A Commentary On Freudenthal’S Didactic Phenomenology Of The Mathematical Structures Associated With The Notion Of Measurement,
2017
University of Montana
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 …
The Historical Connection Of Fourier Analysis To Music,
2017
University of Montana
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 …
Editorial: All Good Things Come In Three,
2017
University of Montana
Editorial: All Good Things Come In Three, Bharath Sriraman
The Mathematics Enthusiast
No abstract provided.
Linking Pre-Service Teachers’ Questioning And Students’ Strategies In Solving Contextual Problems: A Case Study In Indonesia And The Netherlands,
2017
University of Montana
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 …
Subtraction Involving Negative Numbers: Connecting To Whole Number Reasoning,
2017
University of Montana
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.
Students’ Reactions To Reform Mathematics Pedagogy In A Postsecondary Remedial Mathematics Course,
2017
University of Montana
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 …
On Mathematics With Distinction, A Learner-Centered Conceptualization Of Challenge And Choice-Based Pedagogies,
2017
University of Montana
On Mathematics With Distinction, A Learner-Centered Conceptualization Of Challenge And Choice-Based Pedagogies, Boris Koichu
The Mathematics Enthusiast
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 …
A 21st Century Economic, Educational And Ethical Mathematics Curriculum Policy,
2017
University of Montana
A 21st Century Economic, Educational And Ethical Mathematics Curriculum Policy, Glen S. Aikenhead
The Mathematics Enthusiast
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 …
Long And Short-Range Air Navigation On Spherical Earth,
2017
AAR Aerospace Consulting, LLC
Long And Short-Range Air Navigation On Spherical Earth, Nihad E. Daidzic
International Journal of Aviation, Aeronautics, and Aerospace
Global range air navigation implies non-stop flight between any two airports on Earth. Such effort would require airplanes with the operational air range of at least 12,500 NM which is about 40-60% longer than anything existing in commercial air transport today. Air transportation economy requires flying shortest distance, which in the case of spherical Earth are Orthodrome arcs. Rhumb-line navigation has little practical use in long-range flights, but has been presented for historical reasons and for comparison. Database of about 50 major international airports from every corner of the world has been designed and used in testing and route validation. …
College Algebra Through Problem Solving,
2017
CUNY Queensborough Community College
College Algebra Through Problem Solving, Danielle Cifone, Karan Puri, Debra Maslanko, Ewa Dabkowska
Open Educational Resources
This is a self-contained, open educational resource (OER) textbook for college algebra. Students can use the book to learn concepts and work in the book themselves. Instructors can adapt the book for use in any college algebra course to facilitate active learning through problem solving. Additional resources such as classroom assessments and online/printable homework is available from the authors.
Siso Output Affine Feedback Transformation Group And Its Faá Di Bruno Hopf Algebra,
2017
Old Dominion University
Siso Output Affine Feedback Transformation Group And Its Faá Di Bruno Hopf Algebra, W. Steven Gray, Kurusch Ebrahimi-Fard
Electrical & Computer Engineering Faculty Publications
The general goal of this paper is to identify a transformation group that can be used to describe a class of feedback interconnections involving subsystems which are modeled solely in terms of Chen-Fliess functional expansions or Fliess operators and are independent of the existence of any state space models. This interconnection, called an output affine feedback connection, is distinguished from conventional output feedback by the presence of a multiplier in an outer loop. Once this transformation group is established, three basic questions are addressed. How can this transformation group be used to provide an explicit Fliess operator representation of …
A Survey Of Butterfly Diagrams For Knots And Links,
2017
University of Northern Iowa
A Survey Of Butterfly Diagrams For Knots And Links, Mark Ronnenberg
Dissertations and Theses @ UNI
A “butterfly diagram” is a representation of a knot as a kind of graph on the sphere. This generalization of Thurston’s construction of the Borromean rings was introduced by Hilden, Montesinos, Tejada, and Toro to study the bridge number of knots. In this paper, we study various properties of butterfly diagrams for knots and links. We prove basic some combinatorial results about butterflies and explore properties of butterflies for classes of links, especially torus links. The Wirtinger presentation for the knot group will be adapted to butterfly diagrams, and we translate the Reidemeister moves for knot diagrams into so-called “butterfly …
Artin Presentations And Closed 4-Manifolds,
2017
Oberlin College
Artin Presentations And Closed 4-Manifolds, Jun Li
Honors Papers
In this paper we focus on the study of smooth closed simply-connected 4-manifolds. In particular, we study such manifolds arising from Artin presentations. Artin pre- sentations are intimately related to the pure braid group, and they characterize the fundamental groups of closed orientable 3-manifolds. Each Artin presentation r gives rise to a 4-manifold W4(r), whose boundary is a closed orientable 3-manifold M3(r) with fundamental group presented by r. In case the 4-manifold has bound- ary S3, we may close up W 4(r) by attaching a 4-handle to obtain W 4(r) ¿S3 D4. This closed 4-manifold has quadratic form represented by …
Average Shortest Path Length In A Novel Small-World Network,
2017
Oberlin College
Average Shortest Path Length In A Novel Small-World Network, Andrea J. Allen
Honors Papers
We study a novel model of random graph which exhibits the structural characteristics of the Watts- Strogatz small-world network. The small-world network is characterized by a high level of local clustering while also having a relatively small graph diameter. The same behavior that makes the Watts-Strogatz model behave like this also makes it difficult to analyze. Our model addresses this issue, closely mimicking the same structure experimentally while following a constructive process that makes it easier to analyze mathematically. We present a bound on the average shortest path length in our new model, which we approach by looking at the …
Predicting Risk Of Adverse Outcomes In Knee Replacement Surgery With Reconstructability Analysis,
2017
Portland State University
Predicting Risk Of Adverse Outcomes In Knee Replacement Surgery With Reconstructability Analysis, Cecily Corrine Froemke, Martin Zwick
Complex Systems Faculty Publications and Presentations
Reconstructability Analysis (RA) is a data mining method that searches for relations in data, especially non-linear and higher order relations. This study shows that RA can provide useful predictions of complications in knee replacement surgery.
Spot It! Mathematical Structure In A Children's Game,
2017
Dordt College
Spot It! Mathematical Structure In A Children's Game, Tom Clark
Faculty Work Comprehensive List
"Whenever I lead the Northwest Iowa Math Teachers’ Circle I want to use a problem that is easy to explain, unfolds in many directions, and encourages inquiry. Spot It! is the best session topic I have ever seen for this. All you have to do is play the game for a minute or two, and questions arise spontaneously."
Building A Community Of Christ In A Mathematics Classroom,
2017
George Fox University
Building A Community Of Christ In A Mathematics Classroom, Robert Bonner
International Christian Community of Teacher Educators Journal
The prevalence of mathematics anxiety and math phobia is an accepted phenomenon in our culture today (Boaler, 2013; Kimball & Smith, 2013). Multiple research studies have been conducted investigating the levels of mathematics anxiety present in both preservice and in-service elementary education teachers (Bekdemir, 2010; Mizala, Martínez, & Martínez, 2015). This article describes how the creation of a learning community within a two-course sequence of mathematics content courses for elementary teachers addressed the fears and anxieties of a cohort of prospective female teachers. The learning community was founded on three perspectives: Palmer’s (1989) community of truth, Paul’s description of the …
Graph Invariants Of Trees With Given Degree Sequence,
2017
Georgia Southern University
Graph Invariants Of Trees With Given Degree Sequence, Rachel Bass
College of Graduate Studies: Theses & Dissertations
Graph invariants are functions defined on the graph structures that stay the same under taking graph isomorphisms. Many such graph invariants, including some commonly used graph indices in Chemical Graph Theory, are defined on vertex degrees and distances between vertices. We explore generalizations of such graph indices and the corresponding extremal problems in trees. We will also briefly mention the applications of our results.
A Journey To Fuzzy Rings,
2017
Georgia Southern University
A Journey To Fuzzy Rings, Brett T. Ernst
College of Graduate Studies: Theses & Dissertations
Enumerative geometry is a very old branch of algebraic geometry. In this thesis, we will describe several classical problems in enumerative geometry and their solutions in order to motivate the introduction of tropical geometry. Finally, fuzzy rings, a powerful algebraic framework for tropical and algebraic geometry is introduced.
Combinatorics Of Compositions,
2017
Georgia Southern University
Combinatorics Of Compositions, Meghann M. Gibson
College of Graduate Studies: Theses & Dissertations
Integer compositions and related enumeration problems have been extensively studied. The cyclic analogues of such questions, however, have significantly fewer results. In this thesis, we follow the cyclic construction of Flajolet and Soria to obtain generating functions for cyclic compositions and n-color cyclic compositions with various restrictions. With these generating functions we present some statistics and asymptotic formulas for the number of compositions and parts in such compositions. Combinatorial explanations are also provided for many of the enumerative observations presented.
