This article argues that centering dignity in analyses of mathematics classroom activity serves as a necessary rejoinder to histories of oppression, domination, and subjectification baked into US-based schooling and rife in school-based mathematics education. Defining dignity using Lloyd's definition of dignity as struggle against domination, I add a literature-based Framework for Axiomatic Dignity in Mathematics Learning as a heuristic for considering the practices, positions, and micro-enactments of dignity evidenced in one classroom. Situated in a year of ethnographic research in one mathematics classroom at a predominantly Latine-serving high school in California, this article examines how conditions of possibility for dignity might be organized into classroom life and how minoritized youth participate in micro-enactments of dignity in school mathematics spaces. Findings revealed that even in a classroom where instructional practices and local positions strongly aligned with storylines of students as community members, learners, and mathematical thinkers, students at times resisted or renegotiated classroom expectations, particularly if the mathematical thinker storyline might compromise one of the other two. This article contributes to the learning sciences and mathematics education to articulate dignity as a productive analytic lens and better understand what, where, and how dignity may exist in the school-based mathematics classroom.
The literature on historical empathy is clear about the importance of fostering students' engagement with historical figures' positionalities, though the nature of that engagement remains less settled. This descriptive qualitative study examined the proposition that deeper understanding of the convergences between inquirer positionality and historical empathy could reveal nuanced considerations for engagement and instruction. Participants included thirty preservice teachers in a secondary social studies methods course who completed an inquiry-based historical empathy experience focused on lived experiences during the Vietnam war. Operationalization and analysis of inquirer positionality was theoretically framed by John Dewey's pragmatic theory of transactional constructivism, while the conceptual framework for historical empathy employed the interrelated aspects of historical contextualization, perspective taking, and affective connections as an underlying structure that was bolstered by recent empirical findings and additive constructs from social empathy. Analysis revealed four overarching themes in participants' engagement in historical empathy and resultant historical understanding: 1) Identification & Self-Other Awareness; 2) Contextualized Historical Perspectivity & Affective Considerations; 3) Reflexive Historical Perspectivity & Affective Resonance; and 4) Affective Mentalization & Macro Self-Other Awareness. Discussion focuses on each theme's unique contribution to historical empathy, potential implications for instruction, and the consequences of historical empathy as an inquiry-based transactional experience.
We designed a professional learning series for science teachers to support their integration of computational practices into instruction, and to design equitable learning opportunities for students to engage in computation. During the professional learning series, we provided the teachers with two main resources to support their enactment of equitable computational pedagogies: computationally integrated (CI) tasks, and the Equity Quantified in Participation (EQUIP) tool. We also broadcasted a contextual discourse about the importance of equitable computational instruction, and infused this narrative into all professional learning sessions. Our goal for the contextual discourse was that it might shape teachers' personal vision of instruction (their critical pedagogical discourses). We describe two major assertions from the data analysis. First, the primary resources (CI tasks and EQUIP) focused teachers' attention on different kinds of instructional interactions with distinct topical themes for each resource. Second, each teacher's critical pedagogical discourses shaped how they recognized and used the primary resources, and we illustrate differences between teachers using contrasting cases.
Complex scientific equations often appear opaque to students-not just because of symbolic formatting, but also due to how learners activate and coordinate different varieties of mechanistic and mathematical schemas. We present a multimodal analysis of advanced undergraduates' reasoning across three interview tasks involving concepts modeled by the Nernst equation-an equation that models electrochemical equilibrium. Drawing on the Knowledge in Pieces framework, particularly the symbolic-forms framework, we show that students interpret the equation by coordinating the same mathematical structures with different mechanistic schemas-principally equilibrium- and balance-based reasoning. One student, Oscar, highlights dynamic shifts between these reasoning modes compared to his peers who were relatively more stable in their either equilibrium- or balance-based reasoning. We illustrate how an equation's format can sometimes shift students away from productive mathematical schemata coupled to mechanistic schemata that align with a natural system's structure. We argue that instructors should attend not only to students' formal manipulations of equations but also to how task design and equation format jointly co-activate different knowledge resources and modes of reasoning. Implications for instructional design include deliberately cueing conceptual framings that develop mechanistic reasoning in addition to calculation.
In this article, we present a coordination of two prominent theoretical perspectives in mathematics education-spatial structuring and units coordination-for building models of students' spatial enumerations and measurement. The authors, each experienced in either theoretical perspective, hypothesized that a coordination of the two theories may be possible, given their common grounding in Piagetian theory. We argue that such a coordination is not only possible, but important for supporting collaboration across research communities and for building more robust explanatory models of students' mathematics. Indeed, a central claim of this article is that by building a coordinated theoretical framework, researchers can explain students' mathematics better than if they apply either theory alone. Methodologically, our coordination of the two theories was empirically driven. We conducted clinical interviews with pre-service elementary school teachers, analyzed interview data from each theoretical perspective separately, then engaged in a process of coordinating our spatial-structuring- and units-coordination-based models. In addition to our proposed coordination of these two theoretical perspectives, secondary contributions of this article include revised definitions of certain theoretical constructs, a case study of analyzing one pre-service elementary school teacher's reasoning through our coordinated framework (and how our coordinated analysis contributes to insights into this student's spatial-numerical reasoning), and an illustration of how two epistemologically-compatible theories focusing on students' mathematical thinking can be coordinated.
While long recognized as a promising instructional reform, Project-Based Learning (PBL) remains uncommon in U.S. classrooms. This article investigates the outcomes of a practice-based professional development (PD) focused on supporting middle and high school teachers to develop and enact a set of teaching practices for PBL. Grounded in cultural historical activity theory (CHAT), we analyzed teacher interviews and portfolios of practice and found striking patterns in how teachers described each of the PBL practices that were focused on in the PD. While teachers described certain PBL teaching practices as things they did on their own, they described other teaching practices as being significantly enabled or constrained by their school and community. For almost all participating teachers it was the PBL teaching practices that were most countercultural to historical schooling practices that teachers' described as being significantly influenced by communities. Out of these findings, we argue that if professional learning seeks to spark radical transformations in instructional practice, teaching practice itself may need to be reconceptualized as a communal activity rather than an individual one. The authors examine the implications of this reconceptualization for both theory and designs for professional learning.
Indian higher education, while a beacon of opportunity, often becomes a site of profound struggle for Dalit students facing entrenched caste discrimination. This paper moves beyond narratives of victimhood, instead spotlighting the powerful agency of Dalit students as they actively reshape their educational journeys. Through intimate interviews with three marginalized caste students, we uncover how their everyday actions embody transformative defiance. Their stories reveal strategic efforts: challenging pervasive myths about academic merit and reservations, illuminating the complex layers of intersectional discrimination, broadening linguistic practices within university spaces, and directly confronting systemic inequities in admissions and social life. These narratives demonstrate how Dalit students assert their dignity and drive change through both individual and collective resistance. This study ultimately champions Dalit voices and knowledge, calling for educational systems that truly affirm their experiences and foster equitable learning environments.
This study investigated a journalistic learning approach in a high school English class within a civic media literacies framework toward civic intentionality. Informed by social-cognitive theory, this study focused on learning if and how the student experience developed (a) motivational factors for student writing, including self-efficacy, belonging, writing anxiety, agentic engagement, metacognitive self-regulation, flow in writing, and intrinsic writing motivation, and (b) cognitive factors for writing, including critical thinking and digital media literacy. The sequential mixed method study used correlations, pre- to post-program change analysis, and the triangulation of qualitative thematic analyses of student focus group and teacher interview data. Results supported most of the expected relationships, suggesting the experience likely contributed to a positive shift in motivational and cognitive factors for writing. Qualitative data highlighted the most impactful parts of the journalistic learning experience, such as interviewing real-world experts for their stories, that increased students' interest and motivation in writing about real-world issues. The mixed method results build an integrated narrative of students' agentic, cognitive, and metacognitive development in journalistic skills, reinforcing the importance of interest-driven learning opportunities in writing and autonomy-support in skill development, such as in writing, that brings anxiety to many students.
This study examines an expansive shift in the priorities of professional learning within a collective of high school science teachers, scientists, community organizers, youth, and educational researchers who were working together on classroom science projects grounded in community concerns of environmental racism. Through a participatory design-based approach, we challenge the assumed relationship between educational research and priorities for teacher professional learning. The study elucidates the processes of teacher solidarity co-design by which our group decided to refocus a professional development institute for science teachers on learning three realms of historical context: history of neighborhoods, grassroots campaigns for environmental justice, and relationships between science and industry. Our analysis indicates that four elements of our co-design worked together to facilitate an expansive shift in the object of professional learning to prioritize science teachers' learning of history. Specifically, we identified the following elements as supporting teacher priorities to determine the direction of our collective learning: (1) the composition of our "more-than-teacher collective," (2) the dialogic structure of our institutes, (3) the temporal structure of institutes that emphasized praxis, and (4) our decision to focus on a specific real-world problem rather than disciplinary concepts or teaching practices. These findings may inform new relationships between educational research and the professional learning of teachers wherein the priorities of the latter are collectively determined.
Dialogic classroom discussions where students collaboratively share and reason through complex ideas are critical for achieving ambitious reform goals for student learning. However, K-12 classroom talk is predominantly characterized by monologic, "teacher-centered" discourse patterns that have proven exceedingly resilient to change. Teacher learning researchers and practitioners have increasingly emphasized developing teachers' noticing and reasoning about the link between their pedagogical choices and student thinking in reflection as key for transforming teaching practice. Less is known, however, about the mechanisms that link teacher reflection processes to growth in classroom discussion quality. In this study, we conducted in-depth comparative case analyses of two 5th grade teachers' learning trajectories as they participated in a video-based literacy coaching intervention. Findings show a close link between overall levels of growth in teachers' reflection and classroom discussion quality, including the quality of student discussion contributions. Findings also reveal that the extent to which teachers adopted "exclusionary" ideological framings related to learning and learner ability in reflection was highly influential for shaping differential growth in their learning and practice trajectories over time. This study contributes toward a more robust and nuanced theory of how teachers develop adaptive expertise for dialogic forms of classroom discussion.
Facilitating whole-class discussions based on tasks that support inquiry and provide conceptual learning opportunities has been identified as a central, challenging task of teaching. We drew upon practice-based and interactionist research traditions to decompose how eight experienced Grades 5-7 mathematics teachers facilitated whole-class discussions after their students had determined volumes for rectangular prisms. The discussions highlighted ways that students worked with wooden cubes, imposed multiplicative structures, and developed formal calculations. Qualitative analysis of the video-recorded lessons revealed five practices that the teachers used to facilitate whole-class discussions. Three of the practices supported extensive, explicit connections between higher-order and lower-order knowledge elements related to volumes of rectangular prisms. We characterized such instruction as providing deep conceptual learning opportunities. The remaining two practices jumped quickly to calculations and did not make as many explicit connections to the organization of cubes in rows, columns, and layers. We characterized such instruction as providing shallow learning opportunities. Identifying the five facilitation practices contributes to theorizing about relations between teaching and learning that support conceptual understanding and underscores the importance of examining such relations at a micro-level and in the context of specific mathematical topics. Moreover, the results can inform professional development programs that seek to help teachers to enact productive conceptual learning opportunities during whole-class discussions.
This case study, framing teaching as a dialogic relationship between teachers and students, investigates how educators can learn how to manage the complexity of instructional decision-making through a professional learning routine. The study analysis examined how the "Teacher Time Out" routine, when embedded within collaborative teaching environments, allowed educators-school leaders, teachers, and university faculty-to engage with the unpredictability of classroom interactions alongside their colleagues and students. Through this process, educators were able to inquire into mathematical ideas with students, respond to the particulars of students' mathematical thinking, enact shared cultural values, and develop pedagogical judgment to inform future teaching decisions. Using a sociocultural perspective on teacher learning, this case study highlights how pauses during instruction enabled educators to reflect on their practice, collaboratively reaching instructional decisions in the moment and reflecting on them after the teaching enactment. The study contributes to the literature on professional learning, showing the potential of routines such as Teacher Time Out to support teachers in learning both from and with their students during the dynamic process of teaching.
This article examines how fiber crafting as a category of activity can develop mathematics learning and the conditions under which various fiber crafting traditions differentially cultivate mathematical understanding. Modifying the constructionist paradigm with relational materialist principles, this paper advances the notion of "materialized action," which describes the natural inquiry process that results through emergent patterns between learners and the materialized traces of their actions. This paper takes a qualitative approach, combining a design and intervention phase to look closely across a set of materials (i.e., three fiber crafts, knitting, crochet, and pleating) and engagement in a "powerful idea" (i.e., the role of unitizing in multiplicative proportional reasoning), as instantiated across three youth case studies, and as an illustration of how we can better understand micro-developmental learning processes. We identified three levels of unitizing that make up the larger idea of enacting proportional reasoning (PR) through materialized action, which build and catalyze toward one another and support emergent understanding of PR from the intra-action of the material and the learner. In their engagement with PR, youth employed different strategies based on personal choice, affordances of the materials, and practices of the crafting traditions. Materialized actions as a theoretical advancement has the potential to reformulate what counts as mathematics and can guide the design of mathematics learning that is embracing (rather than reducing) worldly concreteness in learning key domain ideas, with implications for the design of more equitable learning environments.
One of the core aims of inquiry-based learning (IBL) approaches to history education is to help students grasp how historical knowledge is constructed. Thus, IBL applications are usually justified through reference to expert historians' research practices. We argue that the current body of empirical research on historians' practices is limited in some important ways. To develop an expanded understanding of the practice of historiography (i.e., historical research and writing), we interviewed 26 Finnish academic historians about activities involved in their practice. We then identified over a hundred epistemic processes of historiography that we divided into 14 categories. Some categories partly aligned with earlier accounts of historians' epistemic processes, although we identified some extensions of these categories. We also recognized five themes that provide an expanded understanding of historians' epistemic processes for IBL: archival work; tools and languages; virtues and affect; broad approaches and methodologies; and social processes. We discuss the implications of our findings for history education and argue for more diversity in studies of epistemic practices in history. Although professional historiography in its full scale cannot-and should not-be brought into all classrooms, educators need a broader understanding of historiography in order to model such a practice at different levels of education.
In this paper, we provide a new framework to analyze the quality of oral and written argumentation based on the Aims, Ideals, and Reliable processes (AIR) model of epistemic cognition and practices. To date, the prevailing analytic schemes for evaluating argumentation have largely focused on argument structure. We show that these schemes, while valuable in attending to structural aspects of good versus bad arguments, do not account for other important yet often overlooked aspects of argument quality. We develop a complementary framework for analyzing arguments that emphasizes the role of epistemic ideals and reliable epistemic processes in argument quality. We outline our theoretical framework and provide examples of how it can capture aspects of quality that are missed by other frameworks. Then we illustrate the application of our method to analyze seventh graders' written essays and oral discourse in science classes implementing model-based inquiry instruction.
This study explores how personal epistemology is entangled with identity and affect and how such entanglements help explain the nature and emergence of teachers' epistemic stances in the classroom. Our focal case centers around a disagreement between a mentor teacher and her teacher intern about how students should engage in scientific argumentation, a disagreement that erupted into debate during class, in front of the students. At first glance, the debate appears to be purely epistemological, a disagreement about what counts as evidence and as "good" arguments. Further exploration through interviews and other data streams, however, illustrates how modeling entanglements among epistemology, affect, and identity can best help us understand the emergence and persistence of the teachers' epistemic stances across three days of debate. The intern's epistemic stance turned out to emerge not from a full-fledged constructivist epistemology of learning but from entangled epistemological and socioemotional commitments to encourage curiosity and to not shut students down. The mentor teacher's epistemic stance, on the other hand, was driven by epistemological beliefs about the empirical nature of science and evidence, beliefs that help constitute aspects of her identity. We see two key takeaways. First, with respect to informing teacher education and professional learning, it matters whether researchers model these entanglements in terms of separable but interacting epistemological, affective, and identity-related elements or in terms of co-constitutive elements that are, for instance, simultaneously epistemological and identity-related. Second, and relatedly, researchers should consider different modeling choices for their data instead of a priori choosing a separable-but-interacting rather than a co-constitutive modeling framework, or vice versa.
Time management for neurodivergent students, including those with learning disabilities (LD) and/or attention-deficit hyperactivity disorder (ADHD), has long been identified as a hurdle impeding college graduation. Building on research in disability studies, mathematics education, higher education, and time management, we propose a framework for time literacy that centralizes and elevates the individual and that individual's needs in the pursuit of college academics. Our investigation seeks to illuminate sociocultural resources that characterize academic support, including the consequential role of time representations. We present a case study of a specialized academic support program for neurodivergent postsecondary students that has an explicit focus on time management. Through interviews with academic coaches and students (N = 9), we identify four interrelated themes emerging from participants' descriptions: time representations, routines, efficacy, and identity. We apply such themes to analyze one-on-one sessions over time to illuminate when and how the four themes arise in situ. We frame time literacy as positioning academic success as one component of overall well-being and thriving that leads to balance in personal and academic needs and goals.
This paper explores how students navigate individual and collective goals in collective embodied modeling activities as part of an elementary science curriculum on states of matter. We propose the Convergent and Divergent Embodied Activity (CDEA) framework to recognize the emergence, adoption, and shifting of goals via students' collective embodied interactions. Drawing on established frameworks for learning in embodied activity and mechanistic reasoning, we use interaction analyssi to illuminate the mediating processes that learners engage in as they develop and pursue different modeling goals through actions, and how these activities promote and reveal students' mechanistic reasoning. We highlight the unique features of embodiment when examining goal formation and pursuit. We conclude with a set of design considerations that attend to how mediated goal convergence and divergence within collective embodied activities contribute to science learning.
Although informal science, technology, engineering, and mathematics (STEM) learning (ISL) has served as a catalyst for inclusive lifelong STEM engagement, research indicates that participation in ISL can still remain inequitable, especially for youths from minoritized communities. To address the continued inequities, youths' rightful presence should be placed at the core of informal STEM education knowledge and practice. Rightful presence refers to youths legitimately belonging in learning spaces by calling out the limits of equity as inclusion. Our study explores the insights youths offered to inform pedagogical practices in support of equitable learning in ISL spaces. We seek such insights, particularly attending to the moments we call 'youth-initiated,' the instances in which youths made visible their bids for rightful presence by seeking shifts in and through their ISL experiences. Drawing on a research practice partnership project in which we co-generated and analyzed data with youths and educator partners, we identify three forms of youths' bids for rightful presence: reorganizing physical and social representations within learning space, mattering beyond educator imagination, and foregrounding the sociopolitical dimension of learning. We illustrate these findings with three focal youth-initiated moments that emerged in the context of three respective ISL programs. We also elaborate on how educators and peers responded to the bids in ways that brought immediate and consequential shifts in ISL opportunities. We discuss our findings and implications regarding research and practice of justice-oriented pedagogies in and beyond ISL spaces.
