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Article

Respect, Responsibility, Relevance, and Reciprocity: What the 4 Rs of Indigenous Research Offer Toward Decolonizing a Mathematics Classroom

by
Maegan A. G. Giroux
* and
Kathleen T. Nolan
*
Faculty of Education, University of Regina, Regina, SK S4S 0A2, Canada
*
Authors to whom correspondence should be addressed.
Educ. Sci. 2025, 15(12), 1579; https://doi.org/10.3390/educsci15121579
Submission received: 28 February 2025 / Revised: 17 November 2025 / Accepted: 20 November 2025 / Published: 24 November 2025

Abstract

Working to decolonize one’s mathematics teaching practice can create tensions between honouring Indigenous ways of knowing and being and not appropriating or tokenizing Indigenous cultures. This paper describes a mathematics teacher’s path towards decolonization in her grade 6/7 classroom in Saskatchewan, Canada. Through self-study research, Giroux created a framework using the 4 Rs of Indigenous research (respect, responsibility, relevance, and reciprocity), posing the research question: What is the value of my 4 Rs pedagogical framework for my professional growth as I aim to disrupt power and control in my mathematics classroom? Data, collected through a research journal, critical friend interviews, and student work, were examined using thematic analyses. Findings point to several semantic and latent themes of noticeable importance in disrupting power and control, while strengthening relationships, within the classroom. In this paper, the themes are presented and discussed in the context of decolonizing the mathematics classroom and for grounding the teaching and learning of mathematics in Indigenous perspectives and pedagogies based in the 4 Rs framework. Implications of the research include possibilities for K-12 educators to embrace and engage with Indigenous perspectives toward disrupting traditional power norms, promoting student agency, and strengthening relationships in the classroom and beyond.

1. Introduction

Pidgeon (2016) describes concerns of tokenism when academic institutions have viewed Indigenizing as a checklist of cultural additions to a colonized educational system. In contrast, the term decolonizing describes pushing against or changing current colonial systems. Decolonizing, as an action, has a wide range of interpretations which leads to varying ways to engage in acts of decolonizing, as noted throughout research and education. For instance, while Grande (2004) believes “decolonization is neither achievable nor definable” (p. 166), some researchers (Smith, 1999; Metha & Henrikson, 2022; Omodan, 2023) connect decolonizing to disrupting power structures, democratizing, and dialogue. Battiste (2013) defines decolonizing education as an act where “Canadian administrators and educators need to respectfully blend Indigenous epistemology and pedagogy with Euro-Canadian epistemology and pedagogy” (p. 168). Battiste’s definition contains no specific mention of including cultural content or curricula, rather a call to reshape how students learn (epistemology) and how teachers teach students (pedagogy). In other words, integrating Indigenous content is not synonymous with embracing Indigenous epistemologies and pedagogies.
For the most part, K-12 mathematics curricula provide little direction for including Indigenous epistemologies and pedagogies; instead, what is provided are outcomes/indicators that are content focused and often disjointed from Indigenous ways of knowing and learning. As an example, consider the K-12 Saskatchewan mathematics curriculum for Grade 9 where an indicator expects students to discuss how First Nations and Métis lifestyles and worldviews, as reflected through a tipi or medicine wheel for example, demonstrates circle properties (Saskatchewan Ministry of Education, 2009). Comparing a medicine wheel or tipi to a circle is not only problematic from a cultural appropriation perspective, but it is also seen as an add-on (checklist item) to enhance Euro-Western mathematics education. Decolonizing mathematics actions should not superficially refer to an Indigenous idea or object as a means to strengthen a Euro-Western mathematics procedure. Indigenous ways of knowing, being, and learning are complex; meaningful epistemologies deserve to be integrated into every level of curricula to reshape how educators think about and engage with/in mathematics.
With regard to reshaping how educators think about and engage with/in mathematics, the study described in this paper shares how Giroux conceptualized her master’s thesis research (Giroux, 2025) by designing and then implementing a personalized framework for her own professional growth toward decolonizing her Grade 6/7 mathematics classroom. Drawing on the 4 Rs of Indigenous research—respect, responsibility, relevance, and reciprocity (Kirkness & Barnhardt, 1991)1—Giroux designed a framework which she used to challenge power structures, strengthen classroom relationships, and embed Indigenous epistemologies and pedagogies in her mathematics classroom through a variety of teacher actions. She used the framework to conduct a self-study (Diacopoulos et al., 2022; Samaras, 2010) on her practice, with the key research question of: What is the value of my 4 Rs pedagogical framework2 for my professional growth as I aim to decolonize my teaching practice by disrupting power and control in my mathematics classroom? This paper shares the self-study research process, presenting the main findings in terms of the semantic and latent themes that were noticeably important in disrupting power and control, while strengthening relationships, within the classroom. This paper also discusses implications of the research for K-12 educators, with a view toward embracing and engaging with pedagogies that feature the 4 Rs (respect, responsibility, relevance, and reciprocity) to disrupt traditional power norms, promote student agency, and strengthen relationships in the classroom and beyond.

2. Research Context

2.1. Situating Giroux and Nolan

Giroux has been an elementary school teacher in the province of Saskatchewan for 13 years and, during the years 2021–2024, she was a master’s student enrolled at the University of Regina. Nolan is a mathematics education professor at the University of Regina and served as Giroux’s thesis supervisor during this period of time. Given that the research on which this paper is based was a self-study (Diacopoulos et al., 2022; Samaras, 2010) conducted by Giroux in her classroom, it is important to offer a few words towards positioning Giroux specifically.
Giroux acknowledges that she is a white settler female who was born and raised on Treaty 4 territory, the original territories of the Nêhiyawak, Anihšināpēk, Dakota, Lakota, and Nakoda peoples, and the homeland of the Michif/Métis nation. She acknowledges the benefits that she has indirectly received from the treaties and recognizes the harms of the past and present, along with the need for truth and reconciliation as called for in the final report from the Truth and Reconciliation Commission of Canada (2015). As part of her own truth and reconciliation journey, Giroux recognizes that decolonizing mathematics teaching and pedagogy is a continuous and ongoing commitment. The research that she conducted for her master’s thesis described here in this paper is one part of her continuing journey towards truth and reconciliation, toward repairing white settler relationships with Indigenous peoples of Canada.

2.2. Situating Pedagogy

For the past few years, the guiding structure for Giroux’s mathematics classroom has been a ‘thinking classroom’ (Liljedahl, 2020). There are 14 main practices used within the Building Thinking Classroom (BTC) framework, all of which are designed to disrupt institutional norms (Liu & Liljedahl, 2012). Institutional norms, described by Liu and Liljedahl (2012), are traditional expectations and structures of classrooms, such as students working individually on textbook questions at their desks. We believe that in order to decolonize mathematics education, some type of reform pedagogy needs to be in place that prioritizes active student engagement, collaboration, and thinking. We are not claiming, however, that the only way to decolonize or disrupt power and control is through BTC. In fact, Liljedahl claims that BTC can help disrupt some of the norms of a classroom, but decolonization needs much more than this (personal communication, 20 April 2024).

2.3. Situating the Classroom and Framework

For Giroux’s research study, the implementation of her 4 Rs framework occurred in a grade 6/7 classroom, where the students were mostly English as Additional Language (EAL) learners. The development of the framework, however, occurred the previous school year while she was teaching K-8 mathematics concurrently in two schools: One was a community school (low socioeconomic status) with a high Indigenous population and the other was a school with students who were largely EAL learners. The framework was built from the collective interactions of both demographics of students. Despite teaching two different demographics of students, Giroux noted that many Indigenous and immigrant students had experienced similar colonial education systems where they were disadvantaged and marginalized by very rigid, traditional structures, as also described in the research (Tuck & Yang, 2012; Ukelina, 2021). In fact, other scholars have suggested that Indigenous research methods, such as the 4 Rs,3 could be applied to support other marginalized communities (Cook, 2023; Lilley, 2024). By observing the intersecting experiences of Indigenous and immigrant students in K-8 mathematics classrooms, Giroux constructed the framework while considering the benefits of the 4 Rs of Indigenous research for Indigenous, non-Indigenous, and other marginalized groups of students. Even still, we recognize that a significant limitation exists regarding the data collected for this study. While the framework was developed with strong connections to Indigenous cultures and ways of being, the data collected for the study being discussed here were primarily from EAL learners.

3. Literature Review

Deficit perspectives with respect to mathematics ability and learning are commonly perpetuated throughout schools and society, highlighting justice/equity issues within mathematics and also from a broader STEM perspective (see, e.g., Archer et al., 2024; Vakil & Ayers, 2019). Research points to large discrepancies between the mathematical performance of children from various minority groups, including Indigenous and EAL learners, with school mathematics serving as a gatekeeper in facilitating or prohibiting access to STEM and other disciplines of higher education (MacPhee et al., 2013; Xenofontos, 2015). Traditionally, mathematics has been dominated by Euro-Western epistemologies, which have sustained inequitable power dynamics and supported colonial structures within classrooms (Madden, 2019; Stavrou & Miller, 2017).
In response, researchers (Beatty & Clyne, 2020; Iseke-Barnes, 2000) have suggested decolonizing as a promising way forward to create more just mathematics classrooms. One approach to decolonizing, as proposed in this text, is to adapt the 4 Rs of Indigenous research (Kirkness & Barnhardt, 1991)—respect, responsibility, relevance, and reciprocity—and focus on the teaching and learning of a mathematics classroom. In research, the decolonizing approach of utilizing the 4 Rs is meant to disrupt the power structures between the researcher and participant when conducting research with Indigenous peoples. While the 4 Rs are highlighted as actions for engaging with Indigenous research participants in a good way, Giroux drew on these actions to inform the creation and application of a framework that could be used, as a mathematics educator, in her continual journey to decolonize her own teaching practice. The 4 Rs pedagogical framework was designed as a professional growth tool to support decolonizing her teaching practice by disrupting power dynamics and fostering ethical relationships. This literature review explores research related to decolonizing mathematics education, the 4 Rs of Indigenous research, and issues of power and control in mathematics education.

3.1. Decolonizing Mathematics Education

Decolonizing mathematics education is an ongoing process for most teachers, as well as for those who design educational systems and curricula. By remaining centered on repairing and building relationships with Indigenous peoples, Canadian society can make progress towards decolonizing education, and specifically mathematics education (Boland & Tranter, 2018; Lipka et al., 2005; Lunney Borden, 2018; Martinez, 2020). One approach taken by teachers and scholars towards decolonizing their classrooms is through culturally relevant pedagogy (CRP). Lipka et al. (2005) researched how students’ learning and participation was affected by engaging in mathematics that was culturally relevant. Their study, taking place in Alaska, followed two teachers who set out to transform their mathematics course from worksheet-based and teacher-centered to project based and student-centered. Students in the two teachers’ classrooms worked on building fish racks with Elders in the community. Lipka et al. noted that, as the students used their cultural knowledge to make sense of the mathematics, their engagement increased, leading the researchers to theorize that projects provide “more promising long-term engagement” (p. 376). Lipka et al.’s study illustrates a roadmap to, and the benefits of, integrating relevant cultural knowledge into mathematics. In another example, Ruef et al. (2020) developed mathematics curricula in Ichishkíin (an Indigenous Yakama language) to provide culturally relevant education for their students. To create their new curriculum, they spent time considering the culture and lived experience of the Yakama people, as opposed to merely translating Euro-Western curricula to Ichishkíin. Through their study, Ruef et al. were able to create a culturally relevant and revitalized curriculum which reflected the needs of the community.
Decolonizing mathematics education is a complex call to action for teachers and mathematics educators in varied contexts. The researchers mentioned in the brief review of literature presented above, as well as many others, are providing meaningful approaches and suggestions for teaching and learning which are grounded in Indigenous perspectives and pedagogies based in the 4 Rs. These approaches and suggestions can support teachers in their ongoing journey toward decolonizing mathematics education.

3.2. The 4 Rs of Indigenous Research

The 4 Rs of Indigenous research (respect, responsibility, relevance, and reciprocity), originally proposed by Kirkness and Barnhardt (1991), were proposed to improve Indigenous students’ participation in higher education and are considered by many to be a promising approach to decolonizing education (Archibald, 2008; Johnston et al., 2018; Kovach, 2021; Nicol et al., 2020). Kirkness and Barnhardt examined how post-secondary institutions could prioritize these 4 Rs in relation to Indigenous peoples, as discussed in the following paragraph.
Beginning with the first R, respect, Kirkness and Barnhardt (1991) claim that, to Indigenous students, “the university represents an impersonal, intimidating and often hostile environment, in which little… cultural knowledge, traditions and core values [are] recognized, much less respected” (p. 7). To counter the lack of respect, educational settings and professionals must work to dismantle combative, colonized environments where one culture has more value than another toward strengthening respect for Indigenous students and their culture. Kirkness and Barnhardt also noticed that irrelevant curricula in relation to Indigenous students’ lives was creating barriers for their success in institutional settings. The second R of responsibility highlights the importance of post-secondary institutions being responsible for creating positive environments where Indigenous students can thrive. Kirkness and Barnhardt (1991) suggest that institutions “create the conditions where the students not only celebrate their own histories but are helped to examine critically how their lives are shaped and molded by society’s forces” (p. 13). Gaining a post-secondary education can create access to broader opportunities in life for many Indigenous students. To create greater relevance (the third R), Kirkness and Barnhardt provide the example of institutions broadening the ways knowledge is conveyed, beyond “perpetuating literate knowledge” (p. 7) to including traditional Indigenous learning styles, such as oral storytelling. The researchers specifically recommend expanding knowledge resources beyond what can be found inside a book. When universities honour Indigenous perspectives, the institutions can be more responsive to their students’ needs. Finally, to create greater reciprocity (the fourth R) in post-secondary institutions, Kirkness and Barnhardt (1991) recommend blurring the lines between those who produce and those who consume knowledge by allowing students to integrate and apply diverse forms of knowledge in their learning. Additionally, they encourage faculty members to endeavor to be more accessible with their Indigenous students, aiming to build upon their students’ cultural background as Ruef et al. (2020) share in their curriculum development research. Through actions like those mentioned above Kirkness and Barnhardt believe teaching and learning may become a two-way process.

3.3. Issues of Power and Control in Mathematics Education

While students experience mathematics as a required discipline in schools, it is important to recognize that mathematics education is part of a schooling system that perpetuates unequal distribution of power (Kollosche, 2014). In fact, many scholars have identified mathematics education as a means to maintain control and perpetuate cultural inequities (Ruef et al., 2020; Stavrou & Miller, 2017). In their research on decolonizing mathematics, Stavrou and Miller (2017) claim that, historically, “Indigenous Peoples [are viewed] as inferior while maintaining that the White culture is the standard of success” (p. 100). When this view persists, Indigenous students may never feel powerful or in control of their learning because their experiences and cultures are consistently devalued. The inequity described above produces institutional power structures within mathematics education to the detriment of Indigenous Peoples and students. Scholars (Beatty & Clyne, 2020; Iseke-Barnes, 2000) suggest that to curb the inequities within the mathematics classroom, teachers should honour all ways of thinking and focus on process and learning, as opposed to product and performance.
Beyond the institutional power structures embedded in mathematics education, teacher-student power dynamics within a mathematics classroom need also be disrupted. However, researchers (Kollosche, 2014; Valero, 2007) agree that power can be a difficult concept to even detect, let alone disrupt. Valero (2007) asserts that “power is not openly overt and easy to identify but subtly exercised in and through social action” (p. 226). Therefore, when considering a dynamic environment like a mathematics classroom, it may not be easy to notice and shift the power from the teacher to the students. Several scholars (Beatty & Clyne, 2020; Dubbs & Herbel-Eisenmann, 2021; Iseke-Barnes, 2000; Valero, 2007) express that, among other approaches, relationship-based learning (RBL) can allow for power disruption within a mathematics classroom. Beatty and Clyne (2020) implemented a multi-year RBL project through an Indigenous beading project with community partners, with a goal of fostering strong relationships with the community as well as the students. They reported positive experiences from students, Indigenous community partners, and settler teachers. These experiences included students feeling stronger connections to community partners, Indigenous knowledge, and mathematical concepts. Similarly, Boland and Tranter (2018) observed a school-wide approach to RBL with the aim of strengthening teacher-student relationships. The approach involved having all staff members focus on eight conditions they believed were necessary for student success, namely safety, regulation, belonging, positivity, engagement, identity, mastery, and meaning. Boland and Tranter observed that students not only appeared happier in school, but their mathematical understanding (as assessed through provincial standardized tests) increased. Both research projects (Beatty & Clyne, 2020; Boland & Tranter, 2018) offer promising road maps to disrupt power within mathematics classrooms.
In summary, the 4 Rs of Indigenous research provided a promising way forward for Giroux to design and implement a framework aimed at disrupting the teacher-student power dynamic in her mathematics classroom. Since the focal point of the 4 Rs is to build strong relationships, enacting her 4 Rs framework through student-centered pedagogical approaches helped her to focus on power and control, while shifting away from traditional teacher-centered structures frequently found in mathematics classrooms. When utilizing the 4 Rs for her own professional growth approach, Giroux worked to bridge theory-practice divides and create more equitable, democratic, and decolonized teaching practices in her mathematics classroom.

4. Theoretical Framing

The 4 Rs pedagogical framework (Table 1) was built from the work of many scholars (Boaler & Anderson, 2018; Boaler, 2019; Johnston et al., 2018; Kirkness & Barnhardt, 1991; Kovach, 2021; Liljedahl, 2020; Lunney Borden et al., 2020; Nicol et al., 2020; Parks, 2010; Zazkis & Liljedahl, 2009), all of whom discuss mathematics education, relationships, the 4 Rs, and/or power and control in education. Although none of these cited research texts present their own table or framework, they each contribute in their own way to the design of the 4 Rs framework used for the study being described in this paper. As can be viewed in Table 1, the pedagogical framework is separated into 4 columns, one for each of the 4 Rs of Indigenous research: respect, responsibility, relevance, and reciprocity (Kirkness & Barnhardt, 1991). Within each column, Giroux proposed outcomes (also referred to as theoretical approaches, based on the scholarly literature mentioned above) and indicators (or practical applications) that she saw as being directly connected to the corresponding R. These outcomes are coded with a number while each indicator is assigned a number and letter. For example, decentering the teacher (outcome) is coded as 4 and being intentionally less helpful (an indicator within this outcome) is referred to as 4b.
When creating the 4 Rs pedagogical framework while teaching K-8 mathematics at the two different schools, Giroux experienced tension between theory and practice. Although she found value in the academic research she was reading (the theory), she struggled with what a practical classroom application, or indicator, could look like. Brown et al. (2019) describe the importance and complexity involved in bridging theory-practice divides. Their research found that without intentional professional growth, teachers’ application of culturally responsive education did not match the spirit of the theory. Therefore, in the design of the framework, Giroux ensured that every outcome (theoretical approach) was appropriately connected to one or more indicators (practical application). The outcomes reflect scholarly approaches found in the research literature designed to reform mathematics teaching, disrupt power, and/or embed Indigenous epistemologies; they are included under what Giroux believed to be the most suitable corresponding R. Below each outcome are example(s) of specific indicators (teacher actions) to support the outcome (theoretical approach). The development of the pedagogical framework, based on the 4 Rs of respect, responsibility, relevance, and reciprocity, serve as an innovative way to ground Indigenous perspectives in K-12 classrooms.

5. Research Methodology and Methods

Given that the goal of this research study was to work towards decolonizing Giroux’s mathematics teaching practice by disrupting power through the 4 Rs of Indigenous research, the methodology selected was self-study. According to Samaras (2010), “self-study [is] a personal, systematic inquiry situated within one’s own teaching context that requires critical and collaborative reflection in order to generate knowledge, as well as inform the broader educational field” (p. 10). In defining self-study, Samaras references five foci methodological components (Loughran, 2018; Samaras, 2010), each of which informs the research design: personally situated inquiry, critical collaborative inquiry, improved learning, transparent research process, and knowledge generation and presentation.
We have come to realize that self-study as a methodology includes many paradoxes within the five foci methodological components. Giroux’s self-study allowed, even embraced, these paradoxes to exist within the research. For instance, as she decentered herself (4) as a teacher in her mathematics classroom, she recentered herself as a researcher in the self-study. Similarly, some days Giroux was introspective on a specific aspect of her pedagogical framework yet found herself openly discussing another aspect with a colleague or critical friend the next day. In other words, Giroux shared with many colleagues how her students were designing their own assessments (9a), but she also often privately reflected on dismantling the inherent hierarchy of students and their mathematical knowledge (2). Utilizing self-study as a methodology offered her the freedom to embrace the subjective, paradoxical, and complex reality of attempting to decolonize, strengthen relationships, and disrupt the power structures in her classroom.
Given that the research methodology was self-study, Giroux was the primary research participant, with data being gathered for a six-month period (October 2023–March 2024) through a reflective researcher journal. She journalled approximately twice per week, expressing her thoughts, concerns, and questions about how the 4 Rs Pedagogical Framework was having an impact on her teaching and professional growth. In addition, she drew on feedback and anonymized classroom work from her 30 Grade 6/7 students. Specifically, Giroux’s students completed an anonymous student questionnaire twice, once in the Fall of 2023 and then again in the Winter of 2024. The third form of data collection consisted of observations and interviews from Giroux’s three critical friends. The critical friends involved in the study were (using pseudonyms): Ada, a multicultural and multilingual coordinator; Blaise, a mathematics education consultant; and Florence, a mathematics education professor. In keeping with the goals of self-study research, all data collected from these secondary research participants were analyzed to understand Giroux’s behaviours and actions/inactions which helped describe the value of her 4 Rs pedagogical framework as a professional growth tool.

6. Data Analysis

To determine the value of the 4 Rs pedagogical framework regarding Giroux’s professional growth toward decolonizing her teaching practices, all forms of data (anonymous student questionnaires, critical friends’ feedback and discussions, as well as Giroux’s personal journaling) were used in the analysis process. The primary approach to data analysis in this study was thematic analysis. According to Braun and Clarke (2006), “thematic analysis is a method for identifying, analyzing, and reporting patterns (themes) within data” (p. 79). Braun and Clarke (2006) describe thematic analysis in six phases: becoming familiar with the data, generating initial codes, searching for themes, revising/refining the themes, defining and naming the themes, and finally reporting on the themes.
Phase one of the thematic analysis began by reading and reviewing the available data, looking for recurring or similar data items noticed across the data such as quotes from post-observation interviews. During phase two, any similar data items were then given descriptive code based on Giroux’s interpretations such as coding a journal quote as ‘time’. In phase 3, she searched for themes within those codes, sorting the codes as either miscellaneous codes or official themes. While sorting the codes, some, such as teacher anxiety in relation to time, became a theme, whereas others, such as valuing process over product, were used as evidence in support of the theme of teacher anxiety in relation to time. Giroux familiarized herself with all the data items, reviewed all the themes, and then reflected on and researched ideas that she noticed were most related to the research question about her own professional growth toward decolonizing her teaching practice by disrupting power and control in my mathematics classroom. From there, during phases four and five, the themes were refined and distinguished as being either semantic or latent. Semantic themes are described as those that are explicitly expressed in the data (interviews or journal entries); that is, the researcher “is not looking for anything beyond what a participant has said or what has been written” (Braun & Clarke, 2006, p. 84). In contrast, latent themes are interpretations and, as Braun and Clarke (2006) explain, these interpretations go “beyond the semantic content of the data, and [start] to identify or examine the underlying ideas, assumptions, and conceptualizations and ideologies that are theorized as shaping or informing the semantic content of the data” (p. 84).

7. Findings

7.1. Semantic Themes

Upon analysis of the data from the journal entries, critical friend interviews, and anonymous student questionnaires, Giroux noticed three semantic themes that were most pervasive: noticeable student voice and choice, comfortability between teacher and students, and the powerful use of stories to engage in mathematics. While Giroux noticed some of these themes more frequently than others, each of the three themes were explicitly mentioned multiple times within her thesis journal, critical friend interviews, and student questionnaires.

7.1.1. Noticeable Student Voice and Choice

In many traditionally structured mathematics classrooms, a lack of recognizing and valuing student voice and agency can perpetuate inequitable power structures and weaken classroom relationships (Choudry, 2023). Giroux intentionally added the outcome of students voicing what is relevant to them (7) to the 4 Rs pedagogical framework to increase student voice and disrupt her power as a teacher. Furthermore, student choice was purposefully included in her framework through embracing mathematical strategies (1) and decentering [herself] as the teacher (4).
A post-observation interview with critical friend Ada led to the first instance where the data suggested noticeable voice and choice within Giroux’s classroom. When Giroux asked Ada to compare her students’ voice and choice to students in a traditional mathematics classroom, Ada offered:
I would say that there was a noticeably higher degree of voice and choice. Students were actively participating, they were engaged, they were talking, and, you know, being EAL, my field, having so many English language learners in that class and seeing how the kids were interacting, how they were talking. There was nobody there worrying about their grammar. No, they were not worrying about their pronunciation. You know, they were confident in speaking and sharing their thoughts. So, that was great to see how the kids were able to participate and voice their choices and their opinions.
(post-observation interview, December 2023)
Framework outcomes 1, 4, 5, and 7 make it clear that Giroux aimed for student voice and choice to be observable in her classroom; however, Ada’s perspective—as a multilingual and multicultural coordinator—was surprising because, until then, the importance of EAL students conversing in relaxed and organic ways had not been considered. Together, Ada and Giroux spoke about how, when students work in groups, they can work to improve their language acquisition and development because it is viewed as a low-risk safe space. The post-interview with Ada clarified the fact that voice and choice are even more necessary when elementary mathematics classrooms include so many students from other countries. Many of these students are overcoming various challenges, from learning a new language to coming from different, perhaps harmful and colonized, educational systems (Chisom et al., 2024; Samuel et al., 2024).
In addition to Ada’s observation offered above, another critical friend, Blaise, also described the overall classroom culture created by Giroux as encouraging student voice and choice. Both critical friends remarked on the importance of having a low-risk and collaborative classroom environment as a necessary precursor for student voice and choice. Another interesting piece of evidence for this theme came from the anonymous student questionnaires. When the questionnaire was administered the first time (in October 2023), the comment section was left blank on all student questionnaires; however, the second time it was administered (in March 2024), all students wrote a comment in this section. While the quality and focus of their comments varied, the shift from complete absence to complete presence is strong evidence for our conclusion that students felt their voices were valued.

7.1.2. Comfortability Between Teacher and Students

Along with student voice and choice, all three critical friends made remarks about Giroux’s relationships with her students and the relaxed demeanor of the students and teacher. The critical friends each mentioned Giroux ‘knowing’ her students and the comfortability she demonstrated with her students, with the class as a whole as well as with individual students. In the context of this study, we describe comfortability as the relaxed outward behaviour of the students and teacher (Giroux). ‘Knowing’ students refers to learning about and understanding them as individuals through shared classroom experiences. Using a collaborative group model (4a), such as BTC, resulted in Giroux feeling that she understood her students more and could make more informed decisions about, for example, whether to let them productively struggle (3b) or to support them during closure activities (8b).
Given that one’s perception of an experience is subjective and based on the observer, it is worth noting that the two critical friends who pointed to relationships and comfortability as a theme within classroom interactions, did so quite differently. For instance, after a classroom observation, Blaise remarked:
I think what stood out most to me was this element of comfortability, not just from you, but from the kids. Like, it’s very clear that they’re very used to this way of teaching now. They’ve kind of clearly been immersed in it, and you’ve been working towards this all year is kind of what I’ve seen. It’s clear to me that the relationships were front and center all the time, you know your kids in and out.
(post-observation interview, February 2024)
Blaise’s remark confirmed two important aspects about building relationships with students. The first is that students need to feel comfortable in the learning environment for teachers to build relationships with them. The second aspect, which is described later as a latent theme in an analysis of a journal entry, was that student comfortability included the teacher, but also the overall classroom structure. Giroux’s teaching style, informed by BTC and the 4 Rs pedagogical framework, was likely very different from what many of the students had experienced in a previous mathematics classroom. Blaise’s feedback served as a necessary reminder that building classroom relationships demands more than just comfort between students and the teacher.
In contrast to Blaise’s comment on the classroom environment, another critical friend, Florence, spoke about comfortability and the ‘knowing’ of students in the context of a specific example. Florence noted an interaction between Giroux and a student where Giroux responded to a student’s unexpected comment without judgement and Florence commented: “the interaction [of not telling him he was wrong] showed me that you know your students.” While building classroom relationships may be built from individual interactions, they also involve being comfortable with the overall classroom structure and actions within; that is, with how the subject of mathematics is being taught and learned.

7.1.3. The Powerful Use of Stories to Engage in Mathematics

Research into ‘relevance’ in mathematics education proposes that teachers incorporate stories to create mathematical context and meaning for students (Nicol et al., 2020). While there are many ways to incorporate stories into a mathematics classroom, two indicators in particular were noted by critical friends and Giroux as leading to high student engagement. In the classroom, Giroux approached relevancy by presenting tasks through stories (6a) and students creating and sharing their own mathematical stories (6b).
Launching or introducing a mathematics task can be very difficult and calls for consistent refinement. For instance, Giroux frequently noted in her research journal that she often explains too much or too little at the beginning of a lesson and, as a result, the success of the activity or task suffers. Through researcher journal analysis, Giroux found that including stories in mathematics lessons showed a noticeable increase in student engagement. She noticed a rise in group discussion, both in the level of detail and in the variety of representations on the VNPS (1), when the tasks were posed as stories, compared to when they were presented in de-contextualized ways. Stories were utilized in the classroom through Giroux’s personal stories, as well as students posing their own stories to make meaning of different mathematical concepts and to engage with stories related to different cultures, including some stories related to Indigenous cultures. While Giroux’s personal stories provided the students with opportunities to hear oral stories and strengthen teacher-student relationships, the act of students posing their own stories as tasks provided students with the freedom to express themselves and their culture. In these situations, the students expressed themselves through, for example, cultural foods and traditions, popular culture, and personal interests. Giroux noticed that inviting the students to tell their own stories created opportunities for her to learn about and understand her students to a deeper level. When engaging with stories from different cultures, Giroux’s class explored number systems different from base-10. Specifically, students learned about a group of Iñupiaq middle school students who created Kaktovik numerals (Bartley, 2022) for their base-20 counting system. Learning about these number systems through story allowed the students to understand not only more about the number system itself but the reasons for contrasting systems.
Liljedahl and Giroux (2024) claim, “students need context. Context not only gives them something to think about, but it also gives them something to think with” (p. 227). The stories in Giroux’s class offered relevance and personal connection to different mathematics topics and provided a context and an application that made sense to the students. Kumaş (2024) also identified the value of stories in mathematics through their research into digital storytelling for kindergarten students with mild intellectual disabilities. Kumaş proposed that “digital storytelling enables the creation of multiple modes of representation and the sharing of interactive content that can facilitate narration and encourage students to actively participate in the learning process” (p. 13). Similar to Giroux’s observations of student engagement with stories, Kumaş found that stories create different entry points for students to engage with the mathematics.

7.2. Latent Themes

Unlike the semantic themes, latent themes were identified based on Giroux’s interpretations of, and reflections on, the data. The latent themes were primarily constructed out of thesis journal entries as well as data provided by the study’s critical friends. The research data were analyzed and coded, with the two latent themes named as teacher anxiety related to time and the positive effect of blurring the lines between producers and consumers (9).

7.2.1. Teacher Anxiety Related to Time

Building strong relationships and creating a safe environment, although worthwhile, is considered too time-consuming by many teachers; instructional time is treated as a valuable but often limited resource (Gracin & Trupčević, 2022; Zunica, 2023). Zunica (2023) offers that “teachers under time pressure focus on specific teaching goals, such as covering content” (p. 5). The time pressure mentioned by Zunica is often cited as the reason teachers avoid professional development experiences or do not focus on growing their classroom pedagogies. In this research, Giroux detected similar tensions, between her desire to enact the 4 Rs pedagogical framework and her anxiety to cover the Grade 6 and 7 curricula within a pre-determined amount of time.
The framework outcome of spending extra time introducing and working with different mathematical representations (concrete, pictorial, abstract) (1) to deepen student learning created some anxiety about time for Giroux. In one journal entry she wrote, “is the curriculum too big and overwhelming to easily ‘slow’ down and focus on deeper issues?” (researcher thesis journal, September 2023). In her journal entry, she describes the inner conflict she experienced between her perception of time and the breadth of the Grade 6 and 7 curricula expected to be taught within her split grade classroom. Often, to save time, some split grade mathematics teachers choose to instruct one grade-grouping while the other grade-grouping is working independently on a different mathematical concept. In Giroux’s classroom, however, she taught her students both curricula concurrently, which enlarged the content to cover and reduced the allotted time given to each curriculum strand, outcome, and indicator. It was apparent that her approach, while beneficial to her and her students, intensified her own anxiety related to time.

7.2.2. Blurring the Lines Between Producers and Consumers

In traditionally structured classrooms (i.e., those that are not characterized by reform and BTC-based approaches), teachers often serve as the active producers of knowledge while the students passively consume that knowledge (Kirkness & Barnhardt, 1991). Such a traditional view of producers and consumers contradicts Indigenous epistemologies, where knowledge is understood to be created and shared by the many, not the few (Battiste, 2013; Deer, 2006). Through Giroux’s journal reflections on producer and consumer roles in the classroom, decentering herself (as teacher) (4) to center the students (as knowledge producers) emerged as an opportunity for her to practice vulnerability. In the pedagogical framework, four important teacher actions (indicators) are included, each of which was designed to shift the focus and responsibility from the teacher to the students. These four indicators are: allowing students to mobilize/share knowledge (4c), being intentionally less helpful (4b) (Liljedahl, 2020; Meyers, 2010), students creating the questions for their own final assessments (9a), and students building a portfolio of their learning (5a). During data collection, while working toward these four indicators, circumstances arose which provided Giroux with the opportunity to notice a secondary action emerging from the indicators, specifically an action that addressed and supported indicator 4c. The secondary action was that of a student acting as the ‘second teacher’, defined as a situation where a student is randomly given a marker that is the same colour as the teacher’s and a sheet with all the activity questions and extensions on it; this student is then asked to go around and help other groups. This action was designed to address and support indicator 4c (allow students to mobilize/share the mathematical knowledge). Upon reflecting on this action, Giroux commented in her journal, “the other students LOVE it! They will always ask their fellow students before me, which decenters me more” (researcher thesis journal, March 2024). All four indicators, from thesis journal entries and critical friend observations, were noticed to be effective tools for Giroux to blur the lines of the producers and consumers of knowledge and thus increase student engagement and agency.

8. Discussion

While the 4 Rs pedagogical framework provided the initial opportunity for Giroux’s professional growth, the themes constructed out of the data prompted further reflection and analyses. Reflecting on the semantic and latent themes revealed which aspects of the framework had the greatest impact on Giroux’s teaching practice and student experiences. For example, while Giroux sought to increase student voice and choice, how it was noticed by the participants varied, from remarks on the general classroom culture to individual interactions with students. In the same vein, comfortability and ‘knowing’ students was an important semantic theme, while also serving as a reminder that comfortability means creating multiple access points within the classroom for students; it also means being attuned to their feelings and having a willingness to adjust in the moment. Finally, Giroux noted that while several aspects of the framework—storytelling, the use of the BTC framework, highlighting various mathematical representations, and the ‘second teacher’—directly impacted her anxiety around time, these same aspects also created opportunities for her to blur the lines between the producers and consumers of knowledge in the classroom. These aspects also encouraged her to look more closely at the full framework, with a view to identifying areas not yet highlighted in her practice, thus providing ideas for moving forward with her own professional growth through a broader implementation of the framework.
Prioritizing student voice and choice is a promising approach for educators looking to enhance classroom relationships and disrupt power in K-12 educational settings (Moses et al., 2020; Treacy & Leavy, 2023). Moses et al.’s (2020) research notes that student agency (5) is complex, and that fostering student agency requires a disruption of traditional power dynamics. Additionally, their research suggests that the process of building student agency “relies on giving students choice, decentering the teacher and centering the student” (p. 219). The findings of the study described in this paper mirror those of Moses et al. in recognizing the value of group work (4a), not prescribing ‘how’ students show their work (1), as well as students voicing what is relevant to them (7) and blurring the lines of the producers and consumers of knowledge (9). Through these actions, Giroux was decentered as the teacher (4), and these opportunities for student choice and voice served to disrupt the traditional power dynamics found in mathematics classrooms. As Giroux released the need for power and control over the learning processes, her students’ learning became more authentic and meaningful. When students are invited to drive their own learning, the teacher-student relationships become more reciprocal, the mathematics becomes relevant, and the students take responsibility for their learning.
Disrupting power through actions such as increased student voice and choice, as well as blurring the lines of the producers, could also be viewed as a form of democratizing the classroom. Some researchers, see for example Smith (1999) and Metha and Henrikson (2022), have made connections between democratizing and decolonizing. Smith (1999) describes democratizing as one of the 25 decolonizing actions that can be utilized when conducting research with Indigenous people and other marginalized groups negatively affected by colonization. While democratizing and decolonizing are not synonymous, we believe we can view democratizing as a method for decolonizing.
Regarding comfortability between teachers and students, the two most prevalent interpretations from Giroux’s thesis journal and critical friends’ data were the concepts of ‘knowing’ her students and the necessity for incremental implementation of the 4 Rs pedagogical framework within the BTC pedagogical structure. With respect to ‘knowing’ students, we claim that ‘knowing’ the students in a mathematics classroom cannot be achieved without fostering strong and reciprocal classroom relationships. Beatty and Clyne (2020) claim that “the ethical relationality may be a powerful step towards reconciliation, and therefore decolonization, in the domain of mathematics education” (p. 126). Ethical relationality cannot exist without a reciprocal relationship. In this study, Giroux made an effort to understand her students’ mathematical personalities through the CPA model (1) and portfolio building (5), and she embraced their lived experiences through their stories (6 and 7). These actions helped her create an environment of ethical and reciprocal classroom relationships. Regarding the second interpretation about comfortability, at one point Giroux wrote in her thesis journal: “I made big changes [like implementing BTC and my framework completely and concurrently], not realizing all the little things that need to be already in place, like relationships and expectations” (researcher thesis journal, November 2023). In other words, Giroux recognized that some basic classroom procedures, expectations, and efforts to build relationships needed to be in place before focusing on large pedagogical shifts. Although the framework includes a focus on utilizing stories, which can support relationship building, more intentional actions were needed first, such as building clear classroom norms and procedures, getting to ‘know’ her students, and listening to their expressed needs (Noddings, 2012). Following these actions, the teacher is in a better position to focus on the framework to build strong ethical relationships.
The use of stories in this study provided an opportunity for Giroux to listen to her students and encourage her students to positively engage with and connect mathematics to their own lives. Kumaş (2024) found that digital storytelling was academically productive and further asserted that “given that stories are inherently engaging and can be adapted to meet students’ learning needs when combined with digital media, it seems inevitable that intervention will be effective” (p. 13). Giroux’s research experiences echo Kumaş’ belief that the students were engaged in their learning and the stories, albeit not in a digital format, allowed students to access the mathematics through context. Making meaning through stories provides students with an access point to support their understanding of the mathematics. Sherwood and Makar (2022) noted similar success when their students used stories to create mathematical understandings of statistics, claiming “stories were found to provide participants active opportunities to access statistics in ways that made sense to them” (p. 198). With regard to her study, Giroux noted that the students tended to engage deeper in the learning process when stories were involved in the mathematics activities; they could connect the content to a specific context. Both studies point to the conclusion that using stories to provide context can support students in meaning making and mathematical understanding.
The latent theme of teacher anxiety related to time was most prevalent in Giroux’s thoughts and experiences while enacting the 4 Rs pedagogical framework. In her thesis journal, Giroux expressed anxiety surrounding time and ‘finishing’ the curriculum. Creagh et al. (2025) refer to this stress or anxiety around workload and time available as ‘time poverty’ and define it as: “… the relationship between (a) the amount of work a teacher does, or perceives that they have to do, and (b) the intensity of that work, which may be expressed as the number, complexity or stakes associated with decisions that need to be made over a given time period” (p. 16).
Giroux’s journal reflections at the beginning of her study’s data collection period could be perceived as an example of ‘time poverty.’ In her journal, she made several comments about the curricula appearing to be too extensive and broad. Although Giroux’s anxieties about time persisted throughout the data collection period, she utilized high yield teacher actions (indicators) which created richer experiences within a smaller time frame. For example, when students were working in groups (4a) and engaging in productive struggle (3b), she observed students making connections to other mathematical concepts. She reasoned that the connections students were making could save time later in the year. Giroux noted: “although the concept of time is very stressful and continues to be stressful, I need to recognize that my perception of time and what time I actually have are divergent. It is not the amount of time but the quality that matters” (researcher thesis journal, October 2023). In other words, students spending an hour quietly practicing, using the same formula repeatedly, is less meaningful and effective for learning mathematics than students spending an hour working through one rich task and then creating or discovering the relationship (Alfieri et al., 2011). In this study, the findings strongly support the claim that students should experience the curriculum through inquiry and productive struggle, not be rushed through the curriculum in a procedural manner because of teacher anxiety about time. These ideas reflect the uncomfortable, challenging, and personal growth that one needs to accept on the journey towards decolonizing. Martinez (2020) asserts that authentic use of decolonizing strategies for mathematics education is a complex process because “there is no perfect recipe to follow” (p. 65). Decolonizing is not a one-size-fits-all checklist; it requires personal involvement, growth, and self-reflection. The time anxiety, although uncomfortable, was one of many necessary by-products of decolonizing work that is aimed at disrupting power and control.
The positive effect of blurring the lines between producers and consumers (9) revealed the importance of teacher vulnerability to create a low-risk environment (3b, 4a, 8) where students are driving their own learning. Teacher vulnerability is also necessary for building reciprocal relationships (Kirkness & Barnhardt, 1991). Lai et al. (2024) used vulnerability as a pedagogical tool, concluding that teacher vulnerability can humanize pedagogy; however, they do warn that a proper classroom environment based in trust needs to be in place to enhance student learning. Teacher vulnerability can also relate to decolonizing a teacher’s mindset (Mawhinney et al., 2020). Mawhinney et al. (2020) implemented a teacher education program where (predominately white) educators focused on social justice and decolonization with their students, which they claim led to an increase in teacher vulnerability and stronger classroom relationships.
In Giroux’s study, the 4 Rs pedagogical framework and the BTC structure promoted a trusting, low-risk environment by focusing on the process over the product (8), centering students over teachers (4), valuing their mathematical strategies (1), and allowing them to productively struggle (3b). In Giroux’s research experience, teacher vulnerability could be a promising approach to disrupting power when paired with a trusting and supportive classroom structure.

9. Concluding Thoughts

When considering this 4 Rs pedagogical framework as it relates to professional growth, one idea is abundantly clear: Disrupting power and control and decolonizing one’s teaching practice is a personal, challenging, and ongoing journey. Disrupting power and decolonizing mathematics classrooms can be valuable and rewarding processes for any teacher to undertake, as they reflect the kinds of teacher practices needed to re-imagine mathematics education toward a decolonized education system. In the context of this study, the 4 Rs pedagogical framework has pushed Giroux to be more reflective, flexible, and aware of the many shortcomings within her pedagogy and practice. She has a deeper understanding of the reasons for a teacher’s perceived ‘time poverty’ but also realizes the importance of spending more time on teaching conceptual mathematical knowledge. At the same time, the framework provided opportunities to practice vulnerability and create empowering experiences for students through, for example, the ‘second teacher’ (to support indicator 4c) and the students creating their own assessments (9a). Additionally, using stories (6) provided her and her students with critical moments to learn about the teacher and each other. This 4 Rs framework has had a lasting impact on Giroux’s pedagogy and approach to mathematics education.
The development of the framework continues, as Giroux’s practice as a mathematics teacher evolves. Presently, the 4 Rs pedagogical framework is being re-conceptualized through a rhizomatic lens, which we believe more aptly reflects the fluid and interconnected nature of the 4 Rs. Through this rhizomatic analysis, Giroux’s teaching practice and research are growing toward embracing further decolonizing actions. Beyond the value of this framework for Giroux, we believe that this self-study approach to research and practice—one that embraces and engages with pedagogies that feature the 4 Rs—models an innovative and promising approach towards decolonizing one’s teaching practice; it does so through relationship building which grounds the teaching and learning of mathematics in respect, responsibility, relevance, and reciprocity. The process not only shows promise for other mathematics educators, but also for those across a broad range of STEM subjects, offering support to teachers as they move beyond surface level professional growth and into deeper and longer lasting decolonizing actions. By personalizing and adapting the framework and research process, educators can contribute to the current research around disrupting power, focusing on the 4 Rs, and decolonizing mathematics education.

Author Contributions

Conceptualization, M.A.G.G. and K.T.N.; data collection, M.A.G.G.; formal analysis, M.A.G.G.; investigation, M.A.G.G.; data curation, M.A.G.G. and K.T.N.; writing—original draft preparation, M.A.G.G. and K.T.N.; writing—review and editing, M.A.G.G. and K.T.N. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

The study was conducted in accordance with the Declaration of Helsinki and approved by the University of Regina Research Ethics Board. Approval Code: REB file #321. Approval Date: 18 September 2024.

Informed Consent Statement

Informed consent was obtained from all participants involved in the study.

Data Availability Statement

The data in this project would be inappropriate to share publicly to protect the anonymity of the participants.

Conflicts of Interest

The authors declare no conflict of interest.

Notes

1
While Kirkness and Barnhardt (1991) do not focus specifically on Indigenous research, their work does focus on improvements to teaching and learning in higher education for Indigenous students. Since their publication in 1991, other scholars (e.g., Archibald, 2008; Johnston et al., 2018; Kovach, 2021) have contributed to and extended this research, such that today the work is commonly referred to as the 4 Rs of Indigenous research.
2
It is important to note that the language of ‘my’ framework is not intended to be viewed in a possessive/ownership form, but to differentiate between Giroux’s framework and other interpretations or frameworks including the 4 Rs.
3
The 4 Rs of Indigenous research have evolved beyond being used in the context of research only; in fact, the 4 Rs have been conceptualized as broader guiding principles to include within both Indigenous research and pedagogy.

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Table 1. The 4 Rs Pedagogical Framework.
Table 1. The 4 Rs Pedagogical Framework.
4 RsOutcome
  • Indicator
Respect(1) Embracing diverse mathematical strategies (Kirkness & Barnhardt, 1991)
  • Selecting student work done (for consolidation) to highlight variety of thinking
  • Valuing concrete, pictorial, abstract (CPA) as equally as possible
(2) Dismantling the inherent hierarchy of students and their mathematical knowledge (Parks, 2010)
  • Shift mathematical learning from a path to a journey
  • Refrain from using comparative language for students and their mathematical knowledge
(3) Supporting the border crossers (Kirkness & Barnhardt, 1991)
  • Allow times for students to be passive and rely on group members, when unsure
Encourage students to make mistakes, productively struggle, and be confused (Boaler & Anderson, 2018)
Responsibility(4) Decentering the teacher (Kirkness & Barnhardt, 1991)
  • Work is done in groups to provide more support
  • Be intentionally less helpful (Liljedahl, 2020)
  • Allow students to mobilize/share the mathematical knowledge
(5) Fostering student agency (Johnston et al., 2018)
  • Students build a portfolio of their learning
  • Students defend their learning journey as a summative assessment
  • Students decide individually what is in their portfolio and defense
Relevance(6) Using oral storytelling for tasks and assessment (Nicol et al., 2020)
  • Give tasks as stories or narratives (Zazkis & Liljedahl, 2009)
  • Ask students to tell stories for formative and summative assessment
(7) Students voicing what is relevant to them (Lunney Borden et al., 2020)
  • Co-create stories that enable students to make sense of the mathematics (problem solving)
  • Give open ended tasks
  • Allow students to create tasks with minimal constraints
Reciprocity(8) Focusing on processes and reasoning over solutions and products (Boaler, 2019)
  • Create a conversation about the process, not the product
  • Support students to reason during consolidation
  • Ask open questions during consolidation
(9) Blurring lines between producers and consumers of knowledge (Kirkness & Barnhardt, 1991)
  • Students create tasks and assessments
  • Students select which mathematical work they would like to consolidate and discuss
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Giroux, M.A.G.; Nolan, K.T. Respect, Responsibility, Relevance, and Reciprocity: What the 4 Rs of Indigenous Research Offer Toward Decolonizing a Mathematics Classroom. Educ. Sci. 2025, 15, 1579. https://doi.org/10.3390/educsci15121579

AMA Style

Giroux MAG, Nolan KT. Respect, Responsibility, Relevance, and Reciprocity: What the 4 Rs of Indigenous Research Offer Toward Decolonizing a Mathematics Classroom. Education Sciences. 2025; 15(12):1579. https://doi.org/10.3390/educsci15121579

Chicago/Turabian Style

Giroux, Maegan A. G., and Kathleen T. Nolan. 2025. "Respect, Responsibility, Relevance, and Reciprocity: What the 4 Rs of Indigenous Research Offer Toward Decolonizing a Mathematics Classroom" Education Sciences 15, no. 12: 1579. https://doi.org/10.3390/educsci15121579

APA Style

Giroux, M. A. G., & Nolan, K. T. (2025). Respect, Responsibility, Relevance, and Reciprocity: What the 4 Rs of Indigenous Research Offer Toward Decolonizing a Mathematics Classroom. Education Sciences, 15(12), 1579. https://doi.org/10.3390/educsci15121579

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