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PNW MAA-NUMS Abstracts Full List
Session: Plenary Talks
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Measuring InequalityKaren Saxe*, Macalester CollegeWhether a resource -- such as income -- is distributed evenly among members of a population is often an important political or economic question. The Occupy Movement has recently drawn more attention to the fact that income inequality in the United States is increasing. How can we measure this...
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The Symmetric Group and Fair Division: Does Knowledge Matter?Brian Hopkins*, Saint Peter's UniversitySports drafts and divorce settlements are examples of situations where players take turns selecting indivisible goods. Like other topics in fair division, the situation is made more interesting because people may
value the goods in different ways. In this talk, we focus on the case of two... -
How efficiently can one untangle a double-twist? Waving is believing!David Pengelley*, Oregon State UniversityCan you do the Philippine candle dance, the Dirac belt trick, or the Feynman plate trick? Whether your answer is yes or no, this event will engage you in this and far beyond in discovering and understanding the most mathematically efficient way to untangle a double-twist in 3-space. Limber up!
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Cryptologic TidbitsStuart Boersma*, Central Washington UniversityCryptology offers an ideal setting to give students a powerful and successful experience in mathematics. Cryptologic examples allow students to connect new content with prior knowledge, and provide students the opportunity for productive struggle with challenging material. Cryptologic contexts...
Subject Area: Geometry
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Laplacians & Laplace Transforms with Respect to Geometric Analysis of 1-Manifolds of Constant CurvatureJonathan David Evenboer*, Oregon State UniversityThis presentation continues on the course begun in past NUMS presentations. Properties of the Laplacian values of the Circle and Aster, and the Laplacian's role in construction of the heat kernel on both manifolds, are covered. Also covered will be properties of the Laplace Transform values of...
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Regular Stars, Polygons, and Musical ScalesMackenzie Koll*, Western Oregon UniversityEdge scales are musical scales constructed from the edges and vertices of a regular polygon. Regular polygons are polygons that have specific structure and they can be constructed from regular stars.
We will discuss this structure using elements of rational trigonometry and discuss regular stars... -
A Visual Expansion of the Pythagorean TheoremViv Diebel*, George Fox UniversityIan Johnson, George Fox UniversityThe poster is a visual expansion of the Pythagorean Theorem.
Subject Area: Mathematics Applications in the Sciences
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The process of representing food webs as interval competition graphsKayla Vincent*, Western Oregon UniversityA food web is defined as an acyclic graph where vertices represent different species and there is a directed edge from species x to species y if species x preys on species y. Food webs are important in Biology because they model the flow of energy in an ecosystem. A competition graph has the same...
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Insects and SpiralsKaylee Church*, Western Oregon UniversityThe logarithmic spiral, also known as the growth spiral, is an interesting form in mathematics that happens to be very applicable to the natural world. We explore the structure of this curve, and how this spiral can be used to model the flight pattern of a moth. Specifically, we investigate...
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Mathematical Modeling of Competition and Coexistence of Phytoplankton SpeciesLuke Campbell*, Central Washington UniversityMicroscopic phytoplankton form the basis of the food chain in the earth’s oceans. A system of differential equations relates phytoplankton population and nutrient concentration in an isolated environment. The equations were modeled with MATLAB. I conducted sensitivity analyses to determine the...
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Eigensystems of Electrical NetworksNikki Carter*, University of PortlandThe eigenvectors of an electrical network are voltages that, when placed at the boundary vertices, produce boundary currents that are a scalar multiple of the boundary voltage. The objective of this research is to gain information about a given electrical network using eigensystems. In particular,...
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Starved? Let's Solve That Math Hunger!TJ Norton, Klamath Community CollegeWe all enjoy that time of day when we get to sit down and enjoy our favorite meal. We typically eat three or more times per day. However, being a hard-working college student and living on a college budget often severely restricts the amount of money we can spend. Essentials like lunch, dinner, and...
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Theatrical! Practical! Mathematical!Thad Joachim*, Klamath Community CollegeMy talk will focus on how mathematics can be used in the real world relating to theatre arts, and I will support my discussion by giving real-world examples. Actors and other theatre individuals should be able to take math seriously when the math is involved with a theatrical performance. I will...
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Fractals in Geology: Measuring Intricate Forms (Cancelled)Will Kugler*, Klamath Community CollegeFirst I will give an introduction to fractals, a naturally occurring mathematical set that repeats a detailed pattern visible at any scale. Then I will connect fractals to real-world applications in Geology and Earth Science. I will discuss how fractals are used by geologists with the use of...
Subject Area: Probability and Statistics
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Applying a Multilinear Regression Model to Predict Air Quality in Burns, OregonTravis Lowe*, Eastern Oregon UniversitySydney Nelson*, Eastern Oregon UniversityAmy Yielding, Eastern Oregon UniversityThe City of Burns, Oregon has a serious air quality issue. The city frequently experiences very high levels of PM2.5. PM2.5 consists of a variety of particulates whose size is less than 2.5 micrometers. Such particulates can be inhaled and generally accumulate in the lungs of humans, displaying a...
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Use and Misuse of Regression for Chemical AnalysisBridget Daly*, Pacific UniversityIt is standard practice in analytical chemistry to use linear regression, particularly to calibrate analytical instruments. If a regression line were used to estimate the output of the instrument for a known concentration of analyte, all would be well. However, chemists use this line in reverse,...
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Predicting Wins and Losses in Division III Women's BasketballCharles Haneberg*, George Fox UniversityA method is presented for predicting future wins and losses in tournament-style games based on previous game outcomes. This method is applied to the recent Division III women's basketball season.
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Logging with Markov chainsDora Bixby*, Southern Oregon UniversityOregon is the U.S.'s top lumber producer and the industry makes up a large portion of the jobs in the Oregon workforce. I will be discussing the use of absorbing Markov chains to model the growth of trees in a stand, then analyzing the model to develop a reliable and steady harvesting schedule.
Subject Area: History of Mathematics
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Infinitesimal-Based CalculusEric Rogers*, Gonzaga UniversityEthan Snyder*, Gonzaga UniversityWhen Newton and Leibniz first developed calculus, they did so by using infinitesimals (really really small numbers). Infinitesimals were used until calculus was made more rigorous by Weierstass. The calculus that we are taught today is based on Weierstass’s ϵ-δ definition of the limit. However,...
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The Math Behind The Rubik’s CubeGarrison Iams*, Klamath Community CollegeCome hear about the intricacies of the Rubik's Cube! I will discuss the history of God's number, which is the least amount of moves it takes to solve a scrambled Rubik’s Cube. There are many techniques to solve a scrambled Rubik's Cube. One solution technique which can be modeled by...
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Rearrangement in an Infinite SeriesLane Thomason*, Southern Oregon UniversityTypically we are free to use associative and commutative properties without problems with real numbers. However, under certain conditions, these can break in infinite series. This talk will look into what happens when these conditions are met.
Subject Area: Ordinary Differential Equations and Dynamical Systems
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Equations for Bacteria GrowthSvetlana Dyachenko*, Western Oregon UniversityBacteria growth is really important in our life. Some bacteria cells help us overcome different diseases, while others bring those diseases to us. We have learned to produce medicine with help of bacteria growth, like insulin, to help those who are ill. Modeling bacteria growth is an important part...
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Mathematical Modeling of Heat Through a Hot BathMcKenzie Garlock*, Eastern Oregon UniversityJeremy Bard*, Eastern Oregon UniversityZach Nilsson*, Eastern Oregon UniversityNo one likes a cold bath. When the bath water starts to get cold a person might turn on a constant trickle of water to keep the water tepid. We attempted to model, and optimize, this behavior with differential equations. To do this we simplified the situation and started with a bathtub that had...
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An Elementary Analysis of Chua's CircuitSteven Beres*, Gonzaga UniversityCaleb Tjelle*, Gonzaga UniversityPrior to the invention of Chua's circuit by Leon Chua in 1983, it was generally believed that it was not possible to design an electronic oscillator which exhibited chaos. In this talk, we provide an overview and analysis of Chua’s chaotic circuit. Principally, we will show the...
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Dynamic of LoveAubrey Ibele*, Gonzaga universityAudrey Gomez*, Gonzaga UniversityDynamical systems both linear and non-linear have the power to describe intricate behavior and provide analysis. In this paper, linear and non-linear models are employed to replicate the interaction between individuals with varying romantic styles. Using traditional analysis methods the goal was...
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How to Take a Hot Bath, if You Can Spare the CPU CyclesThomas Burns*, Southern Oregon UniversityJacob Schultz*, Southern Oregon UniversityWe discuss multiple methods for modelling the temperature of a bathtub taking into account conductance, evaporation, and turbulence. One model uses a system of ordinary differential equations to represent the temperature with respect to time of multiple materials in the system, while another...
Subject Area: Numerical Analysis and Scientific Computing
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Algorithmic Variants of QRSally Peck*, Western Oregon UniversityOne of the fundamental computations in numerical linear algebra is the QR factorization. A QR factorization decomposes a matrix into the product of an orthogonal matrix and an upper triangular matrix. The algorithms that compute these decompositions can often be costly, and at times, do not...
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Perturbing Equilibria of the Three-Body ProblemJoseph Stauss*, Gonzaga UniversityThe Lagrange-Relative Equilibrium and the Figure-8 Equilibrium are the only known periodic solutions of the Three-Body problem in the case of equal masses. These equilibria were analyzed by using a finite-difference method to approximate their perturbation-response for various quantities. The...
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Rat Game ExpandedDavid Calkins*, George Fox UniversityMathematician Aviezri S. Fraenkel wrote a paper on a game called The Rat Game, which involves mathematical moves and strategies. I plan to inform and expand on some of these moves and add to the game.
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Looking for a (Super)resolution to an Image Processing Problem.Alleta Maier*, Linfield CollegeIn recent years sparse coding has been employed to efficiently process images. Since recovering sharp images from images corrupted with noise is a well-known ill-posed problem, small perturbations in the image lead to large deviations in the reconstructed image. We look to combine research in...
Subject Area: Topology
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From Manipulatives to Theory in Knot TheoryBrett Hegge*, Western Oregon UniversityKnot Theory is the study of simple closed curves in three dimensions. Complicated structures can be analyzed using three basic moves and knots can be shown to be equivalent. We discuss ways of using physical manipulation to get middle school students interested in mathematics. We also, explore the...
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A Basis for the Space if Order 5 Chord DiagramsAllison Stacey*, Oregon State UniversityIn the study of Vassiliev Knot Invariants, the algebra of chord diagrams plays a key role. A chord diagram of order n is a circle with 2n vertices around it with chords through the circle connecting the vertices pairwise. The algebra of such diagrams is isomorphic to closed Jacobi diagrams which...
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Separability and the Cantor SetAnthony Dominquez*, Western Oregon UniversityThe Cantor Set is a famous set in point-set topology. There are a wide variety of types of Cantor Sets. However, we will only cover the ternary, or standard Cantor Set. In this talk, we will define and discuss what it means for a set to be separable and prove that the Cantor Set satisfies this...
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Klein links versus torus links, part IRyan Lattanzi*, Gonzaga UniversityBryan Strub*, Gonzaga UniversityHayley Olson, Gonzaga UniversityWe will examine the relationship between Klein links and torus links, using both diagrammatic techniques and link invariants. We begin with definitions of these links and some basic results about Klein links.
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Klein links versus torus links, part IIHayley Olson*, Gonzaga UniversityBryan Strub*, Gonzaga UniversityRyan Lattanzi, Gonzaga UniversityWe will examine the relationship between Klein links and torus links, using both diagrammatic techniques and link invariants. We determine the types of components in a Klein link, and use this result to look at which Klein links are torus links and which are not.
Subject Area: Combinatorics
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Examining Ramsey NumbersAmanda Evola*, Western Oregon UniversityThis paper explores the work of Frank P. Ramsey who founded Ramsey’s Theorem and is centered on the fact that complete disorder is impossible. The goal is to dig into Ramsey’s Theory by examining various Ramsey Numbers and bounds. Through this examination of Ramsey Numbers we will begin to see...
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Adding Color to CombinatoricsEmily Hiscox*, George Fox UniversityEllen Pearson, George Fox UniversityTaking the conclusions found in Candy Crush Combinatorics by Dana Rowland, and expanding them by one color to see how many possible combinations can be found using two rows of candy's and 3 colors.
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Math and Sudoku: Exploring Sudoku boards through graph theory, group theory, and combinatoricsKyle Oddson*, Portland State UniversityEncoding Sudoku puzzles as partially colored graphs, we state and prove Akman’s theorem regarding the associated partial chromatic polynomial; we count the 4x4 sudoku boards, in total and fundamentally distinct; we count the diagonally distinct 4x4 sudoku boards; and we classify and enumerate the...
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On the Turan number of forests (Canelled)Omid Khormali*, University of MontanaA well-known conjecture of Erd\H os and S\'{o}s states that the Tur\'{a}n number for paths is enough for any tree i.e. a graph $G$ on $n$ vertices and more than $\frac{k-2}{2}n$ edges contains any tree on $k$ vertices.
A natural extension of the problem is the determination of the Tur\...
Subject Area: Mathematics Education
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Reading $\pi$: Helping children move from symbol to meaningEmma Winkel*, Pacific UniversityStudents currently learn of $\pi$ in a formulaic context; as a value needed for the effective calculation of the circumference or area of a circle. In this talk, we present an activity that uses manipulatives to help middle grade students develop an understanding of the geometrical meaning of $\pi$.
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Math Anxiety: The Common PlightTiffany Klink*, Klamath Community CollegeThere are multiple causes to Math Anxiety ranging from actual facts to myths about math. Mathematics is a subject that many people struggle with daily. Not just mathematics involved in engineering, but the basic math skills needed for leaving a tip. Some topics discussed will be: how to think about...
Subject Area: Algebra
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Commuting Pairs in Finite Nonabelian GroupsTyler McAfee*, Western Oregon UniversityThe study of the probability that two group elements commute dates back to 1968 with the work of Paul Erdos and Paul Turan. Since then, much has been deduced about these probabilities, including its bound of $5/8$ for nonabelian groups. During this talk, we will look at the associated probabilities...
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Kummer subspaces of Central Simple AlgebrasNhan Nguyen*, University of MontanaLet $F$ be a field containing a primitive $d^{th}$ root of unity $\rho$ and char$(F)\not|d$. Let $A$ be the tensor product of $n$ cyclic $F$-algebras. An element $v\in A$ is Kummer if $v^{d}\in F$. A subspace of $A$ is Kummer if every element is Kummer. Kummer spaces have been used to bound the...
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Analyzing Transition Matrices of Chutes and Ladders Game VariantBryce Boyle*, George Fox UniversityMatt DeBiaso*, George Fox UniversityImagine each directional chute and ladder in the classic board game replaced with bidirectional portals. How does the game change? Expected game play and probabilities of each position are determined by the location and type of eigenvalues. We analyzed the transition matrix and discovered...
Subject Area: Other
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Understanding the Traveler's DilemmaCarter Bedsole*, George Fox UniversityGary Buckley*, George Fox UniversityIn the game theory problem The Traveler's Dilemma, the theoretical and experimental results differ greatly. This discrepancy is explained through evolutionary game theory.
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A Mad Math Tea PartyJillian Welk*, George Fox UniversityThis poster presentation will focus on the research done in an article on cyclic partitions involving an Alice in Wonderland theme.
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Graph Products and Colorings in Relation to the Hedetniemi ConjectureCrystal Susbauer*, Pacific UniversityThere are many types of product operations defined in graph theory. These products use the vertices and edges of two (not necessarily distinct) graphs to create a new graph. We focus on four important types of graph products: the Cartesian product, the direct product, the strong product, and the...
Subject Area: Logic and Foundations
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7 VariablesMimi Miller*, George Fox UniversityProving the number of unique fair games that can be played with seven variables and showing that they are isomorphic.
Subject Area: Number Theory
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Triangular Numbers and Squared NumbersTyler Chin*, George Fox UniversityBen Van Vliet*, George Fox UniversityVisual demonstrations of the relationships between squared numbers and centered squared numbers.
Session: Junior Faculty Research
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Geometric Invariants of KnotsChristian Millichap*, Linfield CollegeGiven two arbitrary knots (tangled up strings with their ends tied together), how can we (easily) tell if they are different or not? In general, this problem is extremely difficult to answer, and has led to the development of a variety of knot invariants. In this talk, we will examine geometric...
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Dispersion reduction schemes for the wave equationsYajun An*, Pacific Lutheran UniversityFinite Difference (FD) schemes have been used widely in computing approximations for partial differential equations for wave propagation, as they are simple, flexible and robust. However, even for stable and accurate schemes, waves in the numerical schemes can propagate at different wave speeds...
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The Difficulty of Classifying Decomposable Torsion-Free Abelian GroupsKyle Riggs*, Eastern Washington UniversityAn abelian group is decomposable if it can be written as a direct sum of two (or more) nontrivial subgroups. Otherwise it is indecomposable. The only indecomposable torsion groups are cyclic groups of the form $\mathbb{Z}(p^n)$, where $p$ is prime (as well as Pr\"ufer groups, $\mathbb{Z}(p^\...
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Introduction to permutation patternsMasaki Ikeda*, Western Oregon UniversityIn enumerative combinatorics, the study of permutation patterns blossomed in the 1980s with the Stanley-Wilf conjecture. In this talk, I will introduce the basic concept of permutation patterns and some approachable examples as well as the final result of my doctoral research.
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An Obstruction to Knots Bounding Mobius Bands in B^4Kate Kearney*, Gonzaga UniversityThe relationship between embedded surfaces and their knotted boundaries has been one of the main topics of knot theory for much of the last half century. This talk focuses on a particular case, namely whether a given knot in the three-sphere can be the boundary of a Mobius band embedded in the four...
Subject Area: Numerical Analysis and Scientific Computing
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Using Eigenvalues to Investigate Numerical OscillationsCorban Harwood*, George Fox UniversityIn numerically solving linear partial differential equations, carefully formed matrices are powered up as the algorithm iterates the solution through time. Depending upon the eigenvalues, the solution either blows up to non-numerical values, stabilizes with bounded oscillations, or stabilizes free...
Session: Algebra and Number Theory
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A Game of 1’s and 2’s: Constructing level 2 Demazure Filtrations of level 1 Demazure modulesJeffrey Wand*, Gonzaga UniversityIn this talk we dive into the representation theory of Lie algebras. Representation theory is an area of math that studies algebraic structures and the objects they “act on.” In addition, it is also a great tool that takes problems in abstract algebra and turns them into linear algebra problems....
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Visualizing p-adic numbersDibyajyoti Deb*, Oregon Institute of TechnologyP-adic numbers after its introduction by Kurt Hensel more than a century ago, has been a mainstay in the field of number theory. An abstract concept by itself, in this talk we will look at how we can visualize p-adic numbers with a tree structure and look at some basic questions in p-adic analysis...
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Systems of parameters and the Cohen-Macaulay propertyKatharine Shultis*, Gonzaga UniversityCohen-Macaulay rings play a central role in commutative algebra and there are many connections between systems of parameters and the Cohen-Macaulay property. In a Cohen-Macaulay ring, every system of parameters is also a regular sequence (roughly speaking it behaves like a set of polynomial...
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Hamiltonian Properties of Toroidal Zero Divisor GraphsShannon Overbay*, Gonzaga UniversityThe zero divisor graph of a commutative ring $R$ is formed by taking the nonzero zero divisors of $R$ as the vertices and connecting two vertices exactly when the corresponding product of the two elements is zero. We will show that all 44 planar zero divisor graphs are subgraphs of planar graphs...
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Decomposable Cyclically Presented Groups and Shift DynamicsKirk McDermott*, Oregon State UniversityA group with a cyclically symmetric presentation admits an automorphism of finite order called the shift. In this talk we look at cyclically presented groups which admit a certain decomposition, and relate the shift dynamics for the group to the components of the decomposition. Topological methods...
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The subregular part of Lusztig's asymptotic Hecke algebraTianyuan Xu*, University of OregonGiven an arbitrary Coxeter system (W,S), Lusztig defined its asymptotic Hecke algebra J, an associative algebra closely related to the usual Hecke algebra and the category of Soergel bimodules for (W,S). The algebra J decomposes as a direct sum of subalgebras indexed by the 2-sided Kazhdan-Lusztig...
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G-Sets and Sequences Associated with nth Order Linear Recurrences Modulo Primes}Robert Ray*, Gonzaga UniversityWe consider nth order linear recurrence relations of the form $S_k=a_{k-1}S_{k-1}+a_{k-2}S_{k-2}+\cdots+a_{k-n}S_{k-n}$ over the finite field $Z_p$, where $p$ is a prime not equal to 2. The results regarding the distribution of elements in the sequence $\{S_0,S_1, \dots \}$ are well known for...
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Categories of Representations of the Lie superalgebra q(2)Nicholas Davidson*, University of OregonI will give an overview of the representation theory of the queer Lie superalgebra q(n), focusing in particular on the representations of q(2) in its BGG category O.
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Overpartition StatisticsThomas Morrill*, Oregon State UniversityMany partition results and $q$-series identities are classically derived through analytical techniques, though the results beg for a combinatoric interpretation. -- the standard examples being the Ramanujan congruences. Historically, the combinatorics were filled in by studying integer valued...
Session: General Papers
Subject Area: Mathematics Education
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An Active STEM-Prep CurriculumFrancisco Savina, University of Texas at AustinThe STEM-Prep Pathway is designed as two one-semester courses created by the New Mathways Project that prepare students beginning at the elementary algebra-level to succeed in college-level calculus. All lessons are designed to be contextual and meaningful, with guided student inquiry at the core....
Subject Area: History of Mathematics
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An Investigation of Subtraction Algorithms Utilized in the US during the 18th and 19th CenturiesNicole Wessman-Enzinger*, George Fox UniversityOver 30 arithmetic texts and 280 cyphering books utilized in the United States during the 18th and 19th centuries were examined for subtraction algorithms. A framework for different types of subtraction algorithms utilized at this time will be presented. The investigation revealed that same...
Subject Area: Logic and Foundations
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Infinity (Still) Blows My MindAaron Montgomery*, Central Washington UniversityDoug DePrekel, Central Washington UniversityAs filler in an undergraduate abstract algebra class, I tossed out a question that I had encountered in a high school math puzzler involving the final state of an infinite process. In the process, chips are added and removed from a bag and the question asks what remains at the end of all additions...
Subject Area: Ordinary Differential Equations and Dynamical Systems
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Propagation of transient behaviour in linear flocking modelsDavid Hammond*, Oregon Institute of Technology - WilsonvilleThis talk will introduce a set of models for describing the behaviour of linear flocks. One application of these models is to describe groups of autonomous automobiles on a one-lane road, where each automobile controls its acceleration based on the differences of its own position and velocity from...
Subject Area: Analysis
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Pathological Continuity: A Zoo of Nowhere-Differentiable Functions (CANCELLED)Nathan Taylor*, University of Montana, MissoulaPoincare said of pathological functions, "logic sometimes makes monsters." We will investigate some classical examples of the monsters which are continuous but nowhere-differentiable real functions. We will take a historical perspective, with emphasis on visualizing the various examples...
Subject Area: Mathematics Applications in the Sciences
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Hypothesis Testing with Person-Time DataTerri Torres*, Oregon Institute of TechnologyIn the area of epidemiology person-time data is a common measurement. I will address the inference associated with this measurement.
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Numerical Inversions of the Broken Ray Transform with fixed initial and terminal directionsBrian Sherson*, Oregon State UniversityThe Broken Ray transform is a transform used in single-scattering tomography, and was introduced by Lucia Florescu, Vadim A. Markel, and John C. Schotland, in 2009, and shown to be invertible in the case of fixed initial and terminal directions. An inversion formula for this case, involving a...
Subject Area: Probability and Statistics
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If You Must Gamble: Minimizing Expected LossCurtis Feist*, Southern Oregon UniversityJake Scott, Southern Oregon UniversityWe consider a typical gambling situation such as red/black roulette bets of a fixed size, with a limited bankroll, a fixed goal (such as doubling one’s money), and a maximum time of play. Through the use of Markov chains, we analyze the expected value of this game for various bet sizes. Unlike in...
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First to Toss N Heads WinsChris Hallstrom*, University of PortlandTwo players play a game, taking turns tossing a coin; the winner is the first to reach $n$ heads for some agreed upon value of $n$. What is the probability that the player to go first wins? In this talk, we will consider this question as well as its application to your lunch-time half-court...
Subject Area: Combinatorics
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Examining Matroids with Unique AddressesRoger MadPlume*, University of MontanaIn the September 2013 issue of Math Horizons Gary Gordon posed the following problem:
For a finite set of points in the plane, write down the following data: For each point P, record the number of 3-point lines through P, the number of 4-point lines through P, and so on. Is there a finite set of... -
Breaking Bad SymmetriesGerald Todd*, University Of MontanaPoint-line configurations in the plane can have many types of symmetries. We will investigate bijections of point-line configurations that preserve a certain structure (automorphisms). Of course, to 'break' these symmetries, we can simply fix all points, but we are interested in the...
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Prospective Teachers’ Reasoning about Integers and TemperatureNicole Wessman-Enzinger*, George Fox UniversityNinety-eight elementary and middle school prospective teachers participated in a study focusing on integer addition and subtraction while enrolled in an introductory mathematics content course emphasizing number concepts and operations. Across two academic semesters, the prospective teachers posed...
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Student Conceptions of IsomorphismKristen Vroom*, Portland State UniversityKate Melhuish, Teachers Development GroupDuring creation of the Group Concept Inventory (GCI), we discovered that the initial question related to isomorphism adapted from Weber & Alcock (2004) (Are Q and Z isomorphic?) contained a number of hidden complexities related to student understanding of isomorphism. We developed two new...
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Impacts of Inquiry Pedagogy on Undergraduate Students’ Conceptions of the Function of ProofEmily Cilli-Turner*, University of Washington TacomaMathematicians and mathematics educators agree that proof has many different roles in mathematics beyond that of verifying the truth of a statement. For instance, some proofs can not only show that a statement is true, but also explain why it must be true. However, students may not appreciate...
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Improving algebra skills of university students through participation in academic service-learningEkaterina (Katya) Yurasovskaya*, Seattle UniversitySeattle University has a long history and a solid institutional structure for implementing academic service-learning in its courses. For the present study, we developed a Precalculus course with a service-learning component, allowing university students to work in the tutoring labs at a local...
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What do students attend to when first graphing planes in R3?Allison Dorko*, Oregon State UniversityThis talk considers what students attend to as they first encounter R3 coordinate axes and are asked to graph y = 3. Graphs are critical representations in single and multivariable calculus, yet findings from research indicate that students struggle with graphing functions of more than one variable...
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Deconstructing and Reconstructing the Multiplication PrincipleElise Lockwood, Oregon State UniversityJohn Caughman*, Portland State UniversityZackery Reed, Oregon State UniversityThe multiplication principle ("MP") is fundamental to combinatorics, underpinning many standard formulas and providing justification for counting strategies. Given its importance, the way it is presented in textbooks is surprisingly varied. In this talk, we identify key elements of the...
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Reasoning with "dx" in the integralRobert Ely*, University of IdahoResearch indicates that in order for students to be able to successfully interpret and flexibly model with definite integrals, they must conceptualize the integral as “adding up the pieces” of a quantity, rather than as (a) a symbolic template, (b) an anti-derivative, or even just (c) an area under...
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Student Generalizations of Distance and the Cauchy PropertyZackery Reed*, Oregon State UniversityThe Cauchy Property is an important characterization of convergent sequences in complete metric spaces. Students were observed reflecting on the nature of Cauchy Sequences on R, and were then prompted to generalize the definition of a Cauchy sequence into more abstract settings. Their...
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Student Attitudes Toward Listing as a Strategy for Solving Counting ProblemsSarah Erickson*, Oregon State UniversityWhile researchers have found that students at a variety of levels struggle to solve counting problems correctly, listing has been shown to be a potentially effective remedy to student difficulties. Motivated by its importance in helping students solve counting problems, this presentation describes...
Session: Panel Discussions
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Career PanelManny Hur*, Oregon State UniversityMatthew Sottile*, GaloisElise Lockwood*, Oregon State UniversityYou’re about to earn a degree in mathematics, now what? You may be surprised to know that teaching isn’t your only option; in the “real world” mathematical knowledge is a valued commodity and there are many interesting job opportunities for mathematicians in non-academic settings. So, whether you...
Subject Area: Other
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Leading a Successful Math ClubKelsey Jewell*, Western Washington UniversityMaureen Sturgeon*, Western Washington UniversityThis session will be an open discussion led by the student leaders of Western Washington University’s math club, Kelsey Jewell and Maureen Sturgeon. The topic of discussion will be leading academic clubs on campus. The goal of the session is to allow clubs throughout the Pacific Northwest to...
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Stimulating Students to Succeed with Standards Based GradingJean Marie Linhart*, Central Washington UniversityStudents often don't master required prerequisite material in foundational courses, and then they struggle in later courses that
require mastery of earlier concepts. To move students towards mastery learning and full proficiency, I implemented Standards Based Grading in Discrete Mathematics... -
Specific Examples, Generic Elements and Size Tuning - Overcoming Student Roadblocks in Linear AlgebraJeffrey Stuart*, Pacific Lutheran UniversityLinear algebra is the often the first math course in which sets play an explicit and fundamental role. Consequently
students typically struggle with writing proofs for set-based results. In this talk, I focus on four key strategies to improve student success.
1. Emphasize the role of specific (... -
Wanna Play? Gamifcation of STEM Courses in Higher EducationJohn Hossler*, Seattle Pacific UniversityWhile the word "gamification" may sound like it means playing games in class, it means something entirely different: the infusion of game principles into an otherwise non-game situation. Gamification is the addition of game elements, mechanics, and principles to non-game contexts--the...
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Creating Websites about Math - Not Just for MathematiciansNick Lassonde*, Klamath Community CollegeEven undergraduate students can create websites with beautiful mathematics displays. MathJax is a free tool that can be used to render math on web pages, and CodeCogs is a free online equation editor with LaTeX translation and HTML embedding of images. Teach your students how to create their own...
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Beyond Email: Reaching Students Where They AreKristin Lassonde*, Klamath Community CollegeEmail is not always the most effective way to reach our students. To improve instructor-student rapport and ultimately student success, consider implementing alternate methods of contact in your classes. Google Voice for texting and social media for other messaging are two powerful tools available...
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The Diversity of the national Math Circle movementBrandy Wiegers*, Central Washington University, National Association of Math CirclesOriginating in Eastern Europe, Math Circles spread to the United States in the 1990s. They emerged approximately at the same time on both the east and west coast, and have spread to almost every state, numbering around 200 today. While the first wave of Math Circles in the United States started...
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Girls' Day or Mädchen-ZukunfstagAnnie Raymond*, University of WashingtonWe discuss what happened when a whole country decided to reach out to its teenage girls to get them to be more involved in math, science and technology.
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Inside the box: college in prisonMatthew Junge*, University of WashingtonPrisoners that receive college education in prison have drastically lower recidivism rates. Mathematicians are in short supply here, and can make a great difference. I will discuss my experience designing and teaching the first-ever for-credit math course in the Washington Corrections Center for...
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Mathday at University of WashingtonJames Morrow*, University of WashingtonMathday is a day in which 1600 high school students and teachers are on the UW campus to attend lectures and activities. We have grants to support the attendance from remote schools and schools with under-represented populations. This is its twenty-sixth year.
Questions? Contact nums@math.oregonstate.edu. Website sponsored by the Department of Mathematics at Oregon State University.
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