Abandoning Hope? What Mathematics Education Researchers Say About Why They Do What They Do

Abstract

A research study was designed to understand how a group of mathematics education researchers describe their scholarly work—why they do it and how their research relates to a specific conceptualization of culturally responsive pedagogy (CRP). In the analysis of interviews with 17 international mathematics education researchers, we distilled the scholars’ descriptions of their hopes for their scholarly action. The themes of these distillations include seven imperatives for research action: ‘communicate’, ‘investigate’, ‘make’, ‘change and move’, ‘position’, ‘humanize’, and ‘reflect’. Drawing on the interview data, each of these action themes is elaborated on and synthesized into action-focused questions (AFQs), intended as prompts for like-minded scholars to use in reflection on and choices for intentional scholarly action. Our rationale for focusing on why scholars do what they do is grounded in our claim that mathematics education research could have a greater impact on the practices in schools if researchers focused more explicitly on unpacking the why of their research.

1. Introduction

This paper builds from interviews with scholars who work in mathematics education contexts that we have identified as having interest in culturally responsive pedagogy (CRP), and its related sub-fields. The interviews were developed to extend and explore ideas emerging from a course offered in a teacher education program at a [country] university. Entitled Culturally Responsive Pedagogy (CRP) in the Mathematics Classroom, the course content drew on scholarly research focusing on many different but related areas (or sub-fields) of mathematics education—culturally responsive pedagogy [CRP], Indigenous education [IE], critical mathematics [CM], ethnomathematics [EM], social justice [SJ], language diversity [LD], and equity-based research [E-b]. In fact, the content of this particular course was structured around the idea that the many intersecting areas of research named above (IE, CM, EM, SJ, LD, E-b) can be seen to shape CRP (Nolan, 2020). In other words, CRP was presented in the course as the umbrella term, with research in each of the other areas (or sub-fields) residing under this umbrella and serving to shape one’s understanding and practice of CRP. This is the conceptualization Kathy (first author) used for her course, and ultimately for the design of the research study on which this paper is based. As each of these “sub-fields” is a fully researched area on its own, emerging from diverse traditions and contexts, we do not, in this paper, focus on providing our own definitions and perspectives on each, but instead allow the scholars’ voices to be heard.

While the aim of the overall research study was to explore a reframing of school mathematics and a new framing of culturally responsive pedagogy (CRP) through disruptive pedagogies in teacher education, we focus here on the parts of the research interviews in which the scholars talked about their hopes for their research—their explanations of why they do what they do in their research and also more widely in their scholarly roles. Specifically, our focus here is on scholars’ responses to the two interview questions: (1) What change are you looking for through your (scholarly) work (your end goals, purposes for your research, desirable outcomes)? (2) What are you hoping others (academics, teachers, etc.) will learn from your (scholarly) work? Our intent is not to criticize, assess or taxonomize their hopes. Rather, we aim to give prompts for action to other scholars, particularly scholars with interest in cultural responsivity in mathematics education, but this will likely be useful for others too. Thus, we will address you, our readers, in the second person: we address you as a scholar interested in thoughtful action. And we will use the first-person plural often too, recognizing that we (the authors) are part of your group, learning together from the experiences and reflections of other CRP scholars.

In our analysis we have distilled the scholars’ reflections and identified distinctions in their reasoning and values, but this distillation and distinction making is aimed at developing repertoires for action, not for comparing one person’s actions or explanations against another’s. Indeed, we are aware that the scholars we quote only told us some of their reasoning for their actions, and in other contexts may talk about their actions and their reasons for their action differently. Our title is intended to be provocative too: we encourage you to abandon wistful hope, and instead move towards intentional, reflective action.

2. Literature and Theorization

Several studies have been identified that focus on what mathematics education researchers (MERs) do (see, for example, Bakker et al., 2021; Dubbs, 2021; Herbel-Eisenmann et al., 2016), though questions about why they do what they do are not generally reported on. For instance, Dubbs (2021) identified his goal of “disrupting assumptions about what has been and can be done in the name of mathematics education research” (p. 16) through the use of citation networks focused on the publications in two specific journals (JRME and ESM). He conceptualized bubbles as similar to research topic clusters, suggesting that these bubbles “embody our hopes for the field, the areas we want to know more about, that we seek to understand” (p. 35). In other words, his focus is primarily on what MERs do. In Bakker et al.’s (2021) survey of MERs on what they value for the future of mathematics education research, eight themes were identified along with a number of challenges that the authors suggest addressing. Most closely connected to the research informing our paper was the theme they named as “equity, diversity, and inclusion”, which they describe as a “triplet to cover any topic that highlights these and related human values such as equality, social and racial justice, social emancipation, and democracy” (p. 9). Again, their research is primarily concerned with describing what MERs do. With a slightly different focus, on what mathematics education researchers can perhaps do better, is Herbel-Eisenmann et al.’s (2016) study that uses positioning theory to explore “plausible action paths for mathematics education researchers, individually and collectively, so that ultimately mathematics education research will inform decisions, policies, and actions” (p. 110). To achieve this influence, the authors offer suggestions for MERs “to strengthen relationships and to shift positionings, storylines, and communication acts” (p. 114). Suazo-Flores et al. (2023, 2025) have a different focus as they conduct a study of how MERs do their work; specifically, they review and highlight research where MERs are working in interdisciplinary research groups, toward new and evolving ways of knowing about their field. Thus, to date, studies concerning the work of MERs have focused on what they do in their research and how they do it, with the question of why being under-explored. We claim that mathematics education research could have a greater impact on the practices in schools if MERs’ focused more explicitly on why we do what we do in our research.

In the study’s interviews with MERs, they were asked about outcomes and hopes for their scholarly work. There are various theorizations of hope, which we find useful in other contexts (e.g., Kim et al., 2021; Matthews et al., 2021), but in this case we take the unusual approach of not theorizing the central focus of our study. In fact, with the explanations of the scholars as our focus, we foreground their conceptualizations of hope and action, not our conceptualization. Nevertheless, we will say that our interest is in reasoned action that is related to hope, not a general sense of optimism. Optimism is often seen as synonymous with the word hope, but hope can mean a range of things.

3. Methodology

As noted in the Introduction, this study was designed to follow up on a teacher education course on CRP in the mathematics classroom. The course was shaped by a belief that dominant, western forms of mathematics need to be disrupted/decolonized through critical and culturally responsive approaches to engaging with students, prospective teachers, and practicing teachers. A distinguishing feature of the course, and one that led to the research study being written about here, was that the course content was structured around a conceptualization of CRP that included many different but related areas (or sub-fields) of mathematics education (IE, CM, EM, SJ, LD, E-b). In this conceptualization, CRP was presented as the umbrella field for all of the other sub-fields (see Nolan, 2020).

Given that this conceptualization is not necessarily the only one possible, questions about the structure often came up from students in the course, who sometimes grappled with ideas around how to categorize and label the different research texts being read and discussed in class. Students commented on how the lines between each area were blurred due to the noticeable intersections and overlaps among the sub-fields. This led to the conceptualization of the research study on these sub-fields and the scholars identified as working within them. Approximately 60 international mathematics education scholars were initially identified as engaging in research associated with CRP and/or one of the relevant sub-fields. It was not possible to create an exhaustive list of such CRP scholars so these 60 were identified through personal knowledge of their publications, conference papers, and so forth, as well as because they were included on the course reading list. Obtaining contact information for each of the 60 proved somewhat challenging, and time to conduct 60 interviews was not available, so once contact information was obtained for 30 of them, they were each contacted while the rest were not. That is, to keep the scope of the study manageable, a convenience sample of 30 scholars was selected and each scholar was invited to be part of the study, with 20 agreeing to participate in a research interview. Since conducting the interviews (in 2021), one scholar withdrew all data from the study while two others chose not to have their data included in the analysis for this paper. Thus, this paper is based on interview data from 17 CRP scholars. The participating mathematics education scholars (who we will primarily refer to as the CRP scholars from this point forward) came from various countries, including Canada, United States, Brazil, New Zealand, Australia, Malawi, and Greece.

The interview questions were constructed using the same conceptualization of CRP and the sub-fields as was used in the CRP course. These invited scholars participated in an interview where they were asked a series of questions in direct relation to their research. For example, they were asked how they would describe/position their research with/in these given sub-fields (most likely and least likely sub-field descriptors); what theories and methodologies they draw on for their work; what change (end goals, purposes, outcomes) they are looking for through their scholarly work; and what they are hoping others (academics, teachers, etc.) will learn from their scholarly work. This paper shares findings from an analysis of these final two questions.

Distillations of Researcher Action

Our interview analysis included three stages. First, we worked with anonymized transcripts of the interviews, focusing on the CRP scholars’ responses to the questions about the change (end goals, purposes, outcomes) they are looking for through their scholarly work and about what they are hoping others (academics, teachers, etc.) will learn from their scholarly work. On the research consent form, some of the participant scholars chose to have their words anonymized while others did not. We use pseudonyms for the anonymized scholars, and we italicize them to distinguish them from the CRP scholars not choosing anonymity. There were four anonymized CRP scholars, identified here as Elaine, Margaret, Morgan and Steve. The remaining 13 scholars not choosing anonymity were: Andrew Brantlinger, Anna Chronaki, Annie Savard, David Wagner (second author), Cris Edmonds-Wathen, Cynthia Nicol, Edward Doolittle, Gale Russell, Nancy Chitera, Ole Skovsmose, Rico Gutstein, Robin Averill, and Ruth Beatty. David’s data were not included in this analysis, as he joined Kathy to work with the anonymized data for this paper.

From this point forward, we refer to the non-anonymized scholars with their given names only. Our analysis does not claim a full understanding of each scholar’s hopes and actions, as our intent is to identify action repertoires, so we try to position the anonymized and non-anonymized scholars similarly.

Because we wanted to focus on action, we looked for verbs (action words) that had the scholar themselves as the subject, either explicitly or by implication. We distilled each instance into an action—either the verb alone or including an object of action if necessary for clarity. For example, when Anna said, “it’s not only their data as such, but the kind of discourses that we try to create as researchers”, our distillation was “create discourses” because it was clear what Anna saw herself (and other scholars) creating. When she shared “we strive for something, we don’t do it just for, you know, just to publish a paper”, the distillation was “strive”; what follows the verb in this case seemed relatively unimportant. The focus seemed to be on effort. In our analysis, we each worked independently to identify the distillations, after which we compared our lists. Where we had different distillations, we found that it was insightful to discuss our reasons for distilling as we did, but we usually kept both distillations because our goal was to identify repertoires, not to make a perfect set of distillations for each scholar.

After developing these distillations, we grouped them into categories for elaboration. We sought a list of categories that would include all (or most of) the distillations, and that had categories with clear enough distinction from each other. We each made a draft set of categories and then discussed them to negotiate a set that we could agree on. For the best fit to our distillations, we labeled the categories as imperatives because we prefer that you see them as possibilities for your action—we want to see them as possibilities for our action too. The categories elaborated on in the next section are, in order of presentation, as follows: “communicate”, “investigate”, “make”, “change and move”, “position”, “humanize”, and “reflect”.

For each category, we read the distillations that fit that category in the context of the full transcript data so as to elaborate on the possibilities for that kind of action, based on what CRP scholars said. In this elaboration stage, we also identified AFQs: action-focused questions. The questions arise from the elaboration of the category and they aim to inform reflective action for other scholars wishing to act in the ways described in the category. We address the uncategorized distillations in the final section of the paper, as we reflect on yet further possibilities for scholarly action. The next section elaborates on each of the action categories.

4. Researcher Action

Here, we elaborate on the six of the seven categories of distillations (communicate, investigate, make, change and move, position, and humanize), and corresponding sub-categories, that constitute our findings as we analyzed scholars’ responses to the questions of what change (or end goals, outcomes) they are looking for through their scholarly work and what they are hoping others will learn from their scholarly work. We address the remaining category (reflect) in our discussion section.

4.1. Communicate

The CRP scholars in this project have said that their actions include communication. Verbs we grouped into this action group include describe, document, elaborate, emphasize, focus, prioritize, promote, publish, share, speak, and write. These and other verbs may be used to describe the communication of scholars. In our elaboration of the CRP scholar reflections, we make distinctions based on audience, to help us all (re)consider our repertoires for communication.

4.1.1. Publish: Addressing the Field

The values of the academy, as enforced through hiring and promotion, compels any scholar to address other scholars through academic publications. Writing can be motivating; as Ole said, “I feel an enormous drive. And every time I finish a paper, I want to think of something more.”

When you write, you think of the people you aim to address and what you want to say to them. In addition to thinking of audience—the people you face—you can think about the people you stand with when you write. When Ole talked about the compulsion to write, he was thinking about how he is part of a community with diverse experiences, addressing the field of mathematics education. He said, “I write together, but I also write much alone, […] it’s inspired by interaction.” But, as he noted, it can also inspire interaction. He gave an example: “I have published this paper about landscapes and investigation, (…) it’s a book with many contributions, there are 18 chapters, a different group of authors in all combinations.”

When you write for the field, it also matters how you write. For example, Cris said “you’ve got to say what you’re doing with the language (…) how can you talk about a student’s verbal error in a certain language, and then just translate the data into English and not mention even the language that the data was collected in?” (Cris’ ideas about her goals regarding language are further elaborated on in Section 4.3). Cris’ caution reminds us that you have choices about which languages you publish in, and which journals. Choices like this impact the audiences you reach, and these choices also impact whose voices are considered most normal or mainstream. You might choose publications that will be read by the scholars most like you or you could choose to write for scholars further from the CRP constellation of theories.

Thus, when you write for the field, you can think about it as heterogeneous, which can motivate you to make choices about the people you address—the people you want to provoke or serve. Elaine reminded us that the writing choices made by scholars are not all relating to publication. You also make choices about whose needs are being served when you decide which peer review invitations to accept and which academic promotion files to assess. Your choices can impact who advances in the field: “my priority for letters for tenure and promotion and reviewing those cases which are really time intensive are almost all for women and scholars of colour. I hardly ever write them if it’s somebody who’s emailing me who’s a white male scholar.”

4.1.2. Diversify Audience

In addition to academic publishing, CRP scholars have other audiences in mind. Margaret reflected: “Who are the people I’m sharing it with? Am I sharing it with general public? Am I sharing it with scholars in the field like you? Am I sharing it with a teacher someday?” A number of CRP scholars talked about addressing teachers directly. Robin said “I can try and make a difference here. […] A lot of the work that we publish, we focus on things for teachers in New Zealand to make a difference for students in New Zealand, which is not always what the university wants, of course.” She continued, “they want high ranking publications which our teachers don’t even know about and so it’s treading that line of trying to do both.”

Margaret’s question about the people she sees herself sharing the research with pushes us to envision an extended list of possible audiences. You may feel compelled to look for ways to address a wider audience because school leaders and the general public have a voice in what teachers do. If these people do not understand the need for the changes mathematics teachers are making, they will erect resistances. Margaret said, “I have not written a single piece for […] just plain folks. We have to be so ambitious, even so competitive that we cannot afford to write for just plain folks.”

As with academic audiences, your choices of what to focus on are important. Ruth described how such choices should be responsive to the needs of the particular people you address: “it’s different for each teacher that we work with. For some teachers, there needs to be a really explicit focus on anti-racist education. For other teachers, there needs to be a really explicit focus on humanizing the interactions that they have with their students.” Ruth’s stance underlines the importance of listening to the people you address. Margaret talked about this too: “Can I go to a place where I can really listen to what they are talking about, people who have not been successful in formal education?”

4.1.3. Focus the Message

Whether you write for academic or other audiences, your choices about what to focus on matter. Sometimes the CRP scholars interviewed were not clear on who they had in mind for audience, but instead, when using the action verbs related to communication, they focused on what they communicated. Ruth spoke about “prioritizing Indigenous voices and […] making math relevant and meaningful to Indigenous students and to the community partners.” She clarified this means “prioritizing them to the same level that we prioritize Western knowledges.”

Steve’s focus on Indigenous voices emphasized the need for relationship, and awareness of the people and communities we stand beside. Steve pointed to the availability of local resources and so he cautioned against generalizing:

I want teachers to see that there are lots of resources, that cover a lot of ground, in what are some local examples of Indigenization. Because I think one of the problems is that it’s a very broad, somewhat vague, term that I think doesn’t really help with […] what it means to be Cree or Dene, Saulteaux, Dakota. I think sometimes just being too general, you lose the nuances of actually being in relationship and actually emphasizing and drawing out those enduring aspects of culture.

4.1.4. Action-Focused Questions (AFQs) for Communicating

• Who can change things? Are you communicating with that audience?
• Whose voices do you (want to) prioritize in your communication?
• How do your communication choices align with your audience and lift up the intended voices?

4.2. Investigate

Another action group we identified in the distillations is the imperative to investigate. CRP scholars said that they investigate phenomena. Verbs we grouped into the category include the following list, which you and other scholars may consider using to describe your investigative action: ask, learn, listen, look for, and study. Choices in investigative action may be focused by asking what the investigation means for you, yourself. We elaborate on the investigative action through two sub-categories: the first in connection to what the researcher learns from the research and the second one focused on becoming a better researcher.

4.2.1. The Researcher as First Learner

To elaborate on the investigations that CRP scholars describe themselves doing, we notice that they often see themselves as learners—the first learners from their research. They tend not to describe this learning as investigation or in terms of research questions but rather in terms of relationship. Indeed, the elaborations from the scholars seem to resist the idea of their action being investigation. Thus, these acts of learning align with the acts of positioning described in Section 4.5; this is learning underpinned by choosing the right relationships, perhaps with the assumption that they learn in those relationships.

Continuing from what Margaret said in Section 4.1 about listening to people, she said she thinks about the examples she uses in her writing to address the experiences of people who have not been successful in formal education: “Unless I do that, I cannot be a scholar myself. I have to be comfortable in both worlds, so that I can communicate, honestly.”

Ruth foregrounded her own learning as a necessary part of bringing learning to others: “I’m not an Indigenous scholar or an Indigenous education scholar. So for me, (…) this has been a huge learning curve and it’s done all in partnership so that I’m learning as much as anybody else (…) more so I think most of the time.”

One of the questions asked of the scholars in this study is what they want others to learn from their work. By looking at the context of their responses within the larger set of their reflections, we take some of their responses to this question as statements about what they themselves have learned in their research. You may also aim to learn in the way the scholars have said they learned. Edward, for example, said he has been learning the importance of listening to Indigenous people: “I think one thing I hope that my colleagues can learn is the importance of listening to Indigenous people.” We note the special significance of Edward’s learning as he is an Indigenous person himself.

We see learning to listen as a general disposition of openness to learning. Some of the scholars in this study described specific things they seek to learn, beyond learning to listen. In other words, they described what they learn with their own listening. Cris said she wants “to know more about how doing and learning maths in different languages—how we think differently when we do (…) that.” Nancy described how she is learning to see language differently: “[instead of] looking at the language as the resource, [I research] language as a socialization tool in a mathematics classroom, in a multilingual classroom,” in contexts where students are “socializing in that particular language, they are learning the mathematics.” Morgan, pointed out that her work in other (Indigenous) cultures, led her to learn about her own culture: “When I worked on Indigenous communities in [country], one of the things that I learned was, I learned about my own culture.”

4.2.2. Becoming a Better Researcher

While learning from their research, the CRP scholars in this study also noted the importance of learning how to be a better researcher—in other words, learning how to learn better. Ruth saw hope in developing skills and experience with participatory research: “I really want to learn how to work together with teachers to support equitable practices to make schools and classrooms more equitable places for children.” Rico pointedly listed things that researchers need to learn. Responding to “What do you hope others will gain from your scholarly work?” he offered the following, which we take as a way of saying that he himself has been learning and continues to want to learn: “One: that [critical math education] is possible. Two: that it’s challenging. Three: that you have to study your own practice. Four: that you have to be connected to the social movements that you’re in the communities in which are involved. And five: that you have to embrace what is the larger project that we’re involved in, why are we doing this work.”

4.2.3. Action-Focused Questions (AFQs) for Investigating

• What do you seek to learn with your research?
• How do you decide what to investigate in your research?
• From whom can you learn?
• How do you know what you need to learn?
• How do you develop situations/conversations that open you up to learning things you didn’t know you need to learn?

4.3. Make

Another action group we identified in the distillations of data on hopes and goals is to make things. In this category, we identified participant quotes containing the verbs create, make, build, design, develop, and come up with. Here, we discuss the various ways these verbs were elaborated by the CRP scholars and the significance in doing so. We organize the elaboration around the imagined question “what do you make?”

We also wondered whether certain making verbs are used for certain kinds of making. When it came to using the word create, the CRP scholars referred to creating discourses, spaces, tools, and revolutionary things. Regarding the word make, we noticed participants interested in making arguments, making more equitable spaces in schools and classrooms, making a difference, and making the world a better place. While the words create and make were more prevalent in the scholars’ discussion of their hopes for their research than other action words focused on making things, we also heard some scholars speak about design and building—particularly designing research better, developing community teachers as well as developing the language of mathematics—and a desire to build up, build something, and build a knowledge base.

4.3.1. Making a Better World

Anna expressed that, for her, research is not just about data and publishing a paper but about “the kind of discourses that we try to create as researchers.” She clarified that this means striving for something more, something that “will make the world better” for students. She referred to this as “clearing the path” for those who want to enter our research field, and she used the metaphor to explain a “meticulous and strategic way of working” (Section 4.5.1 has the fuller quote). Anna spoke about how the sub-fields of this CRP research “become present in anything we are doing all the time,” including discourses of gender, of language, and of culture. Anna drew on Althusser’s language of education as a state apparatus, which sets forth a specific curriculum and set of policies, but she noted that “people from below, who also have power and the potential to do things, are creating revolutionary things from below.”

Ruth used “mak[ing] the world better” when referring to the goals of her research. Making the world a better place, she noted, is done by “disrupt[ing] the inequities that we see”. Her aim is “to learn how to work together with teachers to support equitable practices to make schools and classrooms more equitable places for children… and not just for the sake of learning more math”. Along these same lines, Annie commented: “I want to make a difference.” For her, this means emphasizing sustainability of earth’s resources and teaching students to make good choices. She described a research project in Africa where she was working closely with a local team of teachers: “So, it’s really a team. And I don’t want to impose anything. I really want to co-construct, otherwise it’s still top down, it’s still colonialist.”

Gale shared her thoughts about how mathematics is too-often discriminated against, and that people have limited ideas of what it can be and what it can offer, thus “creating inequities in society.” She referred to this form of discrimination as subject-ism, in a manner similar to other -isms such as sexism, ageism, racism. Her goal is “to try to tackle the subject-ism of mathematics—of there being only one way of thinking about things mathematically.”

4.3.2. Self Making

While making the world a better place was expressed as a goal by several scholars, Morgan had a specific twist on this, indicating that her research is about making herself “a better human being”. Simply put, Morgan noted: “I think that my research is predominantly for me… I need to learn. I need to be changing in order to be a better human being on this planet.” When asked how she positions herself in relation to the keywords and sub-fields associated with this research, Morgan reflected, “it’s all about me and it’s all about me being a better human being so that somebody else might get something better… something else better for learning.” It is worth noting that this excerpt from Morgan appeared in multiple distillation categories. She saw herself as learning to be better (which appears in Section 4.2 on investigation), as changing herself (thus appearing in the Section 4.4 bundle) and as making herself a certain way (this category). Not surprisingly, this focus on what it is to be human will come up again in Section 4.6 on humanizing.

4.3.3. Making Better Conceptions of Mathematics

Elaine spoke about creating spaces that “recognize youth and children’s humanity” with her reasoning being that “putting youths’ humanity ahead of the adults is imperative to future generations”. She believes that “issues of power and authority and voice and all those kinds of positionings are things that are manifestations of recognizing humanity or making other kinds of choices.” In relation to this goal of recognizing humanity, Elaine spoke of working against the ideas of some math teachers “who think math has nothing to do with the people, ‘like oh, we can’t talk about these justice issues because we’re just doing math, and it’s not cultural, it’s not language based’—all those myths that go with what mathematics is.”

Relating to Elaine’s comments on how mathematics is constructed (conceptualized), Cynthia expressed her view that “mathematics itself is very powerful (…) it’s an amazing conceptualization and abstraction to be able to create (…) and predict (…) and build” but that it also has the power “to make people feel as if it’s a very exclusive area, and that we can’t do it, or it doesn’t belong, or it’s not a part of who we are.” Cynthia said she seeks to transform this kind of thinking so that people can see how mathematics is “a study of patterns and we’re always doing it”; in other words, everyone can (and already does) participate in mathematics. Annie also referred to the power of mathematics, sharing that her hopes rest in “empowering people [and] using mathematics as a critical tool to be a citizen”.

Ruth claimed (as noted in Section 4.1) that although she is not an Indigenous scholar, she can make her contribution as a mathematics education researcher toward “making math relevant and meaningful to Indigenous students and to the community partners.” Similar to both Elaine and Cynthia’s comments, Ruth shared how she works against the idea that “math is a proxy for being smart” and toward “the idea that actually everybody is a mathematical thinker, a deeply complex mathematical thinker.” She described “what happens to the partners we’re working with, to the non-Indigenous teachers too, who are blown away by the math that comes out of this work” as fascinating and profound. She added that it is “quite transformational what happens to folks when they start to see themselves from a different viewpoint” which, we claim, relates to seeing and constructing mathematics differently.

4.3.4. Making Strong Communities to Support Students’ Learning

Andrew’s perspective on making things connects with Ruth’s goal of making math relevant and meaningful as well as the ideas put forth by Cynthia and Elaine around a goal of demonstrating that everyone can participate in mathematics and mathematical thinking. Inspired by the work of Danny Martin, Andrew said he tries “to make arguments for bringing community-based teachers” into the schools. Andrew suggested that developing community teachers helps to work against the deficit view that many students and parents have of their culture—a view often expressed as “they’re coming from the same culture of poverty, so why would you ever put those teachers into classrooms”. Andrew noted that his focus has shifted from “fighting the math curriculum [because] that’s something I don’t see changing anytime soon” toward getting “people in schools who are going to stay in schools”. Simply put, Andrew stressed that “kids need to have teachers who are committed to them.” He aims to make a difference by showing the importance of “trusting the community and parents to make the right decisions for what their kids need ultimately.”

When it comes to focusing on local contexts, Robin shared that she aims to “make a difference for students in New Zealand,” her specific context, for two reasons: so that students “in schools learn well and for their cultural practice to be normalized”. Robin observed that most of the work she publishes is focused on the needs of teachers and students in New Zealand which she clarified as being underappreciated by universities (as quoted in Section 4.1).

4.3.5. Not Building, Learning to Live Within

The action word build was used by only two scholars and in quite a different manner in each case. Edward was critical of European- and Western-based cultures who are always trying “to change the world and one way to do that is to build the boxes that we live in”. This, he noted, contrasts with Indigenous cultures who have “the ability and the interest in dealing with reality, as it is, rather than trying to change it.” He noted, “we can build whatever box, but eventually we’re going to face issues like climate change, like energy security, and so on… so, alternatives to building a box are going to become more and more valuable.”

Ruth, on the other hand, in stating that “what matters the most to me is the impact [of my research] on teachers and students, and that we’re working together,” shared the “hope that the analytic and methodological tools that I use are useful for others so that we can continue to build a knowledge base that will reach across multiple diverse contexts.” We note that their comments do not necessarily contradict each other. Referring back to what Elaine, Cynthia and Ruth said (quoted in Section 4.3), it matters what the knowledge base is. The knowledge base could support the kind of thinking that Edward described, or it could follow the well-worn and destructive path that he warned against.

4.3.6. Building Language Repertoires

Cris and Nancy both commented that they strive to make language considerations a more significant focus in their research and in research by others too—that is, building language repertoires for mathematics students, for mathematics educators, and for mathematics education researchers. Cris observed that research is often published where the original data is in one language, and the paper written in English, but the authors do not even let the reader know that they have translated their data into English for publication. This, according to Cris, serves to “make that process [of translation] invisible” which does “a huge disservice” to research and practice around language diversity. She offered that if she can “help promote this understanding that the language matters, then people will have to treat their language data for mathematics education research better”. For her, this also means that researchers should “be able to design their research better (…) to conceptualize the impact that a difference of language might have in their research questions”.

Nancy’s concerns about language were more at the level of teacher education, where she “wants to see students develop a mathematical language” that reflects that of mathematicians. In her view, “the students should be able to develop at the end of the day… the right mathematical language; they should be able to talk mathematically.” She continued: “And not only developing their mathematical language, but that they should be able to understand the mathematics and be able to bring the mathematics close to them, so that they can understand and be able to apply it.” Nancy added that, presently, she focuses her research on how to use tools to “build up”, “to develop” teacher education students’ mathematical language. In fact, Nancy extended this focus toward noticing a significant theoretical gap in teacher education programs—instead of teacher education programs “trying to come up with theories on how to teach in grammar schools,” she said more focus is needed on both contexts; that is, a focus on “coming up with theories that should help the teacher educator to teach and prepare mathematics teachers”.

4.3.7. Making Sense

Finally, it seems appropriate to close this account of making things by drawing on Cynthia’s and Elaine’s data. Elaine commented about making sense—making sense of the world and making sense of research funding. Cynthia offered that “living mathematically means that we’re always engaged in trying to make sense of noticing things and how they connect and how they’re related or how they aren’t. And if we didn’t do that we wouldn’t survive.” She noted: “I think part of my goal will be to kind of transform that thinking” for math students and math teachers.

4.3.8. Action-Focused Questions (AFQs) for Making

Focus in this distillation category seems to be on creating or making things that are currently being noticed as missing, absent or inadequate. Thus, our action-focused questions encourage you to reflect on exactly that:

• What is missing, absent or inadequate in the field (and sub-fields) of CRP?
• What is missing, absent or inadequate in math students’ experiences of learning mathematics?
• With your making, are you building or rebuilding? (i.e., have we lost the missing aspects, or did we never have them?)
• Could everyone (even a subset of all mathematics educators) ever agree on what it means to “make the world a better place?”
• Does your scholarly action require mathematics educators (or a subset) coming to agreement? Does your scholarly action rest on the resilience of others who disagree with you?

4.4. Change and Move

Another action group identified in the interview data around the question of hopes or end goals for CRP scholars was that of change and movement. Initially, we distinguished between movements associated with discourses (with verbs including bring, disrupt, inspire, lead, normalize, nurture, push, reform, steer, strategize and transform) and other movements associated with physical, albeit metaphorical, moves or changes (with verbs including give, move, offer, play, tackle and use). As we gathered evidence of these changes/movements in the data, we found the lines blurred between them. Thus, here we refer to these actions together as we describe the scholars’ hopes and goals around change/movement.

To discuss this action group, we divide the defining verbs into three sub-groups. The first includes language such as disrupt, steer, push, move, decouple, fight, and tackle as they all, in one way or another, suggest a change in direction by abrupt or strongly persuaded means, perhaps even an aggressive-sounding action. The second group includes actions that could be considered gentle movements which are not necessarily about sudden or abrupt moves as compared to the words in the first sub-group; these second sub-group action verbs are nurture, offer, bring, give, inspire, play, and lead. We note that the shades of intensity associated with any one of these verbs likely vary according to the person using or reading them—the verbs do not have an objective level of intensity. We are fully aware that each scholar speaks from their own experiences and practices within their own context, and that this context may be fraught with norms around acceptable use of ‘stronger’ or ‘gentler’ language. We remind you (and ourselves) that, in this paper, we can present only a snapshot of each participant’s views; our hope in doing so is to offer a range of practices/actions toward providing readers with insight into repertoires for action. The point is not to compare the intensity of the scholars, but rather to guide us to consider a range of possible intensities. As noted in our methodology, our intent is not to compare scholars: we do not want to say one person is more subtle than others. Rather, the intent is to identify repertoires for action, so these two categories prompt us to think about our own choices about how hard we push change. The third sub-group are action words that we often hear in education and management circles—words that have varied uses and meanings in conversation, such as reform, transform, strategize, and normalize.

4.4.1. Strong Persuasion

In the first sub-group, we read about actions directed toward students, communities, mathematics, other scholars and self, with verbs including disrupt, steer, push, move, decouple, fight, and tackle. In a focus on students, Ruth declared that her goal is to “disrupt the inequities we see.” She elaborated that she wants “to learn how to work together with teachers to support equitable practices to make schools and classrooms more equitable places for children. And not just for the sake of learning more math.” Ruth said that an equitable space is key, where students can understand themselves as “a mathematical knower and doer and thinker” but also as someone with agency and the opportunity to “make the world a better place.”

Andrew aims, in his scholarly work, toward building greater trust in communities and in teachers from the communities by “mak[ing] arguments that will support the community base” and that will counter the “pushback” from so-called experts and academics who perpetuate “a deficit view of their culture” as they seek to hire teachers from outside the communities. Also referring to pushback, especially on matters related to Indigenous culture and the classroom, Steve spoke about resources for a course he teaches on Indigenous education, and how he believes “teaching these types of courses will get pushback from some teachers.” Steve said his hope or “end goal is that there’s enough resources that teachers can go ‘oh yeah, I can just use this in my class’.”

Moving outside of the realm of classroom spaces and into collegial research spaces, Elaine commented that her goals have “shifted over time” such that her focus now is on “supporting other people to do the work they want to do” and, for her, this means “a different way of steering the field (…) making sure different kinds of work gets funded.” She said she aims “to continue pushing the boundaries in what constitutes research in math education” and to “keep pushing researcher positionality.” Elaine holds out hope that her efforts to make a difference in this area “might at least help other white math teacher educators think more about issues of race and racism and ideology.”

In claiming there is a lack of movement around problems in mathematics education, Andrew reflected on what problem is best for him to work on “because, I think, you know people smarter than me were working on this [math curriculum reform] for 50 years and it hasn’t really moved the needle a whole lot and (…) I also don’t believe that we should be teaching as much math as we do”. He continued: “I’m not convinced by our own kind of official rhetoric around math, and so I think, on the whole, what I’ve concluded is maybe it would just be better if we just teach less of it, if we can decouple it somehow from the power structures.”

Drawing metaphorically on the word tackle, Gale suggested there is a need to address the “inequities in human society” that are created through perpetuating a limited view of mathematics, as noted also in Section 4.3: “my end goal is to try to tackle the subject-ism of mathematics” to overcome the forces “creating these inequities in human society.”

Both Anna and Rico spoke about movement within contexts of social movements. When Rico was asked what he hoped others will gain or learn from his scholarly work, he replied that his hopes are “connected to the social movements” (see the longer quote in Section 4.2). In a way that also brings in communities and social movements, Anna claims: “And this is exactly part of clearing the path. It’s not only us who clear the path, it’s the social movement, it’s (…) the communities of those people who have already started many years ago clearing the path, and we somehow aligned with them in a political way maybe or in a post political way.”

At another point in the interview, Anna referred to “we people from below” who have power and “the potential to do things.” She drew on the idea of fighting for change or movement:

I’m working currently on some issues about citizenship and the learner as a citizen, and you see… nothing is given to us. We have to fight for whatever is taught in a particular time as rights, or even duties, we have to think about all those things. So, something which is there, like a policy for bilingual students or multicultural inclusion or whatever policy, is because people have, already have, done activist work for that.

4.4.2. Gentle Movements

The second sub-group of action verbs around change and movement is characterized by gentler movements: we heard the scholars use the words nurture, offer, bring, give, inspire, play, and lead to speak about their hopes or end goals in connection with their research.

Robin used the word nurture to discuss hopes for the research she does in her context of New Zealand (also quoted in Section 4.4.4), where universities “want high ranking publications.” Robin said her goal is “first and foremost, for my students to be able to succeed in education—being themselves and having their cultural identity nurtured.”

Using the words offering and giving as he spoke about “the trauma that Indigenous people have experienced in Canada,” Edward shared something about his own Mohawk culture: “we have a tradition of condolence to deal with death and to deal with loss… and one of the roles is that of offering condolence. So you receive condolence or you offer condolence.” In expressing his hopes for mathematics education and Indigenous culture, Edward clarified:

we don’t always know still what we need. And that’s something that I think is important, to give Indigenous people a bit of space to sort this out on their own, instead of constantly saying ‘well, you need to improve your test scores, or else your young people are not going to become doctors and lawyers and whatever’. You know this constant barrage… and I don’t think that’s really what Indigenous people want to… need… at this stage, they want to be given some space to sort it all out.

Not only did Edward use gentle verbs to describe his action, but he was advocating for gentle approaches to education.

The word bring suggests companionship in some way—the idea of carrying someone or something to a place. In Cynthias’s interview, she shared how, in her research, she aims “to expand our notions of what [mathematics] is so that we can begin to think about how mathematics can be a place that brings us together, that idea of community and love, that mathematics is a place for that… it can bring us together… it can be something that brings us joy.” Edward also drew on the word bring in speaking about the strengths “that Indigenous people have and can bring.” In describing “what success looks like to [him]”, Edward aspires to realize “a whole education system that is actually built around those strengths, instead of built around our weaknesses.” Also suggesting a form of companionship through the use of the word bring, Nancy aspires, in her research, “to help the students develop their mathematical language… they should be able to understand the mathematics and be able to bring the mathematics close” (also quoted in Section 4.3). One other scholar used the word bring in the context of what critical mathematics education can offer students. Ole described critical mathematics education as being “concerned about something—it’s concerned about the social inequalities in this world; it’s concerned about injustices; it’s concerned about students’ foreground, to bring students in situations where they can get out of the difficulties, get a better life”.

When it comes to play, the word took on different meanings for each of the three scholars using it. For Anna, she referred to discourses at play; for Cynthia, it was about wanting students to enjoy, understand, and play with mathematics; for Edward, he wants to see “Indigenous people play on their strengths,” which is, as Edward expressed it, “the interest in dealing with reality, as it is rather than trying to change it”.

Aiming to lead the way toward change or movement, Elaine warned that we need to “follow the lead of what people of color are telling us right now in this country” instead of pretending that values and ideologies are not involved. She admitted that some of her hopes and end goals are not so math-focused for her these days, even though, as she shared, “I really think that math teachers… if they can help lead the way to do different things other people will follow because they’d be so shocked that math can be something so different, right?” Edward commented on “the importance of listening to Indigenous people” and of going to Elders, the leaders, to learn about what is really needed or wanted (see also Section 4.2 and Section 4.5). He advised that his colleagues, “who are so anxious to help,” should focus on “seeking out, rather than walking into a situation assuming they know what’s good”.

4.4.3. Discursive Movements

A third sub-group of actions oriented around changing and moving relate to changes/movements in relevant discourses, using verbs such as reform, transform, strategize, and normalize. We note that the other two sub-groups also address changes to discourses/practices, but we made a separate category for when they chose verbs that are more specific to discourse change. Separating these into the three categories helped us see that the word choices—the flavour of these verbs—each give a different sense of the relationships and action, the different positioning. While the words that suggest changing and moving physical things tend to be metaphorical, referring to discourses, we also observe that changes to discourse actually can and do impact the movement of things—particularly in school contexts, where resources move and people move because of how safe and secure they feel.

Nevertheless, these verbs—particularly reform, transform and strategize—are often used in institutional (education and management) settings. Two scholars mentioned the word reform when they were discussing hopes and goals for their research. For Andrew, he offered that when it comes to school mathematics, he knows “how frustrating reform is”. He shared that much work is being done with teachers to have them do more problem-based and inquiry approaches which, he claimed, he is not against but he worries about who gets left behind in these reform efforts: “I’m worried about… like we’re going to totally just revamp the curriculum and who gets it? … it’s like what who gets what and who gets advantaged, that is what the issue is for me.” Related to what Gale said in Section 4.3.1 and Section 4.4.1, Gale spoke about “justice for mathematics”. She said she wants “to reform how we think about mathematics and what it is”.

We suggest that Gale’s use of reform closely connects to the use of transform, transformation and/or transformational, as drawn upon by Ruth and Cynthia (it is our interpretation that all these words have similar meaning in these data, but we are aware that in some contexts one or more of the words might have special meaning—e.g., reform pedagogy). All three spoke in the context of re/transforming one’s thinking about mathematics. Comments from Ruth were mentioned previously in the ‘make’ category, when she spoke about making math relevant and meaningful to Indigenous students and to the community partners. She followed that idea by sharing:

it’s quite transformational what happens to folks when they start to see themselves from a different viewpoint, because I think, in our society, we still think of math as like this proxy for being smart (…) this idea that only certain people are mathematical thinkers and those are the smart people. And so, when you get to introduce this idea that actually everybody is a mathematical thinker, a deeply complex mathematical thinker, it’s really fascinating what happens to folks.

Similarly, Cynthia described her interest in transforming thinking that presently positions mathematics as “a very exclusive area, and that we can’t do it, or it doesn’t belong or it’s not a part of who we are.” Cynthia hopes that, in transforming this kind of thinking, “we have students graduating from elementary school, from high school feeling— maybe they don’t necessarily want to… study further, but they can appreciate it, they can enjoy it, they can do it on their recreational time, they can see it, they can understand it, they can jump into a problem and play with it.”

In the case of the action word strategize, Anna spoke about “a strategic way of working” as that which helps clear the path for others (as noted above) and Nancy used the word strategies in connection with her scholarly work around language.

As we shared earlier, Robin clarified that her first “hope” or end goal was to nurture students’ cultural identity. Fitting in this third category of change and move, Robin offered additional thoughts about her hopes to “make a difference” for students toward an understanding of “this Indigenous heritage of our country, our place names, our protocols, understanding one another; it’s a joint shared heritage were founded on a treaty.” In other words, Robin’s research is tied into a hope “for cultural practice to be normalized… for all students to be able to richly enjoy and treasure the cultural heritage of Aotearoa New Zealand… by normalizing cultural practice and reflecting the modern world in respectful, suitable, creative ways across the education sector, and more widely.”

4.4.4. Action-Focused Questions (AFQs) for Changing and Moving

• What needs to change or move in mathematics teaching practices? What needs to change or move in mathematics education research practices?
• How might transformations of practice impact the people you care about (research participants, etc.)?
• In what cases do you think a gentler force is warranted, and what cases require ferocity? How do you decide whether gentleness or ferocity is appropriate?
• What fights (if any) do you see that need to come out into the open?
• What types of movement are different from discourse change?

4.5. Position

Another action group we identified in the distillations is the imperative to position. The CRP scholars said that their actions work at their relationships, often referred to metaphorically as positioning. The verbs we grouped into the category include align, attach, connect, engage, help, participate, recognize, serve and trust.

To elaborate on the positioning that the CRP scholars describe themselves doing, we think about relationship building, which might otherwise be seen as connection making, and something that may be seen as an opposite, which is distinction making— identifying and clarifying oppositions.

4.5.1. Connection Making

When describing their hopes, the scholars in this study spoke more about connection making than distinction making. They described hope in people listening to each other and positioning themselves in networks of relation. For example, Cynthia noted how mathematics is often viewed as not being “a part of who we are, in just living on the Earth, who we are in relation to each other”. As shared in Section 4.3, Cynthia described mathematics as potentially helping students/us to see the relations: “living mathematically means that we’re always engaged in trying to make sense of noticing things and how they connect and how they’re related or how they aren’t and if we didn’t do that we wouldn’t survive.” She pointed to the need to extend mathematical vision to strengthen its potential for enabling relation recognition: “we can begin to expand our notions of what it [mathematics] is so that we can begin to then think about how mathematics can be a place that brings us together—that idea of community and love—that mathematics is a place for that. [It] can bring us together.”

The scholars in this study were often specific about the people and communities they work to connect with. Anna described her work to connect with other activists, sharing “the communities of those people who have already started many years ago clearing the path” (quoted more fully in Section 4.1). Ole described his compulsion to connect with current and emerging activists, particularly new scholars: “I feel too engaged in what I’m doing here. Here in Brazil, I have five PhD students. And this enormous dynamic… working with PhD students, new PhD students, new problems. It gives enormous drive in the writing”. He also talked about wanting to connect with other scholars who will read his work: “if people, by reading my words somehow come to recognize, maybe share some of their concerns, I would feel very happy.” He added, “They don’t need to share my notions or my ideas,” thus emphasizing that his vision was not about aligning ideas, but about living in relation.

Other scholars focused on making connections with more general populations. Perhaps we could say that scholars seeking connection with other scholars and activists put hope in networks of special people, whom we might see as thinkers, activists, leaders, or scholars. Others in this study were more focused on recognizing the wisdom of communities, thus attending to students’ desires, community members and culture (which is carried in language).

Elaine described her motivation to position mathematics (i.e., the mathematical activity of students) with community concerns: “I think my overall goal is to help teachers, math teachers in particular who think math has nothing to do with the people stuff.” Elaine spoke of youth in communities (including students) as key partners in moving math learning toward stronger connections with community: “Until we can recognize everybody’s full humanity (…) we’re never going to be engaging in justice-related work or even equity-related work—trying to create spaces that (…) actually recognize youth and children’s humanity.” Similarly, Ruth pointed to the value of promoting mathematics learning that helps students to recognize themselves and their community as significant in mathematical action: “the students who see community members as mathematical teachers, as models for mathematical teaching and learning, has been really profound.”

Nancy described getting “the pride of mathematics back into the community.” She pointed to language as central to that, identifying the importance of attachment to mathematical language—”they should be able to attach themselves to the language of mathematics rather than detach themselves from math because of the languages”—and we note that this interest could also foreground local languages, attaching cultures together through attachment and connection making among languages (including technical and local languages).

4.5.2. Distinction Making

While community building and connection making were the dominant perspectives on positioning among the participant scholars in this study, we also noticed that the CRP scholars recognize difference and the need to articulate different points of view. This positioning comes out clearly in the sections on making (Section 4.3) and changing and moving (Section 4.4). Anna talked about the need to see herself and her work in opposition to other forces: “We have to fight for whatever is taught in a particular time” (the longer quote is in Section 4.4). Anna reminds us that it can be important to identify opposing forces, specifying what values and assumptions underline those forces so that we can counter those forces. We see in the literature examples of such scholarship (e.g., Herbel-Eisenmann et al., 2016; Johnson et al., 2021; Pais, 2019; Pomeroy et al., 2024), but the scholars talking about their hopes in this study did not say much about this imperative.

Further, while some of the scholars quoted under our heading of “connection making” (Section 4.5.1) spoke positively about connections they have sought to build, Andrew pointed to such connection making as a choice about whom to align with: “trusting in the community, not just community-based teachers, but parents (…) to make the right decisions for what their kids need ultimately, and less coming from experts and academics.”

Edward also provided a caution that the nature of the connections is important too. It is more than having relationships, but having the right kind of relationships:

one thing I hope that my colleagues can learn is the importance of listening to Indigenous people; of seeking out rather than walking into a situation assuming they know what’s good. I’m afraid I see that often. People are so anxious to help, which is a lovely sentiment and it’s a beautiful thing and I’m glad. But what other people see as help is not always help.

Edward continued to describe the right kind of relationship, one that we feel is also reflected in the words of the other scholars: “All you have to do is listen to what people really want”, suggested Edward. He pointed to the need to listen to the right people in a community, which may seem contradictory to others eschewing experts (as quoted above). We do not see this as necessarily contradictory—we see a range in expertise, with Edward pointing to community experts instead of mathematics education experts: “People are confused too, so they don’t always know what they really want. I think you have to go to Elders, you have to go to wise people, you have to go to leaders.”

4.5.3. Action-Focused Questions (AFQs) for Positioning

• When do you find it necessary to distinguish yourself or your views from others? (other mathematics educators, other CRP scholars, etc.)
• When do you find it helpful to position yourself as an ally?
• How do you shift your alignments? And when?

4.6. Humanize

Another action group we identified in the distillations is the imperative to humanize. Some CRP scholars in this study said that their actions include moves to humanize. Two verbs we grouped into the category include humanize and embrace. This imperative connects in some ways with the connection making we described under the action theme of positioning in Section 4.5, but we felt that humanizing warranted its own category, one which describes action that highlights human decision making and responds to collective human needs.

This category has particular importance in mathematics education, as compared to other disciplines, because (humans doing) mathematics very often obscure(s) human decision making and sensitivity to context. The scholars in this study talked about humanizing in different ways but we see a common theme of positioning mathematics as serving collective human needs. Ruth identified the importance of teachers working to humanize mathematics teaching: “There needs to be a really explicit focus on humanizing the interactions that they have with their students. (…) Maybe they’re just so focused on content that they’ve sort of lost the human element.” We note that humanizing mathematics teaching and humanizing mathematics have elements in common but they are not the same thing.

When Elaine talked about humanity, she saw the embrace of everyone’s humanity as a motive for paying attention to discourse and discourses in her research: “Until we can recognize everybody’s full humanity (…) we’re never going to be engaging in justice-related work or even equity-related work. And so I think one of the ways [is] recognizing people’s humanities are embedded in all kinds of aspects of discourse, and I’m using it like little d, big D.”

Some of the CRP scholars noted that humanization means focusing attention on people associated with groups whose humanity is too often ignored. Elaine saw hope in recognizing youth as being fully human: “trying to create spaces that (…) actually recognize youth and children’s humanity, and in my work with teachers trying to do that too.” She noted that such focus may seem like ignoring the humanity of others: “I recognize that sometimes putting youths’ humanity ahead of the adults is imperative to future generations.” Rico’s focus was on the people working together on social justice goals: “you have to embrace what is the larger project that we’re involved in, why are we doing this work.”

Margaret described the struggles that can come with developing relationships and community, noting that the scholarly world is “so ambitious, even so competitive, that we cannot afford to write for just plain folks”. In wishing that she could have plain folks as her colleagues, she asks:

Will they accept me as a colleague? (…) We are so different. We speak the same language; that’s the only thing that’s common. But we live in different parts of the world. [I live elsewhere], not in their village. Class- and caste-wise, I’m different. I’m a woman, I’m older; everything is different, except that we speak the same language. And we have a huge overlap there. And still, we are not that close. We think we are very close, but we are not. (…) So, how do you embrace them as a part of your community? That they accept me as a part of their community?

We see Margaret’s reflections as an indication that she wants to be responsive to the needs of a wider range of people—not only responsive to scholarly structures and values.

In contrast to this community perspective on humanizing, Morgan instead focused on her own project of becoming a better human: “I need to be changing in order to be a better human being on this planet.” (as previously noted in Section 4.3).

Action-Focused Questions (AFQs) for Humanizing

• How do you justify your focus on humanizing mathematics when other mathematics educators see the subject more abstractly?
• How do you know when to humanize mathematics explicitly (claiming that math should be more humanistic) or when to do it subversively (promoting approaches that will make math more humanistic without saying that is your goal)?

5. Reflections Through Hope

Bringing together the reflections on how hopes are expressed in action for the culturally responsive pedagogy (CRP) scholars in this study, we first comment on an all-encompassing action category—reflection. We then invite you to see our action categories as examples of possible action, and thus to consider expanding your repertoires for action beyond those identified here. Finally, we bring together the list of action-focused questions (AFQs) as a handy guide for reflective action. As noted in our introduction, we are accustomed to finding overviews of research foci in our field and others, but we see a general lack of attention to the why, the reasoning that motivates the research, writing, and other action choices of scholars. Our focus is on CRP scholars because we position ourselves in this work, but we think the action categories, reflections, and AFQs presented here could be helpful prompts for reflective action for any scholars, especially scholars researching professional contexts. We think that mathematics education research in particular (and other contexts of scholarly action) could have a greater impact on the practices in schools if researchers focused more explicitly on unpacking the why of their research.

5.1. An All-Encompassing Action Category: Reflect

From our distillations of the CRP scholars’ reflections, we had an action category named reflect. We moved this category into our discussion section because it seems to sit outside or above the other action categories. In a sense, all the actions are acts of reflection, and the interviews certainly are examples of the CRP scholars reflecting on their scholarly action. The verbs in the distillations of this category include conceptualize, celebrate, consider, enjoy, feel, let, reflect, theorize and treasure. Most of the quotes associated with these distillations appear at least once in the six parts of Section 4, which underscores our sense that this category sits in a different place than the other categories. In this way, we consider all parts of Section 4 as elaboration on reflective action. Thus, we draw from our reflection on this category in relation to all the categories and we cut immediately to the AFQs as an introduction to our discussion section.

Action-Focused Questions (AFQs) for Reflecting

• How do you know if you are acting without reflection?
• How do you make space for yourself to reflect in your research action?
• Are you including reflection in all the aspects of your research action? Or does it fit more appropriately with certain kinds of research action?
• When would it be appropriate, smart, or wise to act without reflection?

5.2. Repertoires for Research Action

In addition to the verbs in the categories of action that we connected together in themes (elaborated in Section 4), we identified in the distillations several further imperatives, where some of them were do’s and others were don’ts. For example, CRP scholars drew on the verbs contribute, keep, know, persist, and support through the language of do (this action). On the other hand, some actions expressed were don’ts—things they said they don’t want to do, such as apologize, control, deficit frame, and detach.

We decided not to elaborate on these action words with examples, because our point here is not to make an exhaustive list of CRP scholar actions. Our goal is to prompt reflection for scholars, to develop your repertoires for action. We note that there are even more verbs that you could use to describe your scholarly action: acknowledge, break, cultivate, document, embrace, foster, grasp, heal, illuminate, and the list goes on. Each of these verbs act as metaphors that could add meaning to how you conceptualize your action. We encourage you to reflect on your actions, and to extend your scope of activity with different kinds of research-inspired action. Also, we encourage you to observe and talk with even more scholars whose actions you admire, considering how you can engage in similar action. What actions are most appropriate for you, and which will you want to avoid?

5.3. Further Reflections on Hope

For us, an important result of this research is the data-informed development of AFQs (action-focused questions).

Table 1. Summary of AFQs for the categories of research action.

Action	AFQs
Communicate	4.1 Action-focused questions (AFQs) for communicating Who can change things? Are you communicating with that audience? Whose voices do you (want to) prioritize in your communication? How do your communication choices align with your audience and lift up the intended voices?
Investigate	4.2 Action-focused questions (AFQs) for investigating What do you seek to learn with your research? How do you decide what to investigate in your research? From whom can you learn? How do you know what you need to learn? How do you develop situations/conversations that open you up to learning things you didn’t know you need to learn?
Make	4.3 Action-focused questions (AFQs) for making What is missing, absent or inadequate in the field (and sub-fields) of CRP? What is missing, absent or inadequate in math students’ experiences of learning math? With your making, are you building or rebuilding? (i.e., Have we lost the missing aspects, or did we never have them?) Could everyone (even a subset of all mathematics educators) ever agree on what it means to “make the world a better place?” Does your scholarly action require mathematics educators (or a subset) coming to agreement? Does your scholarly action rest on the resilience of others who disagree with you?
Change and Move	4.4 Action-focused questions (AFQs) for changing and moving What needs to change or move in mathematics teaching practices? What needs to change or move in mathematics education research practices? How might transformations of practice impact the people you care about (research participants, etc.)? In what cases do you think a gentler force is warranted, and what cases require ferocity? How do you decide whether gentleness or ferocity is appropriate? What fights (if any) do you see that need to come out into the open? What types of movement are different from discourse change?
Position	4.5 Action-focused questions (AFQs) for positioning When do you find it necessary to distinguish yourself or your views from others? (other mathematics educators, other CRP scholars, etc.) When do you find it helpful to position yourself as an ally? How do you shift your alignments? And when?
Humanize	4.6 Action-focused questions (AFQs) for humanizing How do you justify your focus on humanizing mathematics when other mathematics educators see the subject more abstractly? How do you know when to humanize mathematics explicitly (claiming that math should be more humanistic) or when to do it subversively (promoting approaches that will make math more humanistic without saying that is your goal)?
Reflect	5.1 Action-focused questions (AFQs) for reflecting How do you know if you are acting without reflection? How do you make space for yourself to reflect in your research action? Are you including reflection in all the aspects of your research action? Or does it fit more appropriately with certain kinds of research action? When would it be appropriate, smart or wise to act without reflection?

presents a summary of the AFQs offered throughout this paper. These AFQs are designed to help you scrutinize your actions in terms of your hopes. How do your actions embody your hopes? If they do not seem to embody your hopes, perhaps your hopes are not what you think they are, or perhaps you will be motivated to adjust your actions.

Keeping in mind the words of the CRP scholars presented in this paper and these generated AFQs, we encourage you to reflect on your own hopes and wishes for your research, perhaps journalling or publishing your reflection. We also encourage you to identify further AFQs or to refine ours. We would love to hear from you on this.