Digital Commons Network^™

High Algal Biomass Is Decoupled From Metabolism In The Gallatin River, Cora Mae Steinbach

Graduate Student Theses, Dissertations, & Professional Papers

Assessing eutrophication in rivers is difficult compared to lakes and coastal waters, because most algal biomass occurs on the riverbed and flows interact and co-vary with production (Biggs and Close, 1989; Bernhardt et al., 2018). Riverine eutrophication is typically assessed using algal biomass and water column nutrients (U.S. Environmental Protection Agency, 2000), but biomass is highly variable and labor-intensive to measure, while nutrient concentrations often underestimate enrichment due to rapid biological uptake (Dodds and Smith, 2016). Reach-scale river metabolism can help evaluate long-term functional change in rivers recovering from nutrient enrichment (Arroita et al., 2019; Jankowski et al., 2021; Diamond …

Probing Proficiency-Related Neural Representations With Pca And Ica, Onila R. Narayana Mudalige Don

Graduate Student Theses, Dissertations, & Professional Papers

How proficiency-related information is represented in task fMRI depends not only on the data themselves, but on the representational lens used to summarize them. This thesis examines second-language (L2) proficiency as a problem of representational organization rather than as a simple classification exercise. Using task fMRI from adult language learners performing semantic animacy judgments in their native language (L1) and second language (L2), I derive shared low-dimensional network representations with principal component analysis (PCA) and independent component analysis (ICA), then evaluate those representations under matched leakage-controlled decoding pipelines.

Across analyses, the central comparison is between representational frameworks rather than between …

Superintendent Accountability In High Achieving School Districts: A Qualitative Multiple Case Study In The State Of Washington, Kristin Lind Jacobs

Graduate Student Theses, Dissertations, & Professional Papers

The primary goal of a school district is to promote and support student academic achievement. Superintendents of public school districts across the United States should therefore be held accountable for student performance within their districts. Establishing a successful public school district requires interconnected relationships among the superintendent, the school board, accountability structures, and evaluation processes.

The purpose of this qualitative multiple case study was to understand how superintendent accountability, in regard to student achievement, was conducted and accomplished by school boards who believe they hold the superintendent accountable for student learning. This study focused on school boards governing high-achieving school …

Instructional Coaching And The Development Of Data-Driven Decision-Making Cultures: A Quantitative Study Of Montana Schools, Kaitlyn Watts Hess

Graduate Student Theses, Dissertations, & Professional Papers

Over the past several decades, education policies in the United States have increasingly emphasized the use of data to guide instructional improvement to raise student achievement. While these policies have increased attention to data use in schools, many educators report limited preparation and support for effectively interpreting and applying student data in classroom practice. As a result, schools continue to face challenges in developing sustainable data-driven decision-making (DDDM) cultures that support continuous improvement.

This study examined the relationship between instructional coaching and the development of DDDM cultures in Montana schools. The purpose of this research was to determine whether statistically …

Bridging The Gap: Evaluating Gnss-Derived Total Water Storage As A Groundwater Monitoring Tool In The Colorado River Basin, Michelle Lee Barton

Graduate Student Theses, Dissertations, & Professional Papers

Groundwater resources in the Colorado River Basin are critically stressed yet remain under-monitored and under-regulated, creating urgent need for reliable, continuous observations at multiple spatial scales. This study evaluates the performance of the University of Montana Global Navigation Satellite Systems (GNSS) terrestrial water storage dataset as a tool for bridging groundwater monitoring gaps across the Upper and Lower Colorado River Basins between 2006 and 2024. We compare GNSS-derived total water storage and groundwater storage estimates against NASA’s Gravity Recovery and Climate Experiment (GRACE) satellite observations and in-situ groundwater well measurements at regional and sub-regional scales. We employ a Bayesian autoregressive …

From Mandate To Implementation: A Qualitative Content Analysis Of Early Childhood Coursework In Educational Leadership Preparation Programs, Anna Louise Puryear

Graduate Student Theses, Dissertations, & Professional Papers

Research on principal leadership in the P-3 continuum is limited, even though leadership is second only to teaching in its impact on student outcomes. Most leadership preparation programs emphasize K–12 content, with little focus on early childhood education. Illinois is the only state to codify legislation requiring early childhood content in educational leadership programs, offering a unique case to examine how such mandates are implemented. This study employed qualitative content analysis to investigate how institutions of higher education represent mandated early childhood content in graduate-level coursework. Data sources included program-level documents from 22 Illinois leadership preparation programs and course-level materials …

Cormac’S Court: Knights Without God In A Savage Land; Or, Chivalry And Existentialism In Cormac Mccarthy’S The Road, Zoë Margaret Metelerkamp

Graduate Student Theses, Dissertations, & Professional Papers

Cormac McCarthy scholars have examined the influence of romantic grail quest literature and existential philosophy on McCarthy’s oeuvre, but they have treated these subjects independently of each other. This thesis offers a novel exploration of McCarthy’s use of these specific philosophical and literary precedents by focusing on the ways The Road unifies medieval literary principles in Chretien’s Perceval with the existential chivalry Søren Kierkegaard extrapolates in Fear and Trembling.

Real-Time Immersive Wildfire Simulation: A Game Engine Approach, Jake Bova

Graduate Student Theses, Dissertations, & Professional Papers

Wildfires are growing in frequency, size, and severity, placing escalating demands on firefighting resources and putting lives, property, and ecosystems at risk. Accurate prediction of fire behavior is critical to suppression planning, evacuation decisions, and firefighter training, yet the operational models that fire managers rely upon face a persistent tradeoff. High-fidelity physics-based models capture fire–atmosphere interactions faithfully but are computationally expensive, often running far slower than real time on CPU hardware, while faster empirical models sacrifice the dynamic coupling between a fire and the wind field it generates. Furthermore, most existing tools produce abstract, two-dimensional outputs that offer limited visual …

Chapter 5: The Chemical Calculator, Garon C. Smith

G. Wiz’s Book of Spells

The Chemical Calculator combines invisible ink with a sophisticated math trick. The audience is poled for digits to use in either a 2-digit or 3-digit set of calculations. Once the digits have been obtained, a difference is calculated between the original set of digits and the same digits in reverse order. That answer is added to a reversed version of itself. The chemical calculator is a solution in a spray bottle. When the spray bottle has had a chance to examine the problem, it contents are sprayed at the bottom of the sheet. The correct answer appears. A bit of …

Montana Kaimin, November 6, 2025, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

Montana Kaimin, October 2, 2025, Students Of The University Of Montana, Missoula

Montana Kaimin, 1898-present

Student newspaper of the University of Montana, Missoula.

Part 1: Mathematical Alchemy, Corey Brady, Luis Moreno-Armella

The Mathematics Enthusiast

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 …

Part 2: Sailor On The Seas Of Infinity, Luis Moreno-Armella, Corey Brady

The Mathematics Enthusiast

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 …

David Tall: Some Personal Reflections, Matthew Inglis

The Mathematics Enthusiast

Matthew Inglis’s memories of David Tall.

A Tribute To The Life And Work Of David Tall, Sepideh Stewart

The Mathematics Enthusiast

David Tall was my academic grandfather, a wonderful mentor, and a brilliant mathematics educator. He earned two PhD degrees in mathematics and mathematics education. His edited book, Advanced Mathematical Thinking, and many of his publications that followed carved the path to shape many advances in mathematics education. His work on the framework of the three worlds of mathematics resonated well with mathematicians, giving them a language to express their thought processes as they reflected on their teaching and research. His latest framework, A Meaningful Long-term Framework for Mathematical Thinking, extended his ideas further and captured more on the complexity of …

Memorial - Simon Goodchild (1950-2024), Raymond Bjuland

The Mathematics Enthusiast

Raymond Bjuland’s tribute to Simon Goodchild.

Memories Of Simon Goodchild, Paul Ernest

The Mathematics Enthusiast

Paul Ernest’s recollections of Simon Goodchild.

Simon Goodchild Recollected, Kenneth Ruthven

The Mathematics Enthusiast

Kenneth Ruthven’s recollections of Simon Goodchild.

First-Year University Students’ Mathematics Capital And Identities, Paola Valero, Lisa Österling, Nhu Truong, Anna Danielsson, Bruna Nunes, Maria Berge

The Mathematics Enthusiast

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 …

From Problem Solving To Problem Posing: Two Classroom Examples, Suzana Antunović, Ljiljana Arambašić, Anđa Valent

The Mathematics Enthusiast

In 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.

A Tribute To Emeritus Professor David Tall: A Mentor, Scholar, And Academic Father, Kin Eng Chin

The Mathematics Enthusiast

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.

Remembering Simon Goodchild – His Light Still Shines, Merrilyn Goos

The Mathematics Enthusiast

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

Tall And Goodchild: In Memoriam David Tall (1941-2024) & Simon Goodchild (1950-2024), Bharath Sriraman

The Mathematics Enthusiast

I offer some remembrances of David Tall and Simon Goodchild, their impact on the mathematics education community, in addition to the aims and scope of this particular journal issue.

Part 3: Mathematical Thinking And Rigor, First Steps, Luis Moreno-Armella, Corey Brady

The Mathematics Enthusiast

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 …

David Tall (15 May 1941 – 15 July 2024), Ian Stewart

The Mathematics Enthusiast

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

David Tall And Advanced Mathematical Thinking, Keith Weber

The Mathematics Enthusiast

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

Part 4: Epilogue, Corey Brady, Luis Moreno-Armella

The Mathematics Enthusiast

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 …

Recollections Of Simon, Chris Rasmussen

The Mathematics Enthusiast

Chris Rasmussen’s tribute to Simon Goodchild.

Rational Approximations Of Sine And Cosine, Mashrur Azim, Christopher Griffin

The Mathematics Enthusiast

In this paper, we use elementary methods to derive a rational function over the integers to approximate the trigonometric sine function on the interval [0, π/2]. This formula can then be used to derive a quartic polynomial with a root close to π/3 , providing an interesting algebraic approximation to this value. A more accurate rational function over the reals is then computed using numerical optimization. This new formula, while more accurate, provides a worse approximation of π/3 in the corresponding quartic equation, showing the trade-offs in local vs. global approximation. This paper is accessible to undergraduates and illustrates a …

Rethinking Equality In Mathematics Education With Category Theory, Kelly Paton

The Mathematics Enthusiast

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 …