Digital Commons Network^™

On The Definition Of Linear Independence, Yonah Cherniavsky, Artour Mouftakhov

The Mathematics Enthusiast

We discuss a certain very common flaw in the definition of linear independence, which is one of the most important concepts taught in any college or university course of Linear Algebra. This note may be useful to lecturers and students which teach and study Linear Algebra of any level and like the mathematically rigorous approach.

Numberlines: Hockey Line Nicknames Based On Jersey Numbers, Egan J. Chernoff

The Mathematics Enthusiast

The purpose of this article, in general, is to expound Chernoff’s (2016) notion of numberlines, that is, hockey line nicknames based on jersey numbers. The article begins with a brief discussion of the history of hockey line nicknames, which allows for the parsing of numberlines and quasi-numberlines (nicknames based on numbers associated with hockey players). Focusing, next, on jersey number restrictions for the National Hockey League (NHL), a repeated calculation of the number of possible numberlines winnows down the number from a theoretical upper bound to a practical upper bound. Moving beyond the numbers, the names of natural numbers – …

Developing Mental Rotation Ability Through Engagement In Assignments That Involve Solids Of Revolution, Atara Shriki, Ruthi Barkai, Dorit Patkin

The Mathematics Enthusiast

Spatial ability is essential for succeeding in the STEM (Sciences, Technology, Engineering and Mathematics) disciplines, especially mental rotation. Research points out that spatial ability is malleable, and therefore calls for developing learners’ ability by engaging them in appropriate assignments, starting from kindergarten. Given this, our paper presents several assignments designed for mathematics prospective teachers with the aim of fostering their mental rotation skills. Specifically, these assignments deal with solids of revolution, three-dimensional shapes formed by revolving a planar shape about a given axis that lies on the same plane.

Studying “Moments” Of The Central Limit Theorem, Benjamin A. Stark

The Mathematics Enthusiast

The central limit theorem ranks high amongst the most important discoveries in the field of mathematics over the last three hundred years. This theorem provided a basis for approximation that turned the question of reaction into the art of prediction. This paper aims to map a course for the history and evolution of the famed theorem from its’ initial origins in 1733, from Abraham de Moivre’s inquiries to the most recent expressions of the theorem. The journey encompassing central limit theorem includes reformations of definition, relaxing of important associated conditions, and numerous types of rigorous proofs.

Critical Examination Of Ways Students Mirror The Teacher’S Classroom Practice: What Does It Mean To Be Successful At Mathematics?, Paula Guerra, Woong Lim

The Mathematics Enthusiast

In this paper, the authors report the mathematical learning experiences of “successful” female students in secondary mathematics classrooms taught by a “successful” teacher with the traditional mathematics’ behaviorist approach. The authors’ claim that the traditional view of mathematics held by the teacher and supported by the school system could not promote rigorous mathematics for girls to understand the importance of mathematical thinking as a foundation for success in mathematics-related professions. The authors recommend future studies creating opportunities for discussion in the field about the teacher’s view on mathematics, classroom practice, and how these resonate with girls’ experiences of learning mathematics.

Coherence And Enrichment Across The Middle And Secondary Levels: Four Mathematically Authentic Learning Experiences, Keith A. Nabb, Jaclyn M. Murawska

The Mathematics Enthusiast

This article discusses four mathematically rich settings with origins in the elementary, middle, and secondary school curricula. Depending on the questions asked and the connections made within each setting, the problem spaces allow the instructor to import tools leading to sophisticated extensions appropriate for college-level study. These topics include the Heaviside function, randomness, symmetry, modular arithmetic, the generalized Pythagorean Theorem, and the theory of groups. Given the potentially extensive ground covered by these settings, they serve to reward those students who are inherently curious while highlighting the coherence in the curriculum as one progresses through the grades. The mathematical experiences …

Forms Of Knowledge Of Advanced Mathematics For Teaching, Julianna Connelly Stockton, Nicholas H. Wasserman

The Mathematics Enthusiast

In this paper, we explore in more detail why knowing advanced mathematics might be beneficial for teachers, specifically in relation to their classroom practice. Rather than by listing courses or specific advanced topics, as though those were the agents of change, we do so by considering advanced mathematical content for teachers in terms of more general forms of knowledge. In particular, we identify five forms of knowledge of advanced mathematics for teaching: peripheral, evolutionary, axiomatic, logical, and inferential. These categories were derived from analysis of an extensive mapping process linking K-12 content to relevant advanced mathematics. We connect these forms …

A Symbolical Approach To Negative Numbers, Paul M.E. Shutler

The Mathematics Enthusiast

Recent Early Algebra research indicates that it is better to teach negative numbers symbolically, as uncompleted subtractions or “difference pairs”, an idea due to Hamilton, rather than abstractly as they are currently taught, since all the properties of negative numbers then follow from properties of the subtraction operation with which children are already familiar. Symbolical algebra peaked in the 19th Century, but was superseded by abstract algebra in the 20th Century, because Peacock’s permanence principle, which asserted that solutions obtained symbolically would actually be correct, remained unproven. The main aim of this paper is to provide this missing proof, in …

Problem Posing In Consumer Mathematics Classes: Not Just For Future Mathematicians, Jeff Irvine

The Mathematics Enthusiast

Problem posing is recognized as a key component of mathematics (Ellerton, 2013). However, in many curricula, problem solving often dominates over problem posing (Stoyanova, 2003). This focus on problem solving exists despite research that shows that problem posing improves students' problem-solving skills, attitudes, confidence, understanding of concepts, and mathematical thinking (Singer, Ellerton, & Cai, 2013); reinforces basic mathematical skills, increases motivation, responsibility, and thinking flexibility (Ponte & Henriques, 2013); and is useful for teachers to assess students' cognitive processes, identify misconceptions, and modify instruction (Ponte & Henriques, 2013). Further, problem posing can play a large part in student motivation (McLeod, …

Teacher Development And Seventh Graders’ Achievement On Representing And Solving Equations, Sheree T. Sharpe, Analucia D. Schliemann

The Mathematics Enthusiast

We analyze the impact of a teacher development program based on a functions approach to algebra on 7th graders understanding of equations and examine how students’ score gains during the academic year relate to their teachers’ initial level of mathematical knowledge of algebra, functions, and graphs. Students from participating teachers’ and their control peers completed a mathematics assessment at the start and at the end of the school year the teachers were taking the program. We determined teachers’ initial levels of mathematics knowledge through a written assessment given at the start of the program. Although both groups of students improved …

Exploring Population Change Detection By Monitoring Effective Number Of Breeders, Brian Trethewey

Graduate Student Theses, Dissertations, & Professional Papers

Detecting if a population is in decline is an important objective for biologists and conservationists who are monitoring threatened populations. As genetic methods improve effective population size (N_e) and effective number of breeders (N_b) continue to gain popularity as a way to monitor species. Using simulated populations and linkage disequilibrium, we explored detecting population decline through N_b in age structured populations. Through comparisons of sensitivity (1 – false negatives) and specificity (1- false positives) over 1000 replicates, we explored how factors such as starting N_b, number of SNPs, number of individuals …

Response Of Amphibian And Invertebrate Communities To Wetland Mitigation In The Greater Yellowstone Ecosystem, Leah K. Swartz

Graduate Student Theses, Dissertations, & Professional Papers

Wetlands play a critical role in supporting freshwater biodiversity and ecosystem services, but human activities have resulted in large-scale loss and degradation of these habitats across the globe. To offset the decline of wetland area, mitigation wetlands are now frequently constructed, but their ability to replace the functions of natural habitats, including providing habitat for native fauna, remains uncertain. A recent highway reconstruction project in northwestern Wyoming caused impacts to and the destruction of multiple natural wetlands. To mitigate this loss, new wetlands were constructed along the highway corridor. To evaluate the performance of these created wetlands relative to reference …

Mirage: A Novel Multiple Protein Sequence Alignment Tool, Alex Nord

Graduate Student Theses, Dissertations, & Professional Papers

A fundamental problem in computational biology is the organization of many related sequences into a multiple sequence alignment (MSA) [2]. MSAs have a range of research applications, such as inferring phylogeny [22] and identifying regions of conserved sequence that indicate functional similarity [18]. In the case of protein isoforms, MSAs are valuable tools for transitively annotating post-translational modifications (PTMs) by enabling information transfer between known PTM sites and the sites that they align to [11].

For protein MSA tools, one challenging biological phenomenon is alternative splicing, wherein identical genomic sequence will differentially select from a subset of available coding regions …

Longevity Of Ponderosa Pine Fuel Reduction Treatments: A Legacy Of Research At Lick Creek Demonstration/Research Forest In Western Montana, Katelynn J. Bowen

Graduate Student Theses, Dissertations, & Professional Papers

In ponderosa pine ecosystems of the interior western United States, fuels reduction treatments are common, but the persistence of their effectiveness in mitigating fire behavior is poorly understood. We addressed this problem by analyzing ponderosa pine – Douglas-fir stands during more than two decades of response following fuel reduction treatments. An experiment at the Lick Creek Demonstration/Research Forest in western Montana was initiated in 1991 as a partnership between the USDA Forest Service and the University of Montana to evaluate tradeoffs among alternative cutting and burning strategies to reduce fuels and forest fire behavior while restoring historical stand structures and …

Structural Analysis Of A Triangle Zone Culmination, Comb Rock, Lewis And Clark County, Montana, Shane S. Fussell

Graduate Student Theses, Dissertations, & Professional Papers

A triangle zone is a structure commonly found at the leading edge of a thrust belt, characterized by a triangular cross-section of thrust faults. In the Montana triangle zone, west-dipping thrust faults intersect east-dipping ones above a regional detachment fault. Most studies of triangle zones focus on the structure in a cross-sectional sense, but little work addresses variations along the trend. The Canadian Rocky Mountain triangle zone has long been a productive petroleum province, so understanding the southern extent of this zone, where it enters Montana, is of interest for economic purposes as well as geologic understanding. Previous studies have …

Fostering International Mindedness In International Baccalaureate Classrooms: A Case Study Of Two Teachers, Madiha Syeda

Graduate Student Theses, Dissertations, & Professional Papers

International Mindedness is central to the mission of International Baccalaureate (IB) education and may be defined as a frame of mind enabling a person to get rid of prejudices of self and embrace a greater sense of the other. Through this study, I analyzed how International Mindedness (IM) is taught in a high school in the Western U.S. and prepared some suggestions for teachers in my country of origin (Pakistan). In this research, I studied three attributes of IM: multilingualism, intercultural understanding and global engagement. Studying IM was significant because it may address the problem of closed-mindedness in Pakistan and …

Social Justice In Social-Ecological Systems: Resilience Through Stakeholder Engagement, Frederick I. Lauer

Graduate Student Theses, Dissertations, & Professional Papers

Successful management of social-ecological systems (SES) is predicated on quality collaborative exchanges between project stakeholders and management. The Southwest Crown of the Continent Collaborative (SWCC) Collaborative Forest Landscape Restoration Program (CFLRP) provided an opportunity to explore landscape scale collaborative management and SES outcomes. Global change and future uncertainty of landscapes prompted the SWCC to employ restoration treatment alternatives throughout 1.4 million acres of forests, most of which are publicly held. The SWCC currently monitors environmental and economic variables, with plans to monitor social variables. This thesis formalizes a proposed framework to investigate SES resilience, and explores public engagement as an …

K-Mer Analysis Pipeline For Classification Of Dna Sequences From Metagenomic Samples, Russell Kaehler

Graduate Student Theses, Dissertations, & Professional Papers

Biological sequence datasets are increasing at a prodigious rate. The volume of data in these datasets surpasses what is observed in many other fields of science. New developments wherein metagenomic DNA from complex bacterial communities is recovered and sequenced are producing a new kind of data known as metagenomic data, which is comprised of DNA fragments from many genomes. Developing a utility to analyze such metagenomic data and predict the sample class from which it originated has many possible implications for ecological and medical applications. Within this document is a description of a series of analytical techniques used to process …

Fertility And Reproduction's Niche: Human Sexual Diversity, Samuel W. Austin

Graduate Student Theses, Dissertations, & Professional Papers

Abstract: Biologically exploring the origins and forms of human sexuality is of paramount importance. Scientific research has indicated that homosexuality was linked to reproduction, fertility, and adaptive child caring strategies, traits that seem to display cross-cultural similarities. This suggests that sexual diversity may be one of human’s earliest adaptations. While most of the previous research has been on individuals of European descent, little research on Native American populations has been completed to test whether these patterns continue in their population.

The research presented here tests the Sexually Antagonistic Hypothesis for Male Homosexuality, Fraternal Birth Order Effect, and childhood atypical gender …

A Quantitative Study On The Influence Of Persistence Factors On American Indian Graduate Students, Aislinn Rae Heavy Runner-Rioux

Graduate Student Theses, Dissertations, & Professional Papers

The underrepresentation of American Indian students continues to exist at the undergraduate and graduate levels of postsecondary education despite increases of American Indian student enrollment. The purpose of this quantitative survey study was to identify correlations between academic factors and graduate student persistence, as well as to understand how likely graduate degree completion is based on known academic factors for American Indian students. The analyses of the data included survey results, descriptive statistics, bivariate correlation, and multivariate regression. A sample of n=63 American Indian Graduate students represented 41 tribes and villages with over 32 unique tribal languages. The respondents indicated …

The Influence Of Tree Height On Lidar’S Ability To Accurately Characterize Forest Structure And Spatial Pattern Across Reference Landscapes, Haley L. Wiggins

Graduate Student Theses, Dissertations, & Professional Papers

Successful restoration of degraded forest landscapes requires reference models that adequately capture structural heterogeneity at multiple spatial scales. Field-based methods for assessing variation in forest structure are costly and inherently suffer from limited replication and spatial coverage. LiDAR is a more cost-effective approach for generating landscape-scale data, but it has a limited ability to detect understory trees. Increased understanding of appropriate height cut-offs for trees to be reliably included in LiDAR-based analysis could improve applications of LiDAR to assessments of landscape-scale forest structure. Toward that end, I investigated the effect of varying tree-height criterion (minimum height cutoffs of 6, 9, …

Lateral Heterogeneity And Architectural Analysis Of The Wall Creek Member Of The Upper Cretaceous (Turonian) Frontier Formation, John Zupanic

Graduate Student Theses, Dissertations, & Professional Papers

The Upper Turonian Wall Creek Member (WCM) of the Frontier Formation is part of a series of marine sandstones that were deposited on the western flank of the Cretaceous Western Interior Seaway (KWIS). The KWIS was a low accommodation shallow-marine foreland basin system that included many large deltaic complexes on its western margin. Deposition of WCM deltaic deposits was strongly influenced by fourthorder glacioeustatic cycles, oceanographic circulation patterns, and tectonics related to the active Sevier fold and thrust belt to the west. An in-depth field study of the WCM was performed on the western flank of the Powder River Basin …

Predicting Habitat Distribution For Five Rare Plant Species Within The Blackfoot Swan Landscape Restoration Project, Annalisa Suzan Ingegno

Graduate Student Theses, Dissertations, & Professional Papers

This study predicted rare-plant habitat at the landscape scale. Using the Maximum Entropy (MaxEnt) algorithm, relationships to and between each environmental variable were quantified for five species in the Blackfoot Swan Landscape Restoration Project (BSLRP) study area in western Montana. This project is part of a greater vegetation assessment for BSLRP that utilizes remotely sensed products for planning and management purposes. The five rare plant species studied in this analysis were common camas (Camassia quamash), clustered lady’sslipper (Cypripedium fasciculatum), western pearlflower (Heterocodon rariflorum), Howell’s gumweed (Grindelia howellii), and crested shieldfern (Dryopteris cristata). Rare plant models typically do not address dispersal …

Dispersal, Genetic Structure, Network Connectivity And Conservation Of An At-Risk, Large-Landscape Species, Todd Bartholomew Cross

Graduate Student Theses, Dissertations, & Professional Papers

Wide-ranging species face many threats to genetic connectivity. In light of these threats, one major challenge is the efficient use of scarce resources for the conservation of these species. Setting conservation priorities for landscapes and connectivity can be informed using molecular genetics, and can ensure the efficient use of scare resources to maximize returns in biodiversity conservation.

The greater sage-grouse (Centrocercus urophasianus; hereafter sage grouse) is a species of conservation concern that spans eleven state boundaries, land managed by multiple agencies, and one international boundary. Across the species’ distribution, the threats to the genetic connectivity range from agricultural conversion to …

Xic Clustering By Baseyian Network, Kyle J. Handy

Graduate Student Theses, Dissertations, & Professional Papers

No abstract provided.

Baccalaureate Time-To-Degree For Montana University System Two-Year College Transfer Students, Thomas Patrick Gallagher

Graduate Student Theses, Dissertations, & Professional Papers

Two-year college transfer education has been promoted as a cost-effective path for achieving the baccalaureate, but increased time-to-degree could nullify this assumption. The Montana University System (MUS) recently expanded the mission for its two-year college system by adding the transfer function.

This non-experimental quantitative research study examined whether a difference existed in baccalaureate time-to-degree for transfer students from MUS two-year colleges. Three years of MUS graduate data (2014 – 2016) was examined in comparing baccalaureate time-to-degree of non-transfer students (n = 5,953) with transfer students (n = 730). Credit accumulation, GPA, associate degree completion, nontraditional student status, and two-year college …

Fire Management Provisions In Federal Wilderness Law, Erik D. Alnes

Graduate Student Theses, Dissertations, & Professional Papers

No abstract provided.

Vision 2017

Vision

No abstract provided.

The Last Best Hope: Are Voluntary Conservation Agreements Effective Tools For Protecting Imperiled Species?, Sophie B. Tsairis

Graduate Student Theses, Dissertations, & Professional Papers

Candidate Conservation Agreements with Assurances, or CCAAs, are little known, voluntary conservation agreements that protect imperiled wildlife on private lands. These agreements have emerged over the past decade and have had mixed results in providing adequate protections for candidate species.

Landowners, private industries, state and federal agencies, and environmental nonprofits, are using CCAAs as tools to eliminate the need for an endangered species listing. An Endangered Species Act listing can lead to land-use uncertainty for private landowners and this threat is the main incentive to enroll in a CCAA. When landowners enroll in CCAAs they are agreeing to provide specific …

Epistemically Detrimental Dissent In Climate Science, Iheanyi Amadi

Graduate Student Theses, Dissertations, & Professional Papers

Dissent, criticism and controversy are integral to scientific practice, especially when we consider science as a communal enterprise. However, not every form of dissent is acceptable in science. The aim of this paper is to characterize what constitutes the kind of dissent that impedes the growth of knowledge, in other words epistemically detrimental dissent (EDD), and apply that analysis to climate science. I argue that the intrusion of non-epistemic considerations is inescapable in climate science and other policy-relevant sciences. As such there is the need to look beyond the presence of non-epistemic factors (such as non-epistemic risks and economic interests) …