Teacher Education and Professional Development Commons^™

The Set Of Zero Divisors Of A Factor Ring, Jesús Jiménez

ACMS Conference Proceedings 2017

Let A be a ring and a an ideal of A. In this paper we show how to construct factor rings A/ a and a finite set of ideals a1, a2, ... , ak, of A/a, such that: each ideal aj is contained in the set of zero divisors of A/a, the factor ring A/a is a direct sum of these ideals, and each ideal aj is a ring with unity when endowed with addition and multiplication modulo a. Explicit examples are given when A is the ring of integers, Gaussian integers or the ring of polynomials over a field.

Developing The Underutilized Mathematical Strengths Of Students, Patrick Eggleton

ACMS Conference Proceedings 2017

This session is intended for presenting the findings from a Spring 2017 research study conducted at Taylor University regarding influences that contribute to a student's disposition toward mathematics. In the foundation level mathematics course taught for non-majors at Taylor, students are asked to share a reflection on their past mathematical experiences. Analysis of these reflections shows general themes regarding the influences, both good and bad, that have contributed to how these students approach mathematics. We would like to use this information as well as related studies to help instructors of mathematics develop positive dispositions toward mathematics in their students.

Axioms: Mathematical And Spiritual: What Says The Parable?, Melvin Royer

ACMS Conference Proceedings 2017

Relational structure A is compact provided for any structure Jffi of the same signature, if every finite substructure of Jffi has a homomorphism to A then so does Jffi. The Constraint Satisfaction Problem (CSP) for A is the computational problem of determining whether finite structures have homomorphisms into A. We explore a connection between the hierarchy of logical axioms and the complexity hierarchy of CSPs: It appears that the complexity of CSP for A corresponds to the strength of the axiom "A is compact". At the top, the statement "K3 is compacts" is logically equivalent to the compactness theorem. Thus …

A Pre-Calculus Controversy: Infinitesimals And Why They Matter, Karl-Dieter Crisman

ACMS Conference Proceedings 2017

In teaching calculus, it is not uncommon to mention the controversy over the role of infinitesimals with Newton's and Leibniz' calculus, including Berkeley's objections. In a history of mathematics course, it is a required topic! But rancor over infinitesimals and their role in mathematics predates calculus- so much so that a popular new book is dedicated to this topic. In this talk, I will discuss not just the relevant controversies between Cavalieri and the Je

Perspectives On Emotional Climate Associated With Classroom Interactions, Hiro Komatsubara

Dissertations, Theses, and Capstone Projects

It is difficult for students to learn and teachers to teach in today’s classroom environment especially when events involving strong emotional contradictions occur in classrooms. Such events may elicit emotions that negative affect, teaching, learning and wellness. Various studies show that high levels of negative emotions create stressful classroom environments, and that a positive Emotional Energy (EE) in the classroom encourages attentiveness, enthusiasm and interest. Therefore, it is highly likely that creating calm learning environments by ameliorating classroom participants’ emotional intensity and increasing their mindfulness and awareness will produce positive outcomes. Using both quantitative and qualitative measures this study examines …

Embodying Rhythm Nation: Multimodal Hip Hop Dance As A Site For Adolescent Social-Emotional And Political Development, Lauren M. Roygardner

Dissertations, Theses, and Capstone Projects

This exploratory study employed qualitative methodology, specifically values analysis, to learn more about how being involved within Hip hop dance communities positively relates to adolescent development. Adolescence was defined herein as ages 13-23. The study investigated Hip hop dance communities in terms of cultural expertise (i.e. novice, intermediate and advanced/expert) to look specifically at dance narratives (i.e. peak experience narratives and “I dance because” essays) and hip hop dance performances. The primary purpose of this dissertation was to (1) explore how adolescents use multimodal Hip hop dance discourse for social-emotional development and critical consciousness, and to (2) understand how values …

"Resisting From Within": (Re)Imagining A Critical Translingual English Classroom, Kate Anna Seltzer

Dissertations, Theses, and Capstone Projects

This ethnographic case study of an urban, linguistically diverse English classroom explores what happened when space was made for students both to voice their experiences living amidst ideologies that marginalize their language practices and identities and to resist such ideologies through writing that pushed monoglossic boundaries. Intensive one-on-one work with a high school English teacher led to the creation of a year-long curriculum that emphasized metalinguistic inquiry and discussion, linked language, power, and identity, and modeled the ways that writers and other artists take linguistic risks in order to critique monoglossic language ideologies.

Over the course of the year, students …

Escribiendo Para Desahogarme: Release And Resistance In A Middle School Bilingual Writing Workshop, Carla Espana

Dissertations, Theses, and Capstone Projects

This dissertation examines a teacher’s language ideologies, their impact on curriculum modifications and bilingual Latinx middle schoolers’ storytelling, to understand how a bilingual pedagogy builds on their cultural and linguistic resources. This qualitative study was conducted in a sixth grade writing workshop class in New York City as the focus teacher taught the Teachers College Reading and Writing Project Personal Narrative Unit of Study. The first two findings center on the factors that influence a teacher’s stance on language practices and bilingual pedagogy, and how these contributed to curriculum modifications that included using students’ full linguistic and cultural repertoires, integrating …

Do Spellings Of Words And Phonemic Awareness Training Facilitate Vocabulary Learning In Preschoolers?, Robin O'Leary

Dissertations, Theses, and Capstone Projects

The purpose of this study was to examine the contribution of phoneme awareness training and orthography to the learning of new vocabulary words by partial alphabetic phase readers. We hypothesized that four and five year old children taught to segment words with letters would outperform those trained with shape markers and those that received no segmentation training on an invented spelling task. We also hypothesized that students seeing the spellings of new vocabulary words (names) would learn the words in fewer trials, remember the names and features better and would be able to better recognize letter labels when presented alone. …

The Resolved And Unresolved Conjectures Of R.D. Carmichael, Brian D. Beasley

ACMS Conference Proceedings 2017

Even before heading to Princeton University to work on his doctoral degree, Robert Daniel Carmichael started influencing the path of number theory in the 20th century. From his study of Euler's totient function to his discovery of the first absolute pseudoprime, he set the stage for years of productive research. This talk will present a brief overview of Carmichael's life, including his breadth of mathematical interests and his service on behalf of the Mathematical Association of America. It will focus mainly on his two most famous conjectures- which one has been settled, and which one remains open to this day?

"Big Idea" Reflection Assignments For Learning And Valuing Mathematics, Jeremy Case, Mark Colgan

ACMS Conference Proceedings 2017

While participating in a Faculty Learning Community, we explored the "big questions" we wanted our students to take away from our mathematics courses. We called these questions the Big Ideas of the course and developed a Big Ideas Reflection Assignment, which we continue to assign at the end of each of our courses. Students are able to demonstrate understanding and application of their learning as well as their values and appreciation of mathematics. The assignment encourages students to move beyond a focus on technique and symbolic manipulations towards a broader and more holistic approach, including making connections between their learning …

Mentoring As A Statistical Educator In A Christian College, L. Marlin Eby

ACMS Conference Proceedings 2017

In this paper, I present principles based on more than thirty years of intentional mentoring as a statistical educator in a Christian college. I believe this mentoring has been enhanced due to the setting- a Christian college, and the discipline - statistics. I discuss distinctives of the Christian college setting that positively impact mentoring in any discipline with respect to the mentor, the mentee, and the pervading campus atmosphere. I focus on mentoring as a statistical educator by specifically considering the following: attracting students to the discipline of statistics, preparing students for careers using statistics, and preparing students for graduate …

The Daily Question: Building Student Trust And Interest In Undergraduate Introductory Probability And Statistics Courses, Matthew A. Hawks

ACMS Conference Proceedings 2017

Introducing probability or statistics to disinterested undergraduate students is challenging. Adding faith in such a classroom at a secular institution only increases the complexity. We share an unobtrusive way to build trust with students, creating a medium to both naturally share your faith and have your students look forward to attending each class. The context is the United States Naval Academy, a four-year undergraduate institution with an emphasis on leader development. In addition to a calculus sequence, Humanities majors enroll in Probability with Naval Applications or Introductory Statistics. These sophomores or juniors are split between those who have no intention …

The Topology Of Harry Potter: Exploring Higher Dimensions In Young Adult Fantasy Literature, Sarah Klanderman, Alexa Schut, Dave Klanderman, William Boerman-Cornell

ACMS Conference Proceedings 2017

As one of the most beloved series in children’s literature today, the Harry Potter books excite students of all ages with the adventures of living in a magical world. Magical objects (e.g., bottom-less handbags, the Knight Bus, time turners, and moving portraits) can inspire generalizations to mathematical concepts that would be relevant in an undergraduate geometry or topology course. Intuitive explanations for some of the magical objects connect to abstract mathematical ideas. We
offer a typology with a total of five categories, including Three Dimensions in Two Dimensions, Higher Dimensions in Three Dimensions, Two and Three Dimensional Movement, Higher Dimensional …

Start A Math Teacher Circle: Connect K-12 Teachers With Engaging, Approachable, And Meaningful Mahtematical Problems, Thomas Clark, Mike Janssen, Amanda Harsy, Dave Klanderman, Mandi Maxwell, Sharon Robbert

ACMS Conference Proceedings 2017

Many K-12 math teachers are not ready to teach from a conceptual and inquiry-oriented per

Ten Mathematicians Who Recognized God's Hand In Their Work (Part 2), Dale Mcintyre

ACMS Conference Proceedings 2017

Scottish philosopher David Hume (1711-1776) once observed that "Whoever is moved by faith to assent to [the Christian religion], is conscious of a continued miracle in his own person, which subverts all the principles of his understanding, and gives him a determination to believe what is most contrary to custom and experience." Evidently Hume's cynical pronouncement did not apply to Descartes, Newton, Riemann, and other profound thinkers who believed God had commissioned and equipped them to glorify Him in their pursuit of truth through mathematics - And based on their extraordinary achievements the principles of their understanding do not appear …

Stayers, Leavers, Lovers, And Dreamers: Why People Teach And Why They Stay - 2004 Barbara Biber Lecture, Marilyn Cochran-Smith

Occasional Paper Series

Marilyn Cochran-Smith delivers the Barbara Biber Lecture at Bank Street College in memorial of her legacy as a researcher, scholar, and leader in progressive education. Cochran-Smith focuses on what lies at the heart of teaching and learning on an individual level as well as what it will take to improve the current state of urban schools. Her main points address teacher retention and differences among generations of teachers.

Introduction (2017), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2017

No abstract provided.

A Recycling Method For Lst® Contaminated During Heavy Liquid Separation In Palynological Processing, Jennifer M.K. O'Keefe, Brandon G. Van Ness, Morgan K. Black, Clayton R. Gullett

Faculty Research at Morehead State University

An aqueous solution of LST® is one of many heavy liquids used to concentrate palynomorphs. It and aqueous solutions of sodium polytungstate (SPT) are replacing toxic heavy liquids, such as bromoform and zinc bromide, and to a lesser extent zinc chloride, in many palynology laboratories. Both non-toxic heavy liquids can be recycled through filtering and evaporation of water and/or ethanol added to the sample during processing, and commonly are. Both media, and especially LST®, are somewhat reactive with organic matter, and in humic-acid rich samples become contaminated and discoloured. This paper presents the authors' methods for recycling LST® and removing …

Shifts In Teacher Talk In A Participatory Action Research Professional Learning Community, Patrick D. Hales

School of Education, Counseling and Human Development

Most teachers take part in professional development of some kind at some point in their careers. However, many teachers report that professional development neither supports their practice nor improves results. Thus, more work needs to be done on how professional development can meet those needs and what helps to support effective professional learning. A key factor in teacher professional learning is talk. In this study, a group of educators created a professional learning community using concepts from participatory action research to support their interactions and focus their work on achieving their goals. The purpose of this learning community was to …