The 50 most-cited articles in The Mathematics Enthusiast, 2017

There are many approaches to task design (Watson & Ohtani, 2015) from a large number of local and global design heuristics. The purpose of this paper is to present how mathematical modeling cycles, a popular way of describing mathematical modeling processes, were used as a task design heuristic.

In this article, we explore how students attempt to bridge from their whole number reasoning to integer reasoning as they solve subtraction problems involving negative numbers. Based on interviews with students ranging from first graders to preservice teachers, we identify two overarching strategies: making connections to known problem types and leveraging conceptions of subtraction. Their initial connections suggest that rather than identifying the best instructional models to teach integer concepts, we should focus on identifying integer instructional models that build on the potentially productive connections that students’ already make; we propose an example of one such form of instruction.

Creativity is important for young children learning mathematics. However, much literature has claimed creativity in the learning of mathematics for young children is not adequately supported by teachers in the classroom due to such reasons as teachers’ poor college preparation in mathematics content knowledge, teachers’ negativity toward creative students, teachers’ occupational pressure, and low quality curriculum. The purpose of this grounded theory study was to generate a model that describes and explains how a particular group of early childhood teachers make sense of creativity in the learning of mathematics and how they think they can promote or fail to promote creativity in the classroom. In-depth interviews with 30 K- to Grade-3 teachers, participating in a graduate mathematics specialist certificate program in a medium-sized Midwestern city, were conducted. In contrast to previous findings, these teachers did view mathematics in young children (age 5 to 9) as requiring creativity, in ways that aligned with Sternberg and Lubart’s (1995) investment theory of creativity.…

This study examined the relationship between teachers’ questioning techniques and students’ strategies in solving contextual mathematical problems. This case study was undertaken with one pre-service teacher (and 22 Year 4 students) from Indonesia and one pre-service teacher (and 25 Year 4 students) in the Netherlands. Both pre-service teachers assigned the same problems to their students and these problems were novel for the students in both countries. The lessons were observed by the first author and video recorded for data analysis. Qualitative data analysis was undertaken through within-case and cross-case analysis. The findings suggest that the contextual problems, the way pre-service teachers prompt students’ thinking, and the curriculum context were highly influential in the way the students solved the problems.

Tales from a Form Book: Stock Stories and Transactional Documents

This study was conducted to investigate the impact of Foundations of Quantitative Reasoning course on students’ attitudes toward mathematics and students’ achievement. The Foundations of Quantitative Reasoning is a project-based course containing several practical topics which students apply in daily life. It is offered at the University of Cincinnati as an alternative pathway for non-STEM majors to fulfill their mathematics requirements. Pre-survey-post-survey and pretest-posttest designs were used to test the effectiveness of the treatment regarding the attitudes toward mathematics and mathematics achievement respectively. The participants in this study were 21 students enrolled in a Foundations of Quantitative Reasoning course and 20 students enrolled in a College Algebra course offered at the University of Cincinnati Blue Ash College. Statistically significant results were observed for improvement in attitudes toward mathematics and mathematics achievement.

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.

In answer to a call for innovative science and technology education in primary education, we started a design research project to explore how to teach instantaneous speed in grade five. In this article we present the results of a series of teaching experiments that were conducted to design, try out, and improve a local instruction theory on teaching instantaneous speed in grade five. In a retrospective analysis, looking for patterns in the whole data set, encompassing all experiments, we identified a set of key learning moment of the students. Based on these patterns, a potentially viable local instruction theory was formulated that builds on supporting students in constructing a quantitative understanding of instantaneous speed that is not based on taking the limit of average speed.

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, 1992). The potential for problem posing as a motivational tool in nonuniversity track mathematics classes has not received much attention. This case study examines a program based on problem posing, in six grade 11 consumer mathematics classes, over a 3-year period. The program was very successful across a number of dimensions,…

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 of knowledge to particular practices that teachers engage in so as to clarify the perceived relations to classroom practices. We view such work as important to and productive for teacher educators, particularly in conceptualizing and structuring mathematics courses for teachers so that content that truly informs the work of K-12 teaching can be highlighted, and in a manner that facilitates teachers’ formation of…

There is an increasing need for educators at all levels to equip more students with problem-solving skills that better fit our changing work force. Students are largely unaware of many science-, technology-, engineering-, and math-related (STEM) careers. They often do not understand the importance of those careers or what skills are required to pursue them. Students are exposed to some of those skills if they take Career Technical Education (CTE) classes, but rarely do they see the connections in their core math classes. Math teachers have pointed to their dense curricula as making STEM integration impractical. A study of the Common Core State Standards for Mathematics (CCSS-M), however, reveals open doors for integration. There are specific Algebra I CCSS-M that can be met through STEM-oriented, problem-based learning (PBL). STEM PBL has the potential for increasing students' cognitive engagement while, at the same time, introducing interesting STEM careers. These connections need to be integrated in curricula aligned to the CCSS-M. In order to further develop and implement…

System Dynamics (SD) modeling is a powerful analytical method used by professional scientists, academics, and governmental officials to study the behavior patterns of complex systems. Specifically through use of the Stella software, it is a method that I and others have used for over two decades with high school, and even middle school, math and science students. In this paper I describe an introduction to SD modeling intended for an algebra class (in either middle or high school). In the body of the paper, a nested sequence of simple bank account examples, increasing in complexity, is used to demonstrate a comparison between using a closed form approach and using Stella to mathematize each situation. The comparison, showing equivalent recursive equations, closed form equations, and Stella modeling diagrams, is designed to give the reader (algebra teacher, mathematics education decision-maker, researcher, or whomever) an accessible introduction to understanding Stella model diagrams and the mathematical engine operating under the “hood” of the software. In particular, I highlight…

Many students who have to study mathematics as an enabling subject within higher education experience mathematical anxiety to a greater or lesser extent. This affliction can impact student learning and achievement in mathematics and so a number of strategies have been suggested for alleviating mathematical anxiety or at least moderating its effects. This paper reports on a comparison of the mathematical anxiety experienced by two groups of students each studying a different subject discipline. The results indicate that the groups have quite different levels of anxiety and the differing contributing factors between the groups suggest that approaches to remediation need to be tailored to reflect these factors.

Reformulating a mathematics curriculum is a political act, contextualized by economic, educational and ethical considerations, among others. This article represents a political rendition of a rationale to update the Saskatchewan, Canada, curriculum so it harmonizes with a cultural understanding of school mathematics (Ernest, 1988). By revisiting the 19th century definition of school mathematics that we generally follow today, its economic, educational and ethical consequences seem contrary to the expectations of 21st century Saskatchewan.The article’s point form organization, uninterrupted by the appearance of references, conforms to the genre of submissions to government committees. However, footnotes will clarify information for readers unfamiliar with current Canadian events. A lengthy detailed document written for the academy is easily accessible (Aikenhead, 2016). This TME article is a very short synopsis of that document.

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.

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 order to place difference pairs on a rigorous mathematical foundation, so that they may for the first time be the subject of modern classroom based research. The essential ingredient in this proof is a new physical model, called the banking model, a development of the hills and dales model used in schools in New Zealand, which besides improving upon current models in several respects, has the crucial advantage of…

In this paper we investigate the abilities that six high-achieving Swedish upper secondary students demonstrate when solving challenging, non-routine mathematical problems. Data, which were derived from clinical interviews, were analysed against an adaptation of the framework developed by the Soviet psychologist Vadim Krutetskii (1976). Analyses showed that when solving problems students pass through three phases, here called orientation, processing and checking, during which students exhibited particular forms of ability. In particular, the mathematical memory was principally observed in the orientation phase, playing a crucial role in the ways in which students’ selected their problem-solving methods; where these methods failed to lead to the desired outcome students were unable to modify them. Furthermore, the ability to generalise, a key component of Krutetskii’s framework, was absent throughout students’ attempts. These findings indicate a lack of flexibility likely to be a consequence of their experiences as learners of mathematics.

With respect to voluntary intoxication and campus sexual assault, the law can better reconcile the positive and negative autonomy interests without doing violence to important norms against vague criminal prohibitions

The main argument of this article is that “challenging mathematics for all” can be more than just a nice slogan, on condition that all students are empowered to make informed choices of: a challenge to be dealt with, a way of dealing with the challenge, a mode of interaction, an extent of collaboration, and an agent to learn from. Pedagogies supporting such choices are called choice-based pedagogies. The article begins from a theoretical discussion of the relationships between the notions ‘mathematics with distinction,’ ‘giftedness’, ‘challenge’ and ‘choice’. As a result, the learner-centered conceptualization of mathematical challenge is proposed. Then two examples of choice-based pedagogies enabling students with different background and abilities to be engaged in mathematics with distinction are presented. Implications are drawn.

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 – those with a certain panache (e.g., Untouchable, McNugget, Frugal, Hoax, Narcissistic, Unhappy, Superperfect and Powerul numbers) – act as a gateway to the notion of numberlining, the process of attempting to coin a numberline. Two particular examples, The Powers Line and The Evil Triplets provide a window into the process of numberlining. Prior to concluding remarks, which explain how numberlines and numberlining fall in line with the NHL’s…

This research draws upon primary resources regarding women and feminism from ancient to pretwentieth century Chinese thinkers, such as Ban Zhao, He-Yin Zhen, and Ding Ling.Additionally, this research draws upon authors exploring feminist ideas in China in the later twentieth century to the early twenty-first century, such as Wang Zheng and Leta Hong-Fincher.The purpose of this research was to develop a better understanding of how feminism has developed and persisted in China and the reasons it may differ from other nations.

The American Community Survey (ACS) provides disability data across a wide range of variables and geographies. In fact, the ACS provides county-level disability data for variables such as gender, race, veteran status, poverty status and employment for people with disabilities. This is beneficial to rural disability researchers as rural is most commonly classified at the county level. However, though the ACS is a rich and comprehensive data source it is not without limitations. Rural researchers in particular are acutely aware of these limitations. The ACS provides data estimates for disability in rural counties but because of the survey design these estimates are drawn from smaller sample sizes resulting in higher margins of error. These high margins of error make data less reliable at smaller geographies (e.g. counties) and forces researchers to aggregate the data to increase data validity. This limits the ability to analyze county level disability data, particularly for subgroups like race and ethnicity.

Montana, along with many western states, experienced a severe fire season in the summer of 2017. According to the Northern Rockies Coordination Center (NRCC), fires consumed 1,276,456 acres of Montana lands. Nearly half of these lands are U.S. Forest Service owned (Table 1). The severity of the fire season led Montana’s Governor, Steve Bullock, to declare a state of emergency at the beginning of September. At this time, the state had already exceeded the $30 million in its firefighting fund by $14.5 million.1 The NRCC estimates the total costs of fighting Montana’s wildfires topped $390 million.2 The combination of extreme firefighting costs and lower than expected revenues, generated a $200 million shortfall with the state government.3

Bottled water is consumed worldwide as both a matter of necessity and preference. People who need bottled water live in areas with compromised water sanitation, such as developing countries. People who prefer bottled water despite its higher price tag tend to live in areas that already have ready access to clean water, such as developing countries. These preferences for bottled water stem partly from taste and convenience, but are largely driven by advertising efforts by bottled water companies. The preference for bottled water leads to increased sales as well as increased cost. Costs include damages to health and the environment. Since these effects are not taken into account by bottled water companies and must be borne by others, they are considered external costs. Lack of information outside of biased advertising influences consumers to act differently than if they had full knowledge of the indirect consequences from their purchases. Educational efforts can balance out the information asymmetry between bottled water companies and consumers. This can take the form of a blind taste…

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.

In this paper we analyze sample solutions of a number of problems and relate them to their level as prescribed by Bloom’s taxonomy. We relate these solutions to a number of other frameworks, too. Our key message is that it remains insufficient to analyze written forms of these tasks. We emphasize careful observations of how different students approach a solution before finally assessing the level of tasks used. We take the arithmetic series as our starting point and point out that the objective of the discussion of the examples here in no way is to indicate an optimal way towards a solution. Instead, our intent is to demonstrate the potential of well selected tasks and the variation that could be observed as students develop their solutions. A large part of this work is devoted to an analysis of the richness of the square triangular number problem.

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 from the start to the end of the school year, the students from participating teachers showed significantly greater improvement. Moreover, among control students’, improvement in creating, solving, and interpreting equations was positively correlated with their teachers’ initial levels of mathematical knowledge. Improvement among students of cohort teachers in the same items was high regardless of their teachers’ initial performance in the…

This paper will discuss the relevance between mathematics and music throughout a few periods of history. The paper will first discuss how the Ancient Chinese hired mathematicians in order to “perfect the music” used in the court rooms. Mathematics was typically used in music to develop ratios and intervals that are found in music. This paper will then discuss the history of Fourier analysis, as well as give a brief history of Jean Baptiste Fourier. The Fourier analysis was used to find naturally occurring harmonics, to model sound, and to define sound by breaking it up into pieces. Many examples of the Fourier series and Fourier transform can be seen in relation to music. Some more simple examples will also be demonstrated, in order to understand how the Fourier series can model sound waves. While there are many other examples of how math has been used in music, these two aspects will be the main focus of this paper, with favorability placed on discussing the importance and relevance of the Fourier series. However, due to the inability to find sources, Fourier’s derivation of the…

This paper discusses Freudenthal's didactical phenomenology for the mathematical structures related to measurement. Freudenthal starts with the set G of all objects having the attribute of weight, an attribute that is to be measured. He proposes two operations, the first one among the measurements themselves, called “addition". Addition is interpreted in terms of the mental actions associated with measurement and, in the case of weights, it consists on the process of placing weights on one of the two dishes of a balance in order to balance them with a predetermined gauge, its fractions or multiples thereof, which are placed on the other. Their total weight is obtained by comparison with a predetermined gauge. The second operation, between weights and positive integers, allow weights to be amplified (by adding as many times as desired their weight measure). A related operation to amplification is that of contraction (by dividing the weight into as many equal parts as desired.) Freudenthal then extends his definitions in order to assign a meaning to the multiplication of a measure by,…

Residents of rural and frontier counties experience significant disparities in healthcare access and outcomes when compared to their urban counterparts. The organization of health care delivery contributes significantly to these disparities. Simply put, rural residents can face many challenges when they have to go to a hospital in a distant city for treatment and then return home to recover. The transition back home is also problematic because discharge planning generally does not adequately account for limited access to care in rural areas. The specific aim of this research project was to ascertain rural patients’ actual experience of the discharge planning process, and to involve patients and rural providers in designing and testing a contextually appropriate rural model that improves patient outcomes and reduces re-hospitalizations. This manual was used in a research project, Rural Options at Discharge – Model of Active Planning (ROADMAP). Our objective was to develop and evaluate a model that improved the likelihood of a positive recovery and reduced the likelihood of…

MacDonald and Guzmán demonstrate how the Mexican residents in the United States lobbied the Mexican government and Mexican consulates in the U.S. to secure their children's access to schooling from 1910-1929.

Fighting the Rape Culture Wars Through the Preponderance of the Evidence Standard

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 invite disciplinary and interdisciplinary connections and encourage discourse and productive struggle.

The Common Core State Standards make clear that teachers should use the number line to represent integer operations in Grades 6, 7 and 8, continuing the development of number line understanding begun in earlier grades. In this paper, we will investigate the basics of the colored chip and number line models for representing integers and their operations. We will then draw connections between the two models. Finally, we will argue that the number line model is an important one that should be taught alongside or in lieu of the chip model in order to deepen students’ understanding operations with integers, rational numbers, and real numbers in general.

SB56-16/17: Resolution Regarding Presidential Executive Order: Protecting the Nation from Foreign Terrorist Entry into the United States. This resolution passed 24Y-2N-1A at the February 15, 2017 meeting of the Associated Students of the University of Montana (ASUM).

Donald Warren reads Benjamin Kearl's examination of special education history as an advance on the reconceptualization project,not a distraction from the historiographical work Ellis recommends.

Variation in the timing and size of resource fluctuations can influence how plants grow, allocate biomass, and reproduce. Resources are sometimes made available in relatively continuous, reliable pulses while other times they are temporally separated and unpredictable. Native and invasive plant species are thought to respond differently to resource fluctuations, or pulses, which can influence competitive outcomes. The “Fluctuating Resource Hypothesis” predicts that resource fluctuations benefit invasive species more than native species, potentially because many invaders are highly effective at rapidly capturing resources. In a field setting, we examined the effects of varying nitrogen pulses on competition between exotic invasive and native species that are common in the intermountain prairie. We planted pairs of two native and two invasive plant species alone and in competition, and these groups of species received one of three treatments: no nitrogen at all (control), one large pulse of nitrogen (0.31 g N), or three smaller pulses equaling the total amount of nitrogen in the large…

Considering emerging heroines in young adult dystopian fiction, this project first examines them in a literary review. Using feminist ethics of care as a baseline, the review considers their unique worlds, agency, and motivation. Secondly, informed by the research, it attempts to add to their cannon with a new piece of creative writing.

International written communication networks, such as pen pal programs, help spread cultural awareness by connecting people from around the world. Competent intercultural communication is the foundation for strong global partnerships. It encourages diversity, increases academic achievement, and gives individuals a competitive edge in the global workforce. This study examines changes in the cultural awareness of 50 U.S. undergraduate participants enrolled in an intercultural communication course at a northwestern university after they exchange private, online pen pal letters with 50 international partners from across the globe. The U.S. participants were divided into Group A (test-group) and Group B (control-group) and then a pretest was administered to both groups to assess their cultural awareness before the letter exchange began. The Group A exchange was conducted over a two-week period, after which the U.S. participants were re-tested. The Group B began their exchange after the second test. The results of the tests were analyzed to determine whether the pen pal program increased…

The center is NAEYC accredited and a STAR 4 rated program through the Best Beginnings STARS to Quality Program in Montana.Clarke earned a B.S. in Speech and Hearing Sciences from

A collection of 2016 full year and quarterly estimates of nonresident visitation, expenditures by nonresident travelers, and economic impact estimates, including expenditures by purpose of trip, airport of arrival, and international visitors.

This report provides a review of the current socioeconomic trends in northeast Montana in comparison to the state as a whole, followed by an economic analysis of the potential impacts of an expanded recreation amenity. The amenity is characterized by a large, intact grassland prairie ecosystem replete with a large bison herd. Results suggest significant latent demand for nonresident visitation to the region. To begin to capture this demand and ensure continued vitality of other economic sectors will require collaborative efforts between conservation proponents, tourism professionals, and the community at large.

This Article asks whether the troubling nature of the Sagebrush Rebellion and similar movements (e.g., their violence, antienvironmentalism, and racist overtones) has made us overly dismissive of a kernel of truth in their complaints. Commentators often acknowledge that federal lands management may be “unfair” to local communities, but the ethical and legal characteristics of the unfairness concern remain under-explored. Although the Sagebrush Rebellion and federal lands communities are far from synonymous, substantial overlap between the complaints and demands of Sagebrush Rebels and the complaints and demands of many regional local (and state) governments suggests that to explore the one necessitates exploring the other. Yet, the extreme tactics of unsavory figures like Ammon and Cliven Bundy stand to overshadow real problems in the region. To search for the potential kernel of truth, I therefore apply a “pro se analysis” to complaints about unfairness in the public lands regime vis-à-vis communities near federal lands in order to transcend rhetorical blind spots and discern the…

This research consists of an external and internal analysis of, as well as a strategic recommendation for Atlassian, an Australian software company. The external analysis will use various frameworks to analyze the following: changes and trends in the environment, Porter’s Five Forces industry analysis, competitor analysis, industry segmentation and demand issues and opportunities in the industry. The internal analysis will use various frameworks to perform an internal resource assessment, financial resources assessment and assessment of opportunities for the company. The analyses are used to identify the competitive dynamics in the external environment and the strategic factors that make the company stand out, which allows for a thoughtful strategic recommendation to be made. The strategic recommendation for Atlassian is to expand by market development in emerging markets for knowledge workers and tech startups, specifically, the countries of Ireland, Sweden, India and China. The recommendation will include justification, strategic alternatives, an implementation plan, financial…

Despite globalization, indigenous representation in the media continues to be unequal. Without personal narratives and self-representation in their stories, indigenous people continue to be negatively stereotyped in pop culture, film, television and news coverage.

A primary policy of bankruptcy law is to give consumer debtors a “fresh start” by discharging their debt. A rival policy is that the discharge of debt is a selectively conferred privilege that is not granted in some situations. For example, society is unwilling to pardon debt related to embezzlement or a domestic-support obligation. This “discharge restrictions” policy is manifested in part by the Bankruptcy Code’s exceptions to discharge. The U.S. Supreme Court has repeatedly recognized the tension between the fresh start and discharge restriction policies. It has sought to achieve a fair balance between these policies by applying a “plainly expressed” standard when interpreting exceptions to discharge. Surprisingly, the circuit courts have not followed the Supreme Court. Instead, nearly every circuit court has developed a practice of construing exceptions to discharge narrowly in favor of the debtor and against the creditor. This Article highlights this established practice and seeks to challenge it. In essence, the circuit courts have transformed the fresh start policy into a…

Kill rate, defined as the number of prey killed per predator per unit time, is a key component to understanding predator-prey dynamics. A multitude of factors may affect kill rates, including, variation in age, sex, weight, or presence of offspring of either predator or prey species (intraspecific variation) and events such as the theft of a kill made by another animal (kleptoparasitism). These factors may influence the time a predator spends locating prey (search time) and the pursuing, killing, and consumption of prey (handling time). The sum of search time and handling time may be measured as the time between a subsequent kill, a metric I will use to make inferences on what affects mountain lion (Puma concolor) kill rates. Utilizing kill data obtained from Global Positioning System (GPS) collared mountain lions of Colorado, Wyoming, and Patagonia, I investigated the impacts of: 1) mountain lion sex, 2) mountain lion age, 3) accompaniment of offspring with mountain lion females, 4) prey weight, and 5) the presence of bears (habitual kleptoparasites) throughout study periods.…

surrounded by the people, values, and visions that have shaped habitat restoration on Fir Island.This article reflects my experiences, values, aspirations, and commitment to and for this landscape and community; this article is about my home.Most importantly, I also would thank my parents for having the good sense to raise our

Many plant species show variation in phenotypic traits, such as traits related to growth and defense against herbivores, across environmental gradients. Differences in phenotypic traits can be due to selection, leading to local adaptation, or due to the random process of genetic drift. To examine the driver of phenotypic variation, I conducted a Qst (a measure of phenotypic variation among populations) vs. Fst (a measure of genetic variation among populations) analysis for 13 populations of A. speciosa grown in a common garden, using five growth and defense traits and seven microsatellite markers. I found relatively low differentiation at the neutral markers (mean Fst = 0.005), and population differentiation of plant height, leaf shape, and latex production traits (but not trichome density or specific leaf area). These results suggest that the three highly differentiated growth and defense traits are responding to population-specific selection pressures, indicating local adaptation of A. speciosa distributed across an environmental gradient.