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Articles 811 - 840 of 2211

Full-Text Articles in Mathematics

Polygons, Pillars And Pavilions: Discovering Connections Between Geometry And Architecture, Sean Patrick Madden Mar 2017

Polygons, Pillars And Pavilions: Discovering Connections Between Geometry And Architecture, Sean Patrick Madden

Journal of Catholic Education

Crowning the second semester of geometry, taught within a Catholic middle school, the author's students explored connections between the geometry of regular polygons and architecture of local buildings. They went on to explore how these principles apply famous buildings around the world such as the monuments of Washington, D.C. and the elliptical piazza of Saint Peter's Basilica at Vatican City within Rome, Italy.

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Session A-3: Three-Act Math Tasks, Lindsey Herlehy Mar 2017

Session A-3: Three-Act Math Tasks, Lindsey Herlehy

Professional Learning Day

Participants will engage in a Three-Act Math task highlighting the application of properties of geometrical figures. Developed by Dan Meyer, an innovative and highly regarded mathematics instructor, Three-Act Math tasks utilize pedagogical skills that elicit student curiosity, collaboration and questioning. By posing a mathematical problem through active storytelling, this instructional approach redefines real-world mathematics and clarifies the role that a student plays in the learning process. Participants will be given multiple resources where they can access Three-Act Math tasks appropriate for upper elementary grades through Algebra and Geometry courses.

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3d Printing For Mathematics Education, Cecile M. Piret Mar 2017

3d Printing For Mathematics Education, Cecile M. Piret

TechTalks

3D printing is particularly well-suited for teaching concepts of mathematics. We (Drs. Piret and Ellis) have started using 3D printers in a calculus 3 classroom. Our goals are to analyze the impact of the printers on students' understanding and motivation towards calculus, and to further incorporate this new technology in our teaching of mathematics. In this talk, we will show a few examples of projects that were presented to the students in our classes, and we will try to motivate you to also use the printers in your classrooms.

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16, Dan Mcquillan Feb 2017

16, Dan Mcquillan

Journal of Humanistic Mathematics

This 15 word poem suggests that the reader count the words of the poem. Since every line has half as many words as the previous line, and since the poem urges the reader to keep counting forever, one imagines a total of 16 words.

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The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz Feb 2017

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to explain …

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The Graduate Student Blues, Marion D. Cohen Feb 2017

The Graduate Student Blues, Marion D. Cohen

Journal of Humanistic Mathematics

This is a memoir about my rather unconventional path to a mathematics Ph.D. There were difficulties, due partly to university politics, partly to my youth and immaturity, and partly to the thesis material itself – it was, in the words of some of my fellow students, “not what’s being done now”. I had written the thesis entirely on my own, without help from my Master’s thesis advisor or any other professor at my school. This is not the usual procedure of course. Nobody in my department could understand the thesis or was willing to vouch for it. There followed three …

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Gorenstein Projective Precovers, Sergio Estrada, Alina Iacob, Katelyn A. Coggins Feb 2017

Gorenstein Projective Precovers, Sergio Estrada, Alina Iacob, Katelyn A. Coggins

Mathematical Sciences: Faculty Publications

We prove that the class of Gorenstein projective modules is special precovering over any left GF-closed ring such that every Gorenstein projective module is Gorenstein flat and every Gorenstein flat module has finite Gorenstein projective dimension. This class of rings includes (strictly) Gorenstein rings, commutative noetherian rings of finite Krull dimension, as well as right coherent and left n-perfect rings. In Sect. 4 we give examples of left GF-closed rings that have the desired properties (every Gorenstein projective module is Gorenstein flat and every Gorenstein flat has finite Gorenstein projective dimension) and that are not right coherent.

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Ghost Series And A Motivated Proof Of The Andrews–Bressoud Identities, Shashank Kanade, James Lepowsky, Matthew C. Russell, Andrew Sills Feb 2017

Ghost Series And A Motivated Proof Of The Andrews–Bressoud Identities, Shashank Kanade, James Lepowsky, Matthew C. Russell, Andrew Sills

Mathematical Sciences: Faculty Publications

We present what we call a “motivated proof” of the Andrews–Bressoud partition identities for even moduli. A “motivated proof” of the Rogers–Ramanujan identities was given by G.E. Andrews and R.J. Baxter, and this proof was generalized to the odd-moduli case of Gordon's identities by J. Lepowsky and M. Zhu. Recently, a “motivated proof” of the somewhat analogous Göllnitz–Gordon–Andrews identities has been found. In the present work, we introduce “shelves” of formal series incorporating what we call “ghost series,” which allow us to pass from one shelf to the next via natural recursions, leading to our motivated proof. We anticipate that …

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On Gorenstein Fiber Products And Applications, Saeed Nasseh, Ryo Takahashi, Keller Vandebogert Jan 2017

On Gorenstein Fiber Products And Applications, Saeed Nasseh, Ryo Takahashi, Keller Vandebogert

Mathematical Sciences: Faculty Publications

We show that a non-trivial fiber product S×kT of commutative noetherian local rings S,T with a common residue field k is Gorenstein if and only if it is a hypersurface of dimension 1. In this case, both S and T are regular rings of dimension 1. We also give some applications of this result.

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Totally Acyclic Complexes, Sergio Estrada, Xianhui Fu, Alina Iacob Jan 2017

Totally Acyclic Complexes, Sergio Estrada, Xianhui Fu, Alina Iacob

Mathematical Sciences: Faculty Publications

It is known that over an Iwanaga–Gorenstein ring the Gorenstein injective (Gorenstein projective, Gorenstein flat) modules are simply the cycles of acyclic complexes of injective (projective, flat) modules. We consider the question: are these characterizations only working over Iwanaga–Gorenstein rings? We prove that if R is a commutative noetherian ring of finite Krull dimension then the following are equivalent: 1. R is an Iwanaga–Gorenstein ring. 2. Every acyclic complex of injective modules is totally acyclic. 3. The cycles of every acyclic complex of Gorenstein injective modules are Gorenstein injective. 4. Every acyclic complex of projective modules is totally acyclic. 5. …

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Mathematics For Human Flourishing, Francis Su Jan 2017

Mathematics For Human Flourishing, Francis Su

All HMC Faculty Publications and Research

Why does the practice of mathematics often fall short of our ideals and hopes? How can the deeply human themes that drive us to do mathematics be channeled to build a more beautiful and just world in which all can truly flourish?

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Teaching And Learning Mathematics In The Ar/Vr Environment, Alexander Vaninsky Jan 2017

Teaching And Learning Mathematics In The Ar/Vr Environment, Alexander Vaninsky

Publications and Research

This presentation discusses teaching and learning mathematics in augmented (AR) or virtual (VR) reality created by a combination of goggles and earphones. It claims that interactive learning in such an environment is more attractive and efficient. It increases motivation and interest in the subject matter. The approach is underlain by the findings of educational neuroscience considering the learning process as the formation of domains in the brain forming mathematics knowledge centers. The teaching process provides sensory excitation and establishes connections among these and other domains. Hardware and software are available in the market. The suggested approach allows for practical implementation …

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Specifications Grading In A First Course In Abstract Algebra, Mike Janssen Jan 2017

Specifications Grading In A First Course In Abstract Algebra, Mike Janssen

Faculty Work Comprehensive List

Specifications grading offers an alternative to more traditional, points-based grading and assessment structures. In place of partial credit, students are assessed pass/fail on whether or not they have achieved the learning outcomes being assessed on a given piece of work according to certain specifications, with limited opportunities for revision of non-passing work. This talk will describe the learning outcomes and specifications grading system I used in my Fall 2016 abstract algebra course, as well as student responses.

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A Madison-Numeracy Citation Index (2008-2015): Implementing A Vision For A Quantitatively Literate World, Nathan D. Grawe, H. L. Vacher Jan 2017

A Madison-Numeracy Citation Index (2008-2015): Implementing A Vision For A Quantitatively Literate World, Nathan D. Grawe, H. L. Vacher

Numeracy

This editorial recognizes the contributions made by Bernard Madison to the field of quantitative literacy with a bibliographic index of his papers, edited volumes, and works contained therein that were cited in the first eight volumes (2008-2015) of Numeracy. In total, 61 citing papers ("sources") cite 42 Madison works ("citations") a total of 218 times. The source and citation indexes provided in the appendix at the end of this editorial make it easy to see the direct contribution of Madison's work to the arguments and debates contained in the founding years of the journal. For those who are new …

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The Mean Value Theorem, Dave Ruch Jan 2017

The Mean Value Theorem, Dave Ruch

Analysis

No abstract provided.

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Strategies For Using Data Analytics In Testing The Readability Levels Of Textbooks: It’S Time To Get Serious, Emily Wefelmeyer, Mary Beth Backus Jan 2017

Strategies For Using Data Analytics In Testing The Readability Levels Of Textbooks: It’S Time To Get Serious, Emily Wefelmeyer, Mary Beth Backus

Other Student Works

The idea that education in America is deteriorating is emotionally charged and controversial. While there is no disputing that education levels in the United States continue to rise, there is also a pervasive notion that this was accomplished by gradually reducing the readability level and general difficulty of textbooks. One tool often employed in the defense of education is the employment of readability indices in the evaluation of textbooks. There are a variety of these readability indices that serve the purpose of indicating a grade level for a particular piece of writing (Kinkaid, et. al., 1975). It’s relatively easy to …

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Introduction To The Special Issue On Teaching Inquiry (Part I): Illuminating Inquiry, Brian P. Katz, Elizabeth Thoren Jan 2017

Introduction To The Special Issue On Teaching Inquiry (Part I): Illuminating 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. We focus here on Part I: Illuminating Inquiry.

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Introduction To The Special Issue On Teaching Inquiry (Part Ii): Implementing Inquiry, Brian P. Katz, Elizabeth Thoren Jan 2017

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.

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2017-2018 Graduate Handbook For The Master Of Arts In Educational Mathematics, Otterbein Office Of Graduate Programs Jan 2017

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.

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Investigating Difference Equations, Dave Ruch Jan 2017

Investigating Difference Equations, Dave Ruch

Discrete Mathematics

No abstract provided.

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Euler's Rediscovery Of E With Instructor Notes, Dave Ruch Jan 2017

Euler's Rediscovery Of E With Instructor Notes, Dave Ruch

Analysis

No abstract provided.

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Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch Jan 2017

Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch

Analysis

No abstract provided.

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An Introduction To A Rigorous Definition Of Derivative, Dave Ruch Jan 2017

An Introduction To A Rigorous Definition Of Derivative, Dave Ruch

Analysis

No abstract provided.

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Bolzano On Continuity And The Intermediate Value Theorem, Dave Ruch Jan 2017

Bolzano On Continuity And The Intermediate Value Theorem, Dave Ruch

Analysis

No abstract provided.

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Subtraction Involving Negative Numbers: Connecting To Whole Number Reasoning, Laura Bofferding, Nicole Wessman-Enzinger Jan 2017

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

Faculty Publications - College of Education

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.

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A Study Of Fourth-Grade Students' Perceptions On Homework Environment And Academic Motivation In Mathematics, Stefanie Harmon Jan 2017

A Study Of Fourth-Grade Students' Perceptions On Homework Environment And Academic Motivation In Mathematics, Stefanie Harmon

Walden Dissertations and Doctoral Studies

The problem at an elementary school is teachers' lack of knowledge and information on the perceptions and motivation of students to complete independent mathematics homework. The purpose of this study was to identify students' perceptions regarding their homework environment and academic motivation in mathematics. The study's conceptual framework, attribution theory, supported the examination of drivers of motivation for participants related to homework completion. Guiding research questions, supported by Keller's ARCS model, focused on the identification of students' perceptions of homework attention, relevance, curiosity, satisfaction, and their preferred homework environment. This qualitative research study obtained data from semistructured interviews with 44 …

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Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, Kayla Blyman Jan 2017

Influences Of Probability Instruction On Undergraduates' Understanding Of Counting Processes, Kayla Blyman

Theses and Dissertations--Education Sciences

Historically, students in an introductory finite mathematics course at a major university in the mid-south have struggled the most with the counting and probability unit, leading instructors to question if there was a better way to help students master the material. The purpose of this study was to begin to understand connections that undergraduate finite mathematics students are making between counting and probability. By examining student performance in counting and probability, this study provides insights that inform future instruction in courses that include counting and probability. Consequently, this study lays the groundwork for future inquiries in the field of undergraduate …

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Case Study Of Undergraduate Research Projects In Vector Analysis, Alexander Vaninsky, Willy Baez Lara, Madieng Diao, Analilia Mendez Jan 2017

Case Study Of Undergraduate Research Projects In Vector Analysis, Alexander Vaninsky, Willy Baez Lara, Madieng Diao, Analilia Mendez

Publications and Research

This paper presents two examples of the undergraduate research projects in vector analysis conducted under the first author’s supervision at one of the community colleges that is an integral part of a large city university. The projects were accomplished by the students pursuing associated degrees in engineering, during their sophomore year. One project was to obtain an explicit formula for the curvature of a curve in plane defined implicitly in rectangular or polar coordinates. Another project was aimed to develop an alternative procedure for finding potential function for a vector field in space based on simultaneous integration. Participation in these …

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Math And Physics Activities, Maureen Miller, Hope Bragg, Christy Keefer Jan 2017

Math And Physics Activities, Maureen Miller, Hope Bragg, Christy Keefer

Integrated Math & Social Studies Lessons

Mathematics is at the core of the Hidden Figures story. These women were united by their passion for the field of mathematics. Society often portrays that there are “bad” math students, those that struggle with calculations and applications. The structure of these activities, pairing of students, permits students to support each other in working through the problems. The video clip allows students to establish connections between mathematical calculations and scientific concepts. The physics problems that students complete are motion problems that beginning rocket engineers would have solved to determine how high their rocket flew.

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Adult Learners, Learning Disabilities, And Mathematics : A Case Study, Marguerite Sheehan Flood Jan 2017

Adult Learners, Learning Disabilities, And Mathematics : A Case Study, Marguerite Sheehan Flood

Theses, Dissertations and Culminating Projects

The purpose of this research was to understand how mathematics is taught at a small, liberal arts college that self-advertised as accommodating diverse learners. A qualitative case study was conducted on the mathematics program at Waterview College. Waterview College is unique in that almost half of their students self-identify with a disability, including learning disabilities (LD). The number of students with learning disabilities that attend college is increasing; therefore it is important for mathematics instructors to understand and accommodate diverse learners. The data for this research were collected using one-on-one instructor interviews, classroom observations, and student focus group interviews. The …

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