Introduction To The Special Issue On Teaching Inquiry (Part Ii): Implementing Inquiry,
2017
Augustana College, Rock Island Illinois
Introduction To The Special Issue On Teaching Inquiry (Part Ii): Implementing Inquiry, Brian P. Katz, Elizabeth Thoren
Mathematics: Faculty Scholarship & Creative Works
We provide an introduction to the special issue on Teaching Inquiry, through its motivation and themes, focusing here on Part II: Implementing Inquiry.
Mathematical Creativity For The Youngest School Children: Kindergarten To Third Grade Teachers’ Interpretations Of What It Is And How To Promote It,
2017
University of Montana
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 …
Reorganizing Algebraic Thinking: An Introduction To Dynamic System Modeling,
2017
University of Montana
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 …
Generalised Hopficity And Products Of The Integers,
2017
Technological University Dublin
Generalised Hopficity And Products Of The Integers, Brendan Goldsmith
Articles
Hopfian groups have been a topic of interest in alge-braic settings for many years. In this work a natural generalizationof the notion, so-called R-Hopficity is introduced. Basic propertiesof R-Hopfian groups are developed and the question of whether ornot infinite direct products of copies of the integers are R-Hopfian isconsidered. An unexpected result is that the answer to this purelyalgebraic question depends on the set theory assumed.
Examining The Interaction Of Mathematical Abilities And Mathematical Memory: A Study Of Problem-Solving Activity Of High-Achieving Swedish Upper Secondary Students,
2017
University of Montana
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 …
Mathematical Modeling Cycles As A Task Design Heuristic,
2017
University of Montana
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.
Pattern Avoidance,
2017
College of Saint Benedict/Saint John's University
Pattern Avoidance, Emma Christensen
All College Thesis Program, 2016-2019
A set partition avoids a pattern if no subdivision of that partition standardizes to the pattern. There exists a bijection between set partitions and restricted growth functions (RGFs) on which Wachs and White defined four statistics of interest to this work. We first characterize the restricted growth functions of several avoidance classes based on partitions of size four, enumerate these avoidance classes, and consider the distribution of the Wachs and White statistics across these avoidance classes. We also investigate the equidistribution of statistics between avoidance classes based on multiple patterns.
2017-2018 Graduate Handbook For The Master Of Arts In Educational Mathematics,
2017
Otterbein University
2017-2018 Graduate Handbook For The Master Of Arts In Educational Mathematics, Otterbein Office Of Graduate Programs
Graduate School
Graduate Handbook on the MAEM Program at Otterbein University.
A Proposed Local Instruction Theory For Teaching Instantaneous Speed In Grade Five,
2017
University of Montana
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 …
First Passage Statistics For The Capture Of A Brownian Particle By A Structured Spherical Target With Multiple Surface Traps,
2017
University of Notre Dame
First Passage Statistics For The Capture Of A Brownian Particle By A Structured Spherical Target With Multiple Surface Traps, Alan E. Lindsay, Andrew Bernoff, Michael J. Ward
All HMC Faculty Publications and Research
We study the first passage time problem for a diffusing molecule in an enclosed region to hit a small spherical target whose surface contains many small absorbing traps. This study is motivated by two examples of cellular transport. The first is the intracellular process through which proteins transit from the cytosol to the interior of the nucleus through nuclear pore complexes that are distributed on the nuclear surface. The second is the problem of chemoreception, in which cells sense their surroundings through diffusive contact with receptors distributed on the cell exterior. Using a matched asymptotic analysis in terms of small …
A Remark On Non-Integral P-Adic Slopes For Modular Formsune Remarque Sur Les Pentes P-Adiques Non Entières Des Formes Modulaires,
2017
Bryn Mawr College
A Remark On Non-Integral P-Adic Slopes For Modular Formsune Remarque Sur Les Pentes P-Adiques Non Entières Des Formes Modulaires, John Bergdall, Robert Pollack
Mathematics Faculty Research and Scholarship
We give a sufficient condition, namely “Buzzard irregularity”, for there to exist a cuspidal eigenform which does not have integral p-adic slope.
Investigating Difference Equations,
2017
Ursinus College
Investigating Difference Equations, Dave Ruch
Discrete Mathematics
No abstract provided.
Euler's Rediscovery Of E With Instructor Notes,
2017
Ursinus College
Euler's Rediscovery Of E With Instructor Notes, Dave Ruch
Analysis
No abstract provided.
Abel And Cauchy On A Rigorous Approach To Infinite Series,
2017
Ursinus College
Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch
Analysis
No abstract provided.
An Introduction To A Rigorous Definition Of Derivative,
2017
Ursinus College
An Introduction To A Rigorous Definition Of Derivative, Dave Ruch
Analysis
No abstract provided.
Bolzano On Continuity And The Intermediate Value Theorem,
2017
Ursinus College
Bolzano On Continuity And The Intermediate Value Theorem, Dave Ruch
Analysis
No abstract provided.
A Comparison Of Stimulus Presentation Methods In Temporal Discrimination Testing,
2017
St Vincent's University Hospital, Dublin, Ireland
A Comparison Of Stimulus Presentation Methods In Temporal Discrimination Testing, Eavan M. Mcgovern, John Butler, Ines Beiser, Laura Williams, Brendan Quinlivan, Shruti Narasiham, Rebecca Beck, Sean O'Riordan, Richard B. Reilly, Michael Hutchinson
Articles
The temporal discrimination threshold (TDT) is the shortest time interval at which an individual detects two stimuli to be asynchronous (normal = 30-50 ms). It has been shown to be abnormal in patients with disorders affecting the basal ganglia including adult onset idiopathic focal dystonia (AOIFD). Up to 97% of patients have an abnormal TDT with age- and sex-related penetrance in unaffected relatives, demonstrating an autosomal dominant inheritance pattern. These findings support the use of the TDT as a pre-clinical biomarker for AOIFD. The usual stimulus presentation method involves the presentation of progressively asynchronous stimuli; when three sequential stimuli are …
A Mathematical System For Human Implantable Wound Model Studies,
2017
Virginia Commonwealth University
A Mathematical System For Human Implantable Wound Model Studies, Salomonsky Paul-Michael, Rebecca Segal
Mathematics and Applied Mathematics Publications
In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between …
R-Hopfian And L-Co-Hopfian Abelian Groups,
2017
Technological University Dublin
R-Hopfian And L-Co-Hopfian Abelian Groups, Brendan Goldsmith, Katao Gong
Articles
The notions of Hopfian and co-Hopfian groups are well known in both non-commutative and Abelian group theory. In this work we begin a systematic investigation of natural generalizations of these concepts and, in the case of Abelian p-groups, give a complete characterization of the generalizations in terms of the original concepts.
Tropical Derivation Of Cohomology Ring Of Heavy/Light Hassett Spaces,
2017
Harvey Mudd College
Tropical Derivation Of Cohomology Ring Of Heavy/Light Hassett Spaces, Shiyue Li
HMC Senior Theses
The cohomology of moduli spaces of curves has been extensively studied in classical algebraic geometry. The emergent field of tropical geometry gives new views and combinatorial tools for treating these classical problems. In particular, we study the cohomology of heavy/light Hassett spaces, moduli spaces of heavy/light weighted stable curves, denoted as $\calm_{g, w}$ for a particular genus $g$ and a weight vector $w \in (0, 1]^n$ using tropical geometry. We survey and build on the work of \citet{Cavalieri2014}, which proved that tropical compactification is a \textit{wonderful} compactification of the complement of hyperplane arrangement for these heavy/light Hassett spaces. For $g …
