The 50 most-cited articles in The Mathematics Enthusiast, 2024

To 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.

Agustín thus sought to abandon the unsafe use of inductive methods in algebra, as Leonardo had employed them, and to rather recover Euclid's ideal that is crystallized in the Elements of Geometry. Nevertheless, his idea of a limit is grounded in the dynamism of motion or a process: It is an embodied idea. From here, a conceptual exploration of functions and their possible properties begins. The effort of conceptual reorganization that Agustín undertakes is remarkable, and it prepares the ground for the in-depth research suggested by his work. With this arose a tangible need need to review the forms of existence of mathematical objects and what they meant. What was continuity in arithmetic reality? and How can we measure the size of a set? As mathematics pursued these questions, it became almost possible to abandon confidence in intuition completely, and this led to (among other consequences) a profound rupture: the dissociation of continuity from the differentiability of a function. All this awaits us below.

Inquiry-based Learning (IBL) is a pedagogical practice with much supporting research for its effectiveness with all students, but especially among traditionally underrepresented student groups in mathematics. However, IBL classrooms are not easy to implement; in particular, instructors need to know how to write appropriate materials, lead effective class discussions, and deal with student expectations. Primary Source Projects (PSPs) helped me address my deficiencies in these areas and become a more effective instructor. In this narrative, I relate my experiences using PSPs to transform my lecture classroom into a fully student-centered class, starting modestly by utilizing IBL with only one PSP in one class, then adding more PSPs to other classes, and working up towards the majority of my classes being active, even in the parts that do not utilize the historical projects. I highlight some implementation strengths and weaknesses, student perceptions of the projects, and conclude with a discussion of other high-impact teaching practices that can also be readily implemented using…

In this introductory article, the guest editors describe the genesis of this special issue of The Mathematics Enthusiast, provide an overview of its contents, and invite readers to join the authors of these articles and others in contributing to the ongoing efforts to bring primary historical sources to the mathematics classroom and research their impact on students and teachers.

When ethics requirements are confined to courses taught by non-STEM faculty, students may erroneously conclude that such considerations are at most marginal to their professional training. Primary source readings and discussion frameworks can tangibly link data analysis to questions of values within data science, computing ethics, or statistics courses. The particular cases of Sir Francis Galton and Sir Ronald Fisher—both statisticians and eugenicists—provide a rich collection of easily accessible digitized primary source material as well as a vast number of related popular and technical publications. Galton and Fisher figured centrally in the development of statistics as it is currently practiced (a substantial proportion of the technical content of introductory statistics courses were introduced by these men). However, the familiar tools of correlation and hypothesis testing were developed to analyze human data, often in service to the cause of eugenics. This article critically describes how we embedded problematic primary sources from Galton and Fisher into our courses and the…

Teaching undergraduate mathematics using Primary Source Projects (PSPs) has recently shown great promise with regards to creating an inclusive classroom. In this article, the authors share examples of this from their own teaching and conclude with a call to action so that this benefit, perhaps unique to PSPs, may be more fully explored and utilized to the benefit of our students.

A detailed account of my MSW journey through coursework and practicum experiences.

Recap! The Franke GLI Winter Scholarship Reception -- Beat the finals blues! Finals Week with the Mansfield Library -- Intern with GLI! -- Happening Today! Lavender Graduation -- Library Podcast Studio Amplifies Undergrad Voices in Multiple Languages -- Job & Volunteer Opportunity! -- Applications are Open! 2025 Leadership Summit

Student newspaper of the University of Montana, Missoula.

This article examines a Stanford Law School report on mental health screening in lawyer licensing. It finds that states have largely abandoned broad inquiries into bar applicants’ mental health histories but continue targeted screening practices. The report highlights ongoing concerns about stigma, deterrence of treatment, effectiveness, and fairness in bar admissions.

Agenda and meeting minutes from the December 3, 2024 meeting of the Associated Students of the University of Montana (ASUM).

SB19-24/25: Revising Section 28 of the ASUM Fiscal Policy. This resolution passed 2/3 majority 15Y-4N-2A on a roll call vote (RCV) during the December 3, 2025 meeting of the Associated Students of the University of Montana (ASUM).

Advising & Registration! -- You're Invited! The Franke GLI Winter Scholarship Reception -- Intern with GLI! -- Funded Travel Opportunity! Taiwan Summer Study Tour -- Applications are Open! 2025 Leadership Summit -- Save the Date! "Leadership Lessons from the 1960s: A Front-Row Seat to History" with Doris Kearns Goodwin -- Don't Miss! Stress Less Summit -- Get Involved! The Maureen and Mike Mansfield Center is seeking applicants for its Student Advisory Council

Got Verification Docs? -- Advising & Registration! -- You're Invited! The Franke GLI Winter Scholarship Reception -- Free Tonight? Friendsgiving -- Volunteer & Donation Opportunity: Holiday Helpers Gift Drive -- Funded Study Abroad Options! China -- Volunteer Opportunities! Soft Landing

Student newspaper of the University of Montana, Missoula.

Got Verification Docs? -- Advising & Registration! -- Calling all Sophomores, Juniors, and Seniors! We need learning assistants for GBLD110! -- Intern with GLI! -- Funded Study Abroad! -- Applications are Open! Wilderness and Civilization 2024 -- Save the Date! Spring Alternative Break 2025 -- Scholarship Info Sessions! -- Tour the MMAC -- Ticket Giveaway! -- Call all December Graduates! -- Check this Out! -- Volunteer Opportunity! -- Get Involved! Can the Cats -- Looking Ahead! Featured Courses...

Student newspaper of the University of Montana, Missoula.

Agenda and meeting minutes from the November 13, 2024 meeting of the Associated Students of the University of Montana (ASUM).

Agenda and meeting minutes from the November 13th, 2024 meeting of the University of Montana Staff Senate. Guest speakers: UM Legal and Compliance, Lucy France. VP for Student Affairs and Enrollment Management Leslie Webb, and Chief Enrollment Officer, and Drew Riley. Resolutions Voted on: "SB03_24-25 Resolution Encouraging Professional Development and Continu" by Trey Magnuson, Glenn Kneebone et al.

Retreat Recap! -- Advising and Registration! -- Calling all Sophomores, Juniors, and Seniors! We need learning assistants for GBLD110! -- Intern with GLI! -- Save the Date! Cheer for Queer! -- This Week! Grassroots to Global: The Power of Public Health with Cora Neumann -- International Education Week! Dangal & Dialogue: A Cultural Exploration -- The Freedom to Read -- Applying to Grad School? Info Session and Workshop -- Check this out! Record Scratch! Montana's Music Zine -- Scholarship Opportunity! -- New Student Group! XR Endeavors -- Continuing the Conversation... Celebrating Success Stories in Outdoor Recreation -- Get Involved! Can the Cats -- Looking Ahead! Featured Courses

Agenda and meeting minutes from the November 06, 2024 meeting of the Associated Students of the University of Montana (ASUM).

Student newspaper of the University of Montana, Missoula.

It's Election Day! VOTE! -- Beyond the Classroom (BTC) Experience Reminders! -- Attention Seniors! Graduation application -- Calling all Franke GLI sophomores, juniors, and seniors! We need learning assistants for GBLD110! -- Save the Date! Grassroots to Global: The Power of Public Health with Cora Neumann -- International Education Week! Dangal & Dialogue: A Cultural Exploration -- The Freedom to Read Night -- Eloise Cobell Day -- Diverse U! Celebrate Banned Books! -- Call All Artists! Missoula Arts Mixer -- Save the Date! November 7th, President's Lecture Series: "A Framework for Indigenous Health" with Donald Warne -- Scholarship Opportunity! -- Get Involved! Can the Cats -- Looking Ahead - Spring 2025 Courses!

Student newspaper of the University of Montana, Missoula.

Happy Halloween! -- Beyond the Classroom (BTC) Reminders! -- Applying for your Franke GLI BTC Scholarship this semester? -- Attention Seniors! Graduate application -- Freshmen and Sophomores! Advising reminder -- Call all Sophomores, Juniors, and Seniors! Become a GLI Learning Assistant -- Save the Date! Grassroots to Global: The Power of Public Health with Cora Neumann -- Back by popular demand! Salary Negotiation Workshop -- Lauren's Promise! -- Save the Date! President's Lecture Series: "A Framework for Indigenous Health" with Donald Warne -- Scholarship Opportunity! -- Get Involved! Can the Cats -- Vote Early Day! -- Voter Information!

Student newspaper of the University of Montana, Missoula.

Agenda and meeting minutes from the October 23, 2024 meeting of the Associated Students of the University of Montana (ASUM).

Agenda and meeting minutes from the October 30, 2024 meeting of the Associated Students of the University of Montana (ASUM).

GLI Homecoming! -- Beyond The Classroom (BTC) Reminders! -- Attention Seniors! Graduation applications due -- Calling all Sophomores, Juniors, and Seniors! Become a GLI Learning Assistant -- Applying for your Franke GLI BTC Scholarship this semester? -- Wilderness and Civilization is accepting applications! -- Mansfield Dialogue with Reverend Nelson B. Rivers III -- Scholarship Opportunity! The George M. Dennison Civic Engagement Scholarship -- Have an interview coming up? -- Lauren's Promise! -- Course Preview! NPAD 467 - Advanced Nonprofit Administration -- Vote Early Day! -- Voter Information!

Student newspaper of the University of Montana, Missoula.

Beyond the Classroom (BTC) Reminders! -- Attention Seniors! Graduation applications -- Attention Freshmen! Advising -- Applying for your Franke GLI BTC Scholarship this semester? -- Who do you know? Nominate an instructor -- President's Lecture Series: Station Eleven -- Short-term Study Abroad in Japan! -- Academic Opportunity! Global Public Health Minor -- Call for Artists! -- Voter Information!

Gerald Woodahl reflects on growing up in Helena, Montana, and becoming a Business Major at Montana State. From there he discusses his business ventures and how that brought him to the University of Montana. Woodahl fondly recalls going to the University of Montana football and basketball games throughout the 80s, 90s, and 2000s; as well as the fan community interactions behind the scenes. From traveling to Maui, Hawaii in 2001 to making regular drives up to watch the Griz play in Arizona, Woodahl gives insight into what it means to be a Griz fan. Lastly, he stresses the importance of character and value building when it comes to athletes, coaches, and the fan community. Interviewer Ilena Levitt was an undergraduate student working on the Griz Nation Oral History Project as part of the Griz130 History Initiative.

Student newspaper of the University of Montana, Missoula.

Agenda and minutes from the October 9th, 2024 meeting of the University of Montana Staff Senate. The following Resolutions were discussed: SB03-24/25 Resolution on Encouraging Professional Development by Lowering Cost Barriers to Staff. Note: See November meeting minutes when final version was presented, and a vote was conducted. The following Resolution was passed: SB04-24/25 Adding "Monte" the University of Montana Mascot as an Honorary Member of the University of Montana Staff Senate https://scholarworks.umt.edu/staffsenate_resolutions/8 The guest presenter was Brady Schwertfeger - the FOCUS-MFPE Union president to discuss what they do, union roles, bargaining agreement information, and to answer questions.

Beyond the Classroom (BTC) Reminders! -- Attention Seniors! Graduation Application -- Attention Freshmen! Advising Reminder -- Applying for your Franke BTC Scholarship this semester? -- Save the Date: Global Homecoming Reception -- Who do you know? Nominate an instructor -- Mansfield Dialogue with Nicholas Burns -- Call for Artists! -- President's Lecture Series: Station Eleven -- Let's Taco 'Bout it! -- Voter Information!

Student newspaper of the University of Montana, Missoula.

Kenneth Ruthven’s recollections of Simon Goodchild.

In this set of four articles, we invite Calculus teachers to encounter some of the ideas that shaped and motivated the innovation of the subject, presented in story form. We find that in traditional treatments of these topics, the dramatic tension between ways of thinking, representations, and phenomena in the world can be lost in a sea of calculations, procedures, and partially-understood formal proofs. However, the fundamental ideas and insights can be identified in nascent form in students’ ways-of-thinking about Calculus, and in their struggles to connect Calculus with their prior mathematical experiences. We are honored to contribute these Stories of Calculus to this number of The Mathematics Enthusiast, honoring the life and thinking of David Tall. David’s work with technology in Calculus learning brought him into close contact with Jim Kaput, the SimCalc Projects, and the Kaput Center. He and Jim discussed ideas that came to represent his “three worlds” of mathematics, a story he tells in part in his contribution to the volume, The SimCalc Vision and Contributions (Hegedus &…

This tribute reflects on the life and contributions of Emeritus Professor David Tall, a distinguished scholar in Mathematical Thinking and Mathematics Education, who passed away on July 15, 2024. David Tall’s groundbreaking ideas, such as concept image, procept, and the three worlds of mathematics, have profoundly influenced the mathematics education community. His philosophy of reciprocal learning and encouragement of innovative research shaped many scholars, including the author, who considers him not only a supervisor but an academic father. David's legacy will continue to inspire future generations in academia.

Chris Rasmussen’s tribute to Simon Goodchild.

Ian Stewart’s remembrances of David Tall as a colleague at the University of Warwick.

I discuss David Tall’s influence on advanced mathematical thinking.

In closing our set of of articles, we reflect back on the nature of mathematical thinking and learning with representations, especially the computational, executable representations that are enabled by modern dynamic mathematics environments. These aspects of the development of mathematical ideas have profound implications for our approaches to the teaching and learning of Calculus. Our narrative approach has dramatized the radically fruitful and generative nature of the period during which the ideas of Calculus were stabilized (especially in the stories of Guillermo/Leibniz and Leonardo/Euler). An analogy between the development of the field and the development of individual learners, should caution us not to cut short the vivid imaginative life of these ideas in our students through a premature push to formalism and analytic rigor; rather, to encourage students to systematize their thinking in domains of abstraction.

Mathematics is the result of a long process of research with the instruments of rationality that each age makes available to its members. Euclidean geometry crystallizes an impulse of deductive rationality. But this impulse has not always been the dominant one. At other times, such as the one we are going to explain in this part, a form of inductive reasoning has been given primacy. We will see the development of ideas that today constitute the foundations of the Calculus and that indicated the future task of its deductive consolidation. Our protagonist, the bold sailor, was identified as one who calculated without apparent inductive effort, just as eagles hover in the air.

In this article I remember Simon Goodchild, my colleague and friend.

Raymond Bjuland’s tribute to Simon Goodchild.

Based on a survey of 150 respondents and 16 timeline interviews with first-year university mathematics students in Sweden, we explore how the material resources and conditions available to them —mathematics capital— connect to their mathematical identities. We found that mathematics capital has bearing on how early in life students start to consider doing mathematics. We also found individually different trajectories among students with low mathematics capital into university mathematics. The study expands both existing theoretical and methodological ways of researching the material bearings of identity and opens up for new ways of understanding and exploring the conditions that may facilitate access to participation and success in university mathematics. It contributes to understanding on the social and cultural resources that students bring with them to start mathematics, thus complementing the insights that Simon Goodchild’s work had provided on the context of access to university mathematics.