Practitioners share their perspectives on the issues and problems they face in the
classroom; in exchange, researchers share results and ideas for solving those problems (Silver,
2003). This is one view of how currency exchange may operate to blur the boundaries between
research and practice to promote greater “use” of research to inform practice. This exchange may
be initiated by researchers seeking to address the problems of practice practitioners face
(Arbaugh et al., 2010).
Power. If we view communication as a way to share and interact around a broader set of
resources, we can challenge this dichotomy of who is sharing what resources and bring a much
richer set of linguistic and cultural resources to bear. I argue that researchers and practitioners
have more in common than what might otherwise by promoted. Viewed as “commodities,
researchers and teachers alike have shared currency types including various practices,
experiences, methods, theories (lenses or philosophies), data, and results (or outcomes). Figure 3
introduces the currency exchange status quo and re-framed power dimension.
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Status Quo
Re-Framed Power Dimension
Figure 3. Power Dimension: A visual reframing of the shared currencies teachers and researchers
share challenges the status quo of who and what is to be shared (Sketchnote by Fonger, 2020).
Achievement. By challenging the status quo of what is to be shared and by whom, the
field can begin to engage with, exchange, and interact around a much broader scope of resources.
To accomplish the goal of blurring the boundaries between research and practice, there is an
opportunity to shift from researchers sharing results with teachers toward a mutually supportive
co-creation of resources, such as issues, questions, methods, lenses, contexts, and outcomes.
Figure 4 illustrates these shared currencies.
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Figure 4. Achievement Dimension: Researchers and teachers can accomplish shared goals by
focusing on common issues, questions, methods, lenses, contexts, and desired outcomes
(Sketchnote by Fonger, 2020).
Identity. When teachers and researchers alike are positioned as expert participants in
communities of practice, these shared resources can become boundary objects of encounter (cf.
Lave & Wenger, 1991) that help establish new research-practice communities and more effective
communication. Illustrated in Figure 5, such boundary encounters may include inviting
researchers and teachers to share cultural and linguistic resources with broader sets of
constituencies both within and across institutional boundaries.
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Figure 5. Identity Dimension: Researchers and teachers can blur research-practice boundaries by
sharing and interacting around cultural and linguistic resources within and across institutional
boundaries. Some currencies may act as boundary objects of encounter to support belonging and
ways of participating (Sketchnote by Fonger, 2020).
Access. Environments and institutions must adapt to support the curation, co-creation,
and otherwise exchange of resources in ways that are supportive of both research and practice
communities. This may require additional supports that explicitly invite stakeholders to network
around actionable resources, with ease of use and timeliness prioritized. Figure 6 illustrates this.
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Figure 6. Access Dimension: Teachers and researchers need access to networks and communities
that support co-creation and curation of resources across institutional boundaries. Interaction
around commodity sharing must be easy, timely, and appropriate to various participation
structures or networks (Sketchnote by Fonger, 2020).
Equity reframing. The dimensions of equity are interacting and overlapping. Taken
together, as in Figure 7, by reframing the power dynamics of who shares currencies and what
currencies are shared, the status quo of the commodities shared within and across institutional
boundaries is challenged.
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Figure 7. An equity lens expands the currency exchange metaphor through dimensions of power,
achievement, identity, and access (Sketchnote by Fonger, 2020).
Translation
Status Quo of Translation. Current models of translation are often framed as a process
that researchers engage in when they are interested in communicating research (or research
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findings) into actionable recommendations or steps for practitioners to take up and follow. Such
a model often positions the platforms and voices of researchers as having a higher status.
Metaphors may be evoked to describe such power differentials such as researchers who work in
an “ivory tower” and teachers who are engaged “in the trenches” of school classrooms.
Traditionally, achieving a blurred boundary between research and practice may be an individual
accomplishment through a textual-based journal article with limited access behind paywalls.
Power. Challenging the status quo of translation may mean disrupting power dynamics
and social hierarchies of whose voices are brought front and center in order to blur research-
practice boundaries. One action is to provide platforms for teachers and students voices to be
centered along side or in lei of prioritizing researchers’ voices only.
Achievement. Researchers who engage in translating research to practice may
traditionally receive intrinsic or extrinsic rewards for such writing and communication. However,
by taking up the notion of translation as a collective responsibility, mathematics educators may
situate the goals of such work to include influencing storylines (cf. Herbel-Eisenman et al.,
2016), addressing shared visions, and establishing improvement oriented sustainable actions.
Identity. Teachers and researchers alike can be challenged to consider alternative
framings of practices of belonging. For example, teachers may be supported to build agency as
key contributors to the professional knowledge base, and participants in broader discourse
communities.
Access. By moving beyond a text only paywall restricted space, the field can re-imagine
communication acts as those that are freely available in a broad range of media. As a field,
mathematics is at the beginning of advancing alternative forms of communication including
podcasts, sketchnotes, video, and social media. Honoring the discourse practices of various
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communities of practice means opening up the aperture of how ideas are translated, necessarily
moving beyond text-text translation into images, video, and sound.
Equity reframing. In Figure 8, I evoke visuals of the translation metaphor from an equity
lens to illuminate both the status quo as well as alternative conceptions and actions. From an
equity lens, the notion of translation as a “change of language” by some becomes a collective
responsibility for open-access multimedia engagement wherein voices of practitioners and
researchers are valued because all stakeholders in math education are key contributors to a
shared knowledge base.
Figure 8. Reframing the translation metaphor from an equity lens (Sketchnote by Fonger, 2020).
Significance
By leveraging an equity framework and visual metaphors as conceptual tools, this report
helps extend current theorizations of “translation” and “currency” exchange to highlight new
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practices and opportunities for blurring research-practice boundaries in mathematics education.
Such a networked framing situates the domain of work on linking research and practice in a
broader sociopolitical context, a step toward theory development. By bringing these frameworks
together and promoting visualization of this scholarship, my intent is to make salient the often
invisible work of linking research and practice as a starting point for focused collective action. I
invite others to engage with the hypotheses that (a) visualization is a powerful tool for re-
imagining current research-practice connections, and (b) an equity lens highlights opportunities
for advancing theories and methods to grow the field. Such a reframing may help the field move
beyond a deficit orientation of gap gazing between research and practice toward a framework
that highlights systematic ways to initiate and sustain action.
The AERA leadership challenges the field to answer How can we unite with
practitioners, with scholars across other academic fields and disciplines, and with other citizens
beyond academia to strategically address complex social and educational problems?” (Harper,
Davis, Jenkins, Soodjinda, 2021, p. 1). This research contributes novel visualizations of
metaphors for linking research and practice that humanize the work involved in addressing
complex practices that cross institutional boundaries. The positioning of teachers as expert
participants and communicators challenges the status quo of power dynamics that may otherwise
isolate researchers (those who theorize, analyze, and interpret data) and teachers (those who
engage students in learning) in their separate work, without seeing the potential for sharing
currencies and growing from each other’s practices and perspectives through multi-faceted
translation efforts.
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Appendix: Bibliography of Sources for Conceptual Analysis
Arbaugh, F., Herbel-Eisenmann, B., Ramierez, N., Knuth, E., Kranendonk, H., & Quander, J. R.
(2010). Linking research and practice: The NCTM research agenda conference report.
Boerst, T., Confrey, J., Heck, D., Knuth, E., Lambdin, D. V., White, D., . . . Quander, J. R. (2010).
Strengthening research by designing for coherence and connections to practice. Journal for
Research in Mathematics Education, 41(3), 216-235.
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2017a). Making Classroom
Implementation an Integral Part of Research. Journal for Research in Mathematics Education,
48(4), 342 - 347. doi: 10.5951/jresematheduc.48.4.0342
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2017b). A Future Vision of
Mathematics Education Research: Blurring the Boundaries of Research and Practice to
Address Teachers Problems. Journal for Research in Mathematics Education, 48(5), 466-473.
doi: 10.5951/jresematheduc.48.5.0466
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2018a). Building and
Structuring Knowledge That Could Actually Improve Instructional Practice. Journal for
Research in Mathematics Education, 49(3), 238-246. doi: 10.5951/jresematheduc.49.3.0238
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2018b). Using Data to
Understand and Improve Students Learning: Empowering Teachers and Researchers Through
Building and Using a Knowledge Base. Journal for Research in Mathematics Education,
49(4), 362-372. doi: 10.5951/jresematheduc.49.4.0362
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2018c). Reconceptualizing
the Roles of Researchers and Teachers to Bring Research Closer to Teaching. Journal for
Research in Mathematics Education, 49(5), 514-520. doi: 10.5951/jresematheduc.49.5.0514
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., Cirillo, M., Kramer, S. L., & Hiebert, J.
(2020). Working Across Contexts: Scaling Up or Replicating With Variations?, Journal for
Research in Mathematics Education, 51(3), 258-267. Retrieved May 14, 2020, from
https://pubs.nctm.org/view/journals/jrme/51/3/article-p258.xml
Farley-Ripple, E., May, H., Karpyn, A., Tilley, K., & McDonough, K. (2018). Rethinking connections
between research and practice in education: A conceptual framework. Educational Researcher,
47(4), 235-245.
Gersten, R., Vaughn, S., Deshler, D., & Schiller, E. (1997). What we know about using research
findings: Implications for improving special education practice. Journal of Learning
Disabilities, 30(5), 466-476.
Goos, M., & Geiger, V. (2006). In search of practical wisdom: A conversation between teacher and
researcher. For the Learning of Mathematics, 26(2), 33-35.
Gore, J. M., & Gitlan, A. D. (2004). [Re]Visioning the academic-teacher divide: Power and knowledge
in the educational community. Teachers & Teaching: Theory and Practice, 10(1), 35-58.
Heid, M. K., Larson, M., Fey, J. T., Strutchens, M., Middleton, J. A., Gutstein, E., . . . Tunis, H.
(2006). The challenge of linking research and practice. Journal for Research in Mathematics
Education, 37(2), 76-86.
Herbel-Eisenmann, B., Sinclair, N., Chval, K., Clements, D. H., Civil, M., Pape, S., . . . Wilkerson, T.
L. (2016). Positioning mathematics education researchers to influence storylines. Journal for
Research in Mathematics Education, 47(2), 102-117.
Hiebert, J. (2000). What can we expect from research? Mathematics Teacher, 93(3), 168-169.
Kilpatrick, J. (1992). A history of research in mathematics education. In D. A. Grouws (Ed.),
Handbook of research on mathematics teaching and learning (pp. 3-38). New York, NY:
Macmillan Publishing Company.
Langrall, C. W. (2014). Linking research and practice: Another call to action? Journal for Research in
Mathematics Education, 45(2), 154-156.
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Samaras, A., & Roberts, L. (2011). Flying solo: Teachers take charge of their learning through self-
study research. Learning Forward, 32(5), 42-45.
Silver, E. A. (2003). Border crossing: Relating research and practice in mathematics education. Journal
for Research in Mathematics Education, 34, 182-184.
Silver, E. A., & Lunsford, C. (2017). Linking research and practice in mathematics education:
Perspectives and pathways. In J. Cai (Ed.), Compendium for research in mathematics
education (pp. 28-47). Reston, VA: National Council of Teachers of Mathematics.
Van Zoest, L. R. (2006). Introduction to the 9-12 volume. In L. R. Van Zoest (Ed.), Teachers Engaged
in Research: Inquiry into Mathematics Classrooms, Grades 9-12 (pp. 1-18). Greenwhich, CT:
Information Age Publishing.
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Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2017a). Making
Classroom Implementation an Integral Part of Research. Journal for Research in
Mathematics Education, 48(4), 342 - 347. doi: 10.5951/jresematheduc.48.4.0342
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2017b). A Future
Vision of Mathematics Education Research: Blurring the Boundaries of Research and
Practice to Address Teachers Problems. Journal for Research in Mathematics Education,
48(5), 466-473. doi: 10.5951/jresematheduc.48.5.0466
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2018a). Building and
Structuring Knowledge That Could Actually Improve Instructional Practice. Journal for
Research in Mathematics Education, 49(3), 238-246. doi:
10.5951/jresematheduc.49.3.0238
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2018b). Using Data to
Understand and Improve Students Learning: Empowering Teachers and Researchers
Through Building and Using a Knowledge Base. Journal for Research in Mathematics
Education, 49(4), 362-372. doi: 10.5951/jresematheduc.49.4.0362
Equitable Research-Practice Communication Fonger, N. L.
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Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2018c).
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10.5951/jresematheduc.49.5.0514
Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., Cirillo, M., Kramer, S. L., & Hiebert,
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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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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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In 2005, the NCTM Research Committee devoted its commentary to exploring how mathematics education research might contribute to a better understanding of equity in school mathematics education (Gutstein et al., 2005). In that commentary, the concept of equity included both conditions and outcomes of learning. Although multiple definitions of equity exist, the authors of that commentary expressed it this way: “The main issue for us is how mathematics education research can contribute to understanding the causes and effects of inequity, as well as the strategies that effectively reduce undesirable inequities of experience and achievement in mathematics education” (p. 94). That research commentary brought to the foreground important questions one might ask about equity in school mathematics and some of the complexities associated with doing that work. It also addressed how mathematics education researchers (MERs) could bring a “critical equity lens” (p. 95, hereafter referred to as an “equity lens”) to the research they do. Fast forward 10 years to now: Where is the mathematics education researcher (MER) community in terms of including an equity lens in mathematics education research? Gutiérrez (2010/2013) argued that a sociopolitical turn in mathematics education enables us to ask and answer harder, more complex questions that include issues of identity, agency, power, and sociocultural and political contexts of mathematics, learning, and teaching. A sociopolitical approach allows us to see the historical legacy of mathematics as a tool of oppression as well as a product of our humanity.
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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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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).