Physical Sciences and Mathematics Commons^™

Global Fire Emissions Estimates During 1997-2016, Guido R. Van Der Werf, James T. Randerson, Louis Giglio, Thijs T. Van Leeuwen, Yang Chen, Brendan M. Rogers, Mingquan Mu, Margreet J.E. Van Marle, Douglas C. Morton, G. James Collatz, Robert J. Yokelson, Prasad S. Kasibhatla

Chemistry and Biochemistry Faculty Publications

Climate, land use, and other anthropogenic and natural drivers have the potential to influence fire dynamics in many regions. To develop a mechanistic understanding of the changing role of these drivers and their impact on atmospheric composition, long-term fire records are needed that fuse information from different satellite and in situ data streams. Here we describe the fourth version of the Global Fire Emissions Database (GFED) and quantify global fire emissions patterns during 1997-2016. The modeling system, based on the Carnegie-Ames-Stanford Approach (CASA) biogeochemical model, has several modifications from the previous version and uses higher quality input datasets. Significant upgrades …

Relative Importance Of Black Carbon, Brown Carbon, And Absorption Enhancement From Clear Coatings In Biomass Burning Emissions, Rudra P. Pokhrel, Eric R. Beamesderfer, Nick L. Wagner, Justin M. Langridge, Daniel A. Lack, Thilina Jayarathne, Elizabeth A. Stone, Chelsea E. Stockwell, Robert J. Yokelson, Shane M. Murphy

Chemistry and Biochemistry Faculty Publications

A wide range of globally significant biomass fuels were burned during the fourth Fire Lab at Missoula Experiment (FLAME-4). A multi-channel photoacoustic absorption spectrometer (PAS) measured dry absorption at 405, 532, and 660 nm and thermally denuded (250 °C) absorption at 405 and 660 nm. Absorption coefficients were broken into contributions from black carbon (BC), brown carbon (BrC), and lensing following three different methodologies, with one extreme being a method that assumes the thermal denuder effectively removes organics and the other extreme being a method based on the assumption that black carbon (BC) has an Ångström exponent of unity. The …

Multi-Scaled Approaches For Protecting Montana's Watersheds And Water Resources, Elizabeth Yoder

Graduate Student Portfolios, Professional Papers, and Capstone Projects

The central theme carried among my four portfolio pieces is: using scientific and governmental approaches to conserve watershed health. For the purposes of this portfolio, I define watershed health as a very general term that describes the state of water quantity and quality that is available for human and ecosystem needs in a watershed. I see each of my portfolio pieces focusing on a different scale and method (i.e., science or government, including different levels of government, local, state and federal) for conserving watershed health. My first portfolio piece reviews water quality degradation caused by pharmaceuticals and personal care products …

Murray Energy Corporation V. Mccarthy, Sarah M. Danno

Public Land & Resources Law Review

Holding that the widespread effects of environmental regulation on the coal industry constituted sufficient importance, the Northern District of West Virginia ordered the Environmental Protection Agency to conduct analysis on employment loss and plant reduction resulting from regulatory effects. In admonishing the EPA’s inaction, the court ruled that the Agency had a non-discretionary duty to evaluate employment and plant reduction. Furthermore, the court held that the EPA’s attempt to put forth general reports in place of required evaluations was an invalid attempt to circumvent its statutory duty.

Multi-Instrument Comparison And Compilation Of Non-Methane Organic Gas Emissions From Biomass Burning And Implications For Smoke-Derived Secondary Organic Aerosol Precursors, Lindsay E. Hatch, Robert J. Yokelson, Chelsea E. Stockwell, Patrick R. Veres, Isobel J. Simpson, Donald R. Blake, John J. Orlando, Kelley C. Barsanti

Chemistry and Biochemistry Faculty Publications

Multiple trace-gas instruments were deployed during the fourth Fire Lab at Missoula Experiment (FLAME- 4), including the first application of proton-transfer-reaction time-of-flight mass spectrometry (PTR-TOFMS) and comprehensive two-dimensional gas chromatography-time-offlight mass spectrometry (GC×GC-TOFMS) for laboratory biomass burning (BB) measurements. Open-path Fourier transform infrared spectroscopy (OP-FTIR) was also deployed, as well as whole-air sampling (WAS) with onedimensional gas chromatography-mass spectrometry (GCMS) analysis. This combination of instruments provided an unprecedented level of detection and chemical speciation. The chemical composition and emission factors (EFs) determined by these four analytical techniques were compared for four representative fuels. The results demonstrate that the instruments are …

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 …

A Commentary On Freudenthal’S Didactic Phenomenology Of The Mathematical Structures Associated With The Notion Of Measurement, Omar Hernandez Rodriguez, Jorge Lopez Fernandez

The Mathematics Enthusiast

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 …

Dealing With Mathematical Anxiety: Should One Size Fit All?, Jon Warwick

The Mathematics Enthusiast

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 …

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.

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, …

A Proposed Local Instruction Theory For Teaching Instantaneous Speed In Grade Five, Huub De Beer, Koeno Gravemeijer, Michiel Van Eijck

The Mathematics Enthusiast

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 …

Mathematical Modeling Cycles As A Task Design Heuristic, Jennifer A. Czocher

The Mathematics Enthusiast

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.

Common Core And Stem Opportunities, Lane H. Walker, Helene J. Sherman

The Mathematics Enthusiast

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 …

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.

A Dual-Chamber Method For Quantifying The Effects Of Atmospheric Perturbations On Secondary Organic Aerosol Formation From Biomass Burning Emissions, Daniel S. Tkacik, Ellis S. Robinson, Adam Ahern, Rawad Saleh, Chelsea Stockwell, Patrick Veres, Isobel J. Simpson, Simone Meinardi, Donald R. Blake, Robert J. Yokelson, Albert A. Presto, Ryan C. Sullivan, Neil M. Donahue, Allen L. Robinson

Chemistry and Biochemistry Faculty Publications

Biomass burning (BB) is a major source of atmospheric pollutants. Field and laboratory studies indicate that secondary organic aerosol (SOA) formation from BB emissions is highly variable. We investigated sources of this variability using a novel dual-smog-chamber method that directly compares the SOA formation from the same BB emissions under two different atmospheric conditions. During each experiment, we filled two identical Teflon smog chambers simultaneously with BB emissions from the same fire. We then perturbed the smoke with UV lights, UV lights plus nitrous acid (HONO), or dark ozone in one or both chambers. These perturbations caused SOA formation in …

In Situ Measurements Of Water Uptake By Black Carbon-Containing Aerosol In Wildfire Plumes, Anne E. Perring, Joshua P. Schwarz, Milos Z. Markovic, David W. Fahey, Jose L. Jimenez, Pedro Campuzano-Jost, Brett D. Palm, Armin Wisthaler, Tomas Mikoviny, Glenn Diskin, Glen Sachse, Luke Ziemba, Bruce Anderson, Taylor Shingler, Ewan Crosbie, Armin Sorooshian, Robert Yokelson, Ru Shan Gao

Chemistry and Biochemistry Faculty Publications

Water uptake by black carbon (BC)-containing aerosol was quantified in North American wildfire plumes of varying age (1 to ~40 h old) sampled during the SEAC4RS mission (2013). A Humidified Dual SP2 (HD-SP2) is used to optically size BC-containing particles under dry and humid conditions from which we extract the hygroscopicity parameter, κ, of materials internally mixed with BC. Instrumental variability and the uncertainty of the technique are briefly discussed. An ensemble average κ of 0.04 is found for the set of plumes sampled, consistent with previous estimates of bulk aerosol hygroscopicity from biomass burning sources. The temporal evolution of …

Airborne Measurements Of Western U.S. Wildfire Emissions: Comparison With Prescribed Burning And Air Quality Implications, Xiaoxi Liu, L. Gregory Huey, Robert J. Yokelson, Vanessa Selimovic, Isobel J. Simpson, Markus Müller, Jose L. Jimenez, Pedro Campuzano-Jost, Andreas J. Beyersdorf, Donald R. Blake, Zachary Butterfield, Yonghoon Choi, John D. Crounse, Douglas A. Day, Glenn S. Diskin, Manvendra K. Dubey, Edward Fortner, Thomas F. Hanisco, Weiwei Hu, Laura E. King, Lawrence Kleinman, Simone Meinardi, Tomas Mikoviny, Timothy B. Onasch, Brett B. Palm, Jeff Peischl, Ilana B. Pollack, Thomas B. Ryerson, Glen W. Sachse, Arthur J. Sedlacek, John E. Shilling, Stephen Springston, Jason M. St. Clair

Chemistry and Biochemistry Faculty Publications

Wildfires emit significant amounts of pollutants that degrade air quality. Plumes from three wildfires in the western U.S. were measured from aircraft during the Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS) and the Biomass Burning Observation Project (BBOP), both in summer 2013. This study reports an extensive set of emission factors (EFs) for over 80 gases and 5 components of submicron particulate matter (PM1) from these temperate wildfires. These include rarely, or never before, measured oxygenated volatile organic compounds and multifunctional organic nitrates. The observed EFs are compared with previous measurements of temperate …

Mathematical Creativity For The Youngest School Children: Kindergarten To Third Grade Teachers’ Interpretations Of What It Is And How To Promote It, Yinjing Shen, Carolyn Pope Edwards

The Mathematics Enthusiast

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 …

Problems In Relating Various Tasks And Their Sample Solutions To Bloom’S Taxonomy, Torsten Lindstrom

The Mathematics Enthusiast

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 …

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.

Linking Pre-Service Teachers’ Questioning And Students’ Strategies In Solving Contextual Problems: A Case Study In Indonesia And The Netherlands, Rahmah Johar, Sitti Maesuri Patahuddin, Wanty Widjaja

The Mathematics Enthusiast

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 …

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.

Examining The Interaction Of Mathematical Abilities And Mathematical Memory: A Study Of Problem-Solving Activity Of High-Achieving Swedish Upper Secondary Students, Attila Szabo, Paul Andrews

The Mathematics Enthusiast

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 …

The Historical Connection Of Fourier Analysis To Music, Shunteal Jessop

The Mathematics Enthusiast

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 …

Subtraction Involving Negative Numbers: Connecting To Whole Number Reasoning, Laura Bofferding, Nicole Wessman-Enzinger

The Mathematics Enthusiast

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.

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 …

Students’ Reactions To Reform Mathematics Pedagogy In A Postsecondary Remedial Mathematics Course, Luke Smith, W. Gary Martin, Anna Wan, Gilbert Duenas

The Mathematics Enthusiast

The students in this study were enrolled in a remedial mathematics course at a small 4-year university and were taught according to the reform pedagogical principles advocated by NCTM, AMATYC, and MAA. Since most of the students had not been previously exposed to these teaching methods, this study obtained students’ reactions (n = 22) to the course through an anonymous, free-response (not multiple choice) survey at the end of the course. Surveys from students in two equivalent “traditional” lecture courses (n = 44) were also analyzed and served as a baseline by which to gauge students’ responses from the reform …

Reorganizing Algebraic Thinking: An Introduction To Dynamic System Modeling, Diana Fisher

The Mathematics Enthusiast

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 …

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 – …

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 …