In this editorial, I seek to share insights with other mathematics education researchers, especially those early in their journeys, into the long-standing assumptions about what it means to advance the field and how we should think about issues of rigor.
The purpose of this editorial is to consider pathways for doing that work by building on research this journal has previously published. The goal is to offer a vision for creating research that contributes to a gentler, more just, and more curious world, through an argument grounded in a small set of mentor texts.
In democratic societies, education is said to operate as a meritocratic equalizer, granting upward social mobility to those willing to work hard and develop their talents. In the 21st century, however, such mobility has decreased across the globe, particularly in countries with greater economic inequality. As a result, education’s promise to enable a better life has become ever more tenuous.
In a task-based interview, we examined how a high school student with high spatial visualization ability, Andrea, generated three-dimensional objects by rotating two-dimensional shapes about an axis using paper and pencil and hands-on manipulatives. Initially, Andrea interpreted rotation as planar motion, without extending into three-dimensional space. With the use of hands-on manipulatives, she gradually shifted toward a more integrated understanding of spatial rotation, relying on metaphorical associations and visual cues to support her recognition of dimensional transitions. Afterward, she coordinated spatial elements (e.g., the line of rotation and radius) more precisely, constructing increasingly coherent representations of solids of revolution. Our study offers insights that inform future research and instructional design focused on supporting students’ understanding of dimensional transformations.
Women, underrepresented minorities, and low-income students remain underrepresented in STEM disciplines. Among the required introductory courses, the calculus sequence is an obstacle linked to students’ decisions to leave their chosen discipline. Here, we analyzed data on students’ grades across the calculus sequence at a Minority-Serving Institution and examined the following: (a) group-level disparities in performance and the evolution of these disparities over the course sequence, (b) whether and how disparities in performance relate to differences in persistence rates between groups, and (c) whether course grades are linked to underrepresented students’ decisions to continue with subsequent coursework. Findings suggest that the barriers in pursuing STEM majors differ among underrepresented groups and have implications for efforts aimed at diversifying the STEM pipeline.
Educators are often unsure how to support students with disabilities in grade-level mathematics, and special education intervention often focuses exclusively on computational fluency. In this case study, we explore how one third-grade student with learning disabilities successfully engaged in grade-level mathematics problem solving across 45 video-recorded one-on-one instructional sessions. Although she experienced difficulty with foundational number skills (e.g., counting, reading and writing numbers), the analysis identified a set of instructional practices that enabled her to meaningfully engage with grade-level problems. By analyzing these practices through the Teaching for Robust Understanding framework (Schoenfeld et al., 2023), we provide an important counterargument to special education research that claims that students with disabilities require teacher-directed, explicit instruction focused on foundational skills and fluency.
This article is based on my Special Interest Group-Research in Mathematics Education scholar award talk given at the American Educational Research Association 2025. In it, I share five words that I think characterize my research journey in mathematics education. These words are skepticism, surprise, respect, joy, and hope. I selected examples from my more than 30 years of research to engage the audience (and now the readers) in moments of surprise, respect, and joy, while keeping in mind an attitude toward the work we do that is both skeptical and hopeful. By sharing what matters to me as a researcher in mathematics education, I invite the readers to reflect on their work as mathematics educators. What matters to you and why? What are your words?
This Research Commentary highlights the lack of research knowledge about doctoral preparation in mathematics education in the United States and the variability of program requirements across institutions. During the past decade, more than 100 institutions have awarded doctorates in mathematics education, yet very little is known about the nature of the preparation these graduates received. This commentary is intended to share some knowledge about the limited research on doctoral programs that has been reported and to prompt a discussion of the nature and content of doctoral preparation in institutions in the United States. The goal is to encourage more systematic and scholarly research on doctoral preparation in mathematics education to be conducted and reported in scholarly journals.
The United States established a system of Indian boarding schools from the late 1800s through the 20th century. Previous scholarship documented how boarding schools aimed to forcibly assimilate Native children into white American society. However, no study has examined the mathematics curricula in the schools in relation to settler colonialism. Using the logic of elimination framework, we analyze primary documents to reveal how mathematics policies and curricula perpetuated settler colonial ideologies, values, and practices. We present major themes from our findings and argue that mathematics education at the Indian boarding schools worked in conjunction with the 1887 Dawes Act to open what settlers called surplus territory to white farmers and enforce capitalist notions of labor, land, and the natural world.
Researchers have identified both the affordances of engaging students in symbolization activities and the difficulties students have in constructing meaningful representations of contexts through algebraic expressions and formulas. This article includes clinical interviews and teaching experiments with preservice secondary mathematics teachers focused on engaging them with dynamic geometric contexts to understand their representational activity with formulas. I introduce the notion of a multiplicative object in the context of formulas and express its importance in the construction of productive meanings for constructing formulas via covariational reasoning. Specifically, I provide a framework for the different types of multiplicative objects for formulas and connect students' constructions of a multiplicative object with their covariational reasoning within and across different geometric contexts.
In this editorial, I seek to describe the range of articles published in the period during which I had the privilege to be this journal’s editor-in-chief. I offer seven synthetic looks at the content of our publications–through the lenses of themes discussed in prior editorials–and recommend some topics for Research Commentaries.
In my last editorial for JRME, I want to reflect on leadership. Being the editor-in-chief of this journal has given me an opportunity to steward one of our field's institutions—much like opportunities that others have as editors of other journals, officers of professional organizations, program chairs of conferences, directors of funding programs or research centers, or administrators of departments or colleges.
This meta-analysis assessed the effectiveness of problem-posing interventions on learners' cognitive learning outcomes. We system-atically reviewed 26 quantitative studies published between 2002 and 2024. The results show a large, positive, and significant effect (Hedges's g = 0.53 ) of problem-posing interventions. A series of subgroup analyses found that (a) the effect was larger for inter-ventions incorporating problem posing into technology-supported learning environments than it was for problem posing without technological support, and (b) the effect was larger when interventions engaged learners in problem posing using problem examples. These findings provide evidence about the features of problem-posing interventions that are effective in improving learners' cogni-tive mathematical outcomes. We discuss implications for using and selecting problem-posing interventions
Research suggests that the majority of the world's children fail to meet minimum grade-level outcomes in mathematics. Our concern in this Commentary is with the representation of settings where the majority are marginalized from core mathematics grade-level outcomes in the mathematics education research field. Our concern is located amidst a growing mainstreaming of an equity focus in leading international journals. However, despite broader global participation in an increasingly diffuse research field, contexts of majority marginalization from core grade-level mathematical outcomes, especially in the Global South, remain relatively invis-ible in leading journals. We use an overview of publications in JRME between 2021 and 2024 to explore the visibility of this disparity and the challenges it poses for the field.
Society produces storylines about Latin & eacute; communities, including their placement in racial and linguistic hierarchies, that permeate the mathematics classroom and research in mathematics education. We conducted a discourse analysis of the enunciations used in top-tier mathematics education journals about these communities. The majority of articles we examined functioned to maintain white supremacy by centering dominant (white) storylines and values to maintain a racial hierarchy, with whites above Latin & edot; and other marginalized groups. However, our findings also illuminate the counter-stories of Latin & eacute; communities in mathematics educa-tion research literature. We call for a more critical look at the field of mathematics education research and the norms that have been set for conducting, disseminating, and reflecting on research endeavors about marginalized groups.
We examine the meanings students give to points when they are graphing relationships between quantities in dynamic, experiential contexts. Using data from teaching experiments with middle-grades students, we illustrate two main categories of meanings: iconic and quantitative. We then introduce four distinct subcategories of meanings: (a) iconic and transformed iconic translations (a point represents an object or location), (b) nonunited points (a point represents a single quantity's magnitude), (c) spatial-quantitative multiplicative objects (a point is an object or location with quantitative properties), and (d) quantitative multiplicative objects in conventional and nonconventional planes (a point represents two quantities' magnitudes). We discuss the implications of these meanings for research, teaching, and curriculum development.
We investigate proving activities from a monistic embodied perspective, namely the functional dynamic systems (FDS) approach. Using proofs without words, we focus on proving activities that can be conceptualized as identifying and filling gaps. Using a microethnographic methodology enhanced by eye-tracking, we investigate sensory-motor processes in proving and theorize their roles. Findings reveal five theoretical roles of sensory-motor processes: Exploring the environment, Appropriating artifacts, Connecting artifacts, Blocking out the environment for enrichment, and Expanding the environment. Through nonlinear iterative activations of sensory-motor processes serving these roles, a student forms a coherent FDS that constitutes the proof.
In this mixed-methods study, we introduce an activity-based perspective on mathematical authority that considers who leads mathematical activities in a classroom. Our framework for mathematical authority extends existing research that focuses primarily onAuthoring mathematical ideas to include the activities of Visualizing and Speaking. Using data from 129 lessons, we identified six authority structures that reflect consistencies in how mathematical authority was distributed across Authoring, Speaking, and Visualizing. These authority structures provide greater clarity and nuance to prior work on shared authority. We also used loglinear models to identify relationships among co-occurring authoritative activities and found that when students had authority for Visualizing, Speaking, and using Previously Generated Student Work, they were more likely to have authority for Authoring.
We present findings from an analysis of tests of teacher mathematical knowledge identified over a 20-year period of mathematics education literature. This analysis is part of a larger project aimed at developing a repository of instruments and their associated validity evidence for use in mathematics education. We report on how these tests are discussed in the literature, with a focus on validity arguments and evidence. A key finding is that these tests are often presented in ways that do not support their use by the mathematics education community. We offer suggestions on how adopting a validity argument perspective can enable others to build on initial test development efforts.
In editorials during my final year as editor-in-chief of JRME , I have been reflecting on what I have learned about our field and this journal. I am eager to share some of what I have learned because it may provide glimpses of what our field is working on and the initial material available to produce each volume.
