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Learning about human mathematical dialogue from dialogue with chatbots: Babbling, gargling and funnelling
Full text linkIn 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
States of Disarray: Cleaning Data for Gerrymandering Analysis
No full textThe 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
Marcus Welnel & Parker Fleming on collegiate sports mayhem
No full textThis week’s guests are Marcus Welnel and Parker Fleming. Marcus played football for the Griz and now serves as chief revenue officer for Grizzly Athletics. Parker has a PhD in economics and works with the universities on how to set player salaries.
In this conversation, the three talk about the changing landscape of collegiate athletics, particularly the impact of name, image and likeness on the ability for student-athletes to earn income. They also discuss the changing landscape of playing sports for the value of camaraderie and institutional pride or for more lucrative offers.https://scholarworks.umt.edu/anewangle_podcasts/1427/thumbnail.jp
ANA’s Legal Roundup with UM Law Professors
No full textIt’s time once again to check in with A New Angle’s Chief Legal Correspondents Craig Cowie and Constance Van Kley, law professors at the University of Montana. 2026 is sure to bring many consequential legal developments, and Constance and Craig will help us try to make sense of what to expect.In this conversation Justin, Craig and Constance talk about the changing power of the executive and the rise of the unitary executive theory. They discuss the shadow docket and the tendency for courts in this administration to expedite processes, making the path to decisions less clear. Craig and Constance consider the topics they have in focus for the remainder of this year.https://scholarworks.umt.edu/anewangle_podcasts/1431/thumbnail.jp
Teaching talk moves to support the discussion of divisibility content in a trilingual classroom
Full text linkIn this article, we present our study of teaching talk moves and translanguaging practices used to support the discussion of divisibility in a Catalan–Spanish–English trilingual classroom of a secondary school. We examined a sequence of eleven lessons with a focus on seven talk moves – Switching languages, Revoicing, Recapping, Adding on, Focusing, Funneling and Eliciting. Through this we were able to identify some teaching episodes in which the attention was given to discussing specific mathematical–linguistic challenges involved in the learning and understanding of divisibility content. We illustrate this finding using an episode around the least common multiple and how interconnected moves of Switching languages, Recapping, Eliciting, Funneling and Revoicing functioned to distinguish the mathematical meaning embedded in the lcm labelling, alongside the mathematical meaning intended for the individual word names, least, common and multiple, for the noun phrase and for the concept. We comment on more briefly a second episode around the parity concept for elaborating on the same finding. Our contribution adds to recent work on mathematical–linguistic challenges in the literature and does so with unique data from the under-researched context of the trilingual mathematics classroom
Mathematics in Maltese: The compilation of a bilingual English-Maltese glossary to support mathematics teaching and learning in Malta
Full text linkIn Malta, mathematics education is accessed bilingually through Maltese and English. While Maltese is often used for verbal interaction, English is the language of written texts, including assessments. Consequently, switches between the languages is a common feature of Maltese mathematics classrooms. Anecdotal and research evidence indicate that Maltese students benefit from the use of their home language. However, to date, there is no recognised and standardised Maltese bank of mathematics Our project aims to address this lacuna. In this article, we outline the process of compiling a bilingual glossary of mathematics terms intended for kindergarten and elementary school levels in Malta (ages 3–11 years). The purpose of the glossary is to support teachers and students in their use of the two languages for the teaching/learning process. This novel resource can serve to validate the Maltese language for mathematics and to encourage consistency of terminology across school and classroom contexts. The glossary can also be helpful in the future should we choose to introduce written Maltese for mathematics. In this article, we explain how the project was developed and how word choices were made with respect to the Maltese terms
The big (bad?) wolf with Alex Metcalf
No full textThis week’s guest is Dr. Alex Metcalf, associate professor at the University of Montana’s Franke College of Forestry and Conservation. Alex is a social scientist who studies how people make decisions in a wide variety of conservation domains. Alex and Justin collaborate on a variety of projects, including a just released study on the interaction between politics and our attitudes towards wolves.
In this conversation, Alex and Justin talk about how political identity can contribute to the polarization around people’s attitudes towards wolves and discuss how identity-based assumptions can drive division, but also how that can be corrected to bring people back together.https://scholarworks.umt.edu/anewangle_podcasts/1426/thumbnail.jp
GLI Weekly, January 20, 2026
No full textAdvising Information -- Beyond the Classroom Experience Planning -- Nominate a Student Speaker for 2026! -- We\u27re recruiting a VISTA for the Franke GLI -- Save the Date: 2026 Martin Luth King, Jr. Lecture: Resistance, Resilience, and Radical Love with Dr. Regina Shands Stolfzfus -- Winter Welcome Back -- The Mansfield Center is hiring a Student Program Assistant to focus on communications, social media, and events for Spring and Summer 2026 -- Experiential Learning Scholarships -- Democracy Summit: Call for Proposals -- Spend your spring break making a difference with UM\u27s Alternative Breaks -- Looking for an opportunity after graduation? -- Winter Kickback Mixer with The Branch Center -- Free Week at the Gaming Den -- Scholarship Opportunities -- Bella and Murray Ressler Digital Humanities Fellowship at the United States Holocaust Memorial Museum, AY 2026-202
Rural vs. Urban with Trevor Brown
No full textThis week’s guest is Trevor Brown, post-doctoral fellow at the Center for Economy and Society at Johns Hopkins University. Trevor is the co-author of an important new book, Rural Versus Urban: The Growing Divide That Threatens Democracy. Many of the dynamics reported in this book are unfolding here in Montana. In this conversation, Trevor talks about how rural and urban areas have become increasingly polarized, and discusses the economic factors and messaging strategies that have led to that divide. Trevor talks about the dangers of this divide, but also brings up some solutions.https://scholarworks.umt.edu/anewangle_podcasts/1428/thumbnail.jp