2026-03-16
Mary Elizabeth Riley Lloyd et al.
This study replicated an earlier study that explored the beliefs of a sample of K-8 pre-service teachers (PSTs). Results of this study position PSTs’ beliefs along a traditional-reform continuum. The positioning from the current study is compared to that of the former study, to determine the level of progress made toward the National Council of Teachers of Mathematics’ commitment to high-quality instruction. To position beliefs, PSTs completed a Likert survey, including open-ended questions, three times throughout their teacher preparation program (TPP): before taking any of their mathematics education courses, after taking both required mathematics education courses, and after student teaching. On the last survey iteration, PSTs completed additional Likert items and open-ended questions regarding their teaching practices. Analysis centered on the relationship between each iteration of the new survey, comparisons to results from the initial study, and the alignment between beliefs and teaching practices. Overarching results convey that even with the passage of eleven years, the positioning of beliefs and teaching practices remained relatively static. Beliefs related to the power of student ideas, mathematical processes, productive disposition, and productive struggle were categorized as being reform oriented. The perception that mathematics is mostly computation and that the expository teaching is the most effective way to teach mathematics were categorized as being strongly traditional. Beliefs that were categorized more centrally related to collaboration and the emphasis on answers. Suggestions are provided for teacher educators to continue their work toward reforming beliefs about mathematics and how to teach mathematics.
2026-03-11
John Beam et al.
Students are exposed to a variety of mathematical tricks that ostensibly make it easier for them to solve problems. But tricks also undermine their understanding that mathematics is supposed to make sense; they rob students of opportunities to explore and struggle with ideas; and they obscure mathematical structure.
2026-02-23
Jenni Ingram et al.
In concluding the second series of eight articles in the double special issue on ‘Engaging with communication and language in relation to mathematics and its education’, we take the opportunity to reflect across the articles to prompt us all to consider potential and emerging directions for future research. This final article is overall a commentary inspired by the communication-centred and language-centred contributions to mathematics education across the entire collection of articles, that is, all those comments that situate mathematics and its education as language and communication praxis. We explore this relationship between mathematics and its education with communication and language through three themes: time, theories and methodologies, and the nuances of the term ‘relation’ in the title of this double special issue.
2026-02-23
Qiang Lin
This qualitative study examines communication in family mathematics settings, focusing on how embodied communication is constituted during parent–child interaction with a multitouch technology application, TouchCounts . Moving beyond information–transmission perspectives, the study adopts an embodied and relational approach centered on affectivity —conceptualized as the circulation of attunement, resonance, and intensity of movement and feeling across human and non-human components of the parent–child– TouchCounts assemblage. Drawing on close qualitative analysis of two selected video-recorded excerpts, the study traces how mathematical events unfold moment by moment through bodily action and material engagement, and how affective flow shapes how participants respond to one another and to the digital interface. The findings show that affectivity operates as a constitutive dimension of mathematical communication, shaping how mathematical concepts (e.g., addition toward bigness, making two by V-gesture) are enacted, oriented, sustained, and transformed as lived events. By foregrounding affect and embodiment, this study offers a novel perspective on communication in family mathematics and contributes to broader discussions on mathematical meaning-making in technology-mediated contexts.
2026-02-23
Jo Skelton et al.
This paper presents the findings of a study, conducted as part of a PhD thesis, exploring ways in which translanguaging can be used to support the development of conceptual understanding of division. The study focused on 18 8-9-year-old pupils learning mathematics through the instructional languages of English and French in an ‘immersion-style’ bilingual education context in England. The data was collected from four consecutive mathematics lessons focusing on division, the first two taught through English by a monolingual English teacher and the second two taught in French by a bilingual French teacher. Both teachers were interviewed directly following their second lesson and the pupils participated in two focus groups, following their lessons in English and then French. This paper focuses on three of the seven translanguaging cycles that were identified as part of the analysis, each with a different combination of interlocutors. The first extract presents a peer-peer discussion of division involving exchange, the second involves a teaching assistant scaffolding learning for a new-to-French pupil and the third illustrates a pupil seeking clarification from the teacher. The findings reveal that crosslinguistic translanguaging affords a flexible space in which pupils are able to draw upon their linguistic repertoires to make linguistic and conceptual connections. The use of multiple representations and reprocessing opportunities further supported crosslinguistic transfer within these translanguaging cycles.
2026-02-23
Elizabeth Kimber et al.
The shape of a graph arising from the covariation of variables is a crucial idea in reasoning about functions and graphs. Students’ perspectives on graph shape may foreground visual features and consider the shape to be a fixed property of the function (static graphical shape thinking). In contrast, students can perceive the graph as a trace of covarying quantities, through which its shape arises (emergent graphical shape thinking). It is of interest to understand how these perspectives are supported and promoted by teachers in classroom discourse. We present findings from a study of classroom discourse in which we used systemic functional linguistics (SFL) to identify features of how teachers and students described graphs. We identified informal but vivid descriptions of graphs that may have affordances for, and even foreground, emergent graphical shape thinking.
2025-09-08
Ananya Agarwal et al.
The mathematics of redistricting is an area of study that has exploded in recent years. In particular, many different research groups and expert witnesses in court cases have used outlier analysis to argue that a proposed map is a gerrymander. This outlier analysis relies on having an ensemble of potential redistricting maps against which the proposed map is compared. Arguably the most widelyaccepted method of creating such an ensemble is to use a Markov Chain Monte Carlo (MCMC) process. This process requires that various pieces of data be gathered, cleaned, and coalesced into a single file that can be used as the seed of the MCMC process. In this article, we describe how we have begun this cleaning process for each state, and made the resulting data available for the public [AAHSV]. At the time of submission, we have data for 44 states available for researchers, students, and the general public to easily access and analyze. We will continue the data cleaning process for each state, and we hope that the availability of these datasets will both further research in this area, and increase the public’s interest in and understanding of modern techniques to detect gerrymandering.
2025-09-08
David McCune
This article describes an interesting error I committed in the course of my research in voting theory. While embarrassing, the error has led to productive discussions about mathematical failure with my students in my probability and statistics course. I describe my mistake and discuss how the incorporation of such mistakes into the classroom can enhance student trust and engagement.
2025-04-08
Ingólfur Gíslason
In this study, I explore mathematics teaching-learning dialogues between preservice teachers and a chatbot (ChatGPT) with the aim of increasing our understanding of human mathematics teaching-learning dialogues. The dialogues contain wrong solutions (as determined by the preservice teachers), and the teachers try to get the chatbot to reconsider its answers without giving away the answer. The chatbot’s solution attempts are interpreted through and against the concepts of babbling (imperfect efforts to express thought) and gargling (imitation of surface form of expressions), and the dialogues are analyzed by considering whether and how the preservice teacher and the chatbot reach joint attention. The conversations illustrate that chatbots based on Large Language Models (LLMs) may behave analogously to gargling students and that preservice teachers are tempted to direct the chatbot’s attention to specific important aspects of tasks to get it to reconsider its answers, engaging in a language game of funnelling. Funnelling may work in the sense that the chatbot arrives at an acceptable solution. Still, sometimes, it seems that it is extremely difficult to achieve what looks like human joint attention with the chatbot, hindering progress on a mathematical problem.