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Rethinking equality in mathematics education with category theory
Get PDFTo provide an alternative to the flattening operations of equality, which are prevalent not only in mathematics but also in our everyday world, I introduce the relational structures of category theory and their more nuanced notions of equivalence. Instead of defaulting to a binary assignation of equal or not-equal, equivalence posits that contextual relationships are integral to how we conceive of ‘same’ and ‘different’. I draw upon the ideas of philosophers who work against the erasure of diversity and offer ways to uphold difference while searching for commonalities. As I trace the sociopolitical implications of embracing an ontological framework built on relation, I re-imagine—in words and in spatial imaginaries—our conceptions of knowledge and assessment in mathematics education
ProPublica\u27s Dave McSwane on the unfolding medical drama in Helena
Get PDFJ. David McSwane is an award-winning investigative journalist at ProPublica who recently published a story about Dr. Tom Weiner, a prominent oncologist at Helena’s St. Peter’s Hospital whose practices raised significant ethical, medical, and legal questions. McSwane takes us behind the scenes of his reporting process, sharing how he uncovered allegations of malpractice, including fraudulent billing, overprescription of narcotics, and unsettling end-of-life care decisions. The conversation explores the intersection of health care and greed, the power dynamics within the medical community, and the challenges of exposing complex institutional failures in a community divided between admiration for Dr. Weiner and distrust of the hospital system.
Read McSwane’s story on Dr. Weiner, “Eat What You Kill,”https://scholarworks.umt.edu/anewangle_podcasts/1374/thumbnail.jp
Wonders of Multiplication Table
Get PDFThis paper originated as a talk for school teachers, aimed at demonstrating that the multiplication table is more than a simple memory aid. Instead, it is a powerful tool for exploring mathematical patterns and plays an essential role in both the discovery and teaching of mathematics. The initial goal was to illustrate how the table could act as a bridge between arithmetic, algebra, and proof. However, as the author delved into the table, its intricate structure began to unfold, with each idea seamlessly leading to the next. This evolution transformed the table’s utility far beyond its initial educational purpose. This paper chronicles that journey—from its beginnings to its culmination in Faulhaber’s formula and Bernoulli numbers. Rather than immediately diving into symbolic mathematics, the paper lets the multiplication table gradually reveal its potential as a gateway to advanced mathematical concepts
Montana Kaimin, January 30, 2025
Get PDFStudent newspaper of the University of Montana, Missoula.https://scholarworks.umt.edu/studentnewspaper/11163/thumbnail.jp
From Problem Solving to Problem Posing: Two Classroom Examples
Get PDFIn this paper, we present two examples of classroom activities on divisibility and mathematical induction that combine problem solving and problem posing. In our activities, standard tasks of the form ’Prove that the statement holds’ were transformed into ’Think of similar examples,’ with the meaning of ’similar’ left for the students to interpret. This approach not only helps develop problem-solving skills but also teaches students how to pose problems themselves
3D digitization of Yellowstone wolf (Canis lupus) skulls for education, research, and outreach
Get PDFMuseums around the world are using the advancement of digital technology to share scientific collections with broader audiences on a digital landscape. Recent innovations in imaging software and virtual platforms have made it possible for museums to create high-resolution 3D models that can be 3D printed as tangible educational aids, made accessible to researchers worldwide, and used to create accessible virtual museum experiences. Yellowstone National Park (YNP) is home to one of the best-studied collections of wolf (Canis lupus) skulls in the world. Long-term research conducted by the Yellowstone Wolf Project has produced an extensive volume of ecological metadata associated with this collection. Here, we apply photogrammetry to digitize the YNP wolf skull collection (n\u3e225). Photos are processed into high-resolution meshes using photogrammetry software. Resulting models are 3D printable at a low cost. Initial 3D prints were successfully used by Yellowstone Wolf Project staff as durable teaching aids in the field. Additionally, models of well-known wolves may be printed for use as outreach tools. In 2024, the UM Wildlife Biology program began using miniature 3D printed copies of 302M’s skull for public outreach and fundraising. All data from this project will be uploaded to a publicly accessible online repository for 3D biological specimen data. Once uploaded, individuals and organizations will be able to download these data for education, outreach, and collaborative research. For our project, we will use landmark-based geometric morphometrics to answer questions about how skull shape varies as a function of individual and environmental variables. We will also examine spatiotemporal variation in skull shape. These models will be used to create the first virtual 3D gallery made available to the public online by YNP. With the absence of a physical museum gallery, this new medium will increase accessibility and public engagement with natural history of Yellowstone National Park
Juvenile Arthritis, Body Image, and Disordered Eating: An Exploration of Experiences
Get PDFThis qualitative study examined eating and body experiences among youth with juvenile arthritis (JA). JA, an autoimmune condition affecting nearly 300,000 youth in the United States, poses significant challenges including chronic pain, disability, and psychological concerns such as anxiety and depression. Although adolescence is a critical developmental time for body image and disordered eating concerns to emerge, no qualitative research has explored the interactions of JA, body image, and eating behaviors among youth. Twelve youth with a JA diagnosis participated in a semi-structured qualitative interview examining their experiences with JA and their feelings about their bodies and food as they relate to their disease. Interviews were transcribed, description-focused coding was generated, and the data was analyzed for themes. Four primary themes were identified: ability status, symptom severity, medication side effects, and dietary restrictions. Generally, participants attributed lower ability status, increased symptoms, medication side effects, and dietary restrictions to having a negative impact on their body image and relationship with food. However, participants also reported having more positive body image due to feeling stronger and more able-bodied during periods of remission. Findings indicate that mental health providers and JA specialists should be aware of the relationship between JA and eating pathology and body image concerns. The findings also suggest a need to develop eating disorder and body image prevention and interventions that specifically address aspects of juvenile arthritis and chronic illness management (i.e., medication side effects and dietary restrictions). Finally, given the relationship between physical and psychological health, there is a need for additional eating disorder and body image research in youth with autoimmune illnesses
