A SURVEY OF DISTANCE MAGIC GRAPHS

In this report, we survey results on distance magic graphs and some closely related graphs. A distance magic labeling of a graph G with magic constant k is a bijection l from the vertex set to {1, 2, . . . , n}, such that for every vertex x Σ l(y) = k,y∈NG(x) where NG(x) is the set of vertices of G adjacent to x. If the graph G has a distance magic labeling we say that G is a distance magic graph. In Chapter 1, we explore the background of distance magic graphs by introducing examples of magic squares, magic graphs, and distance magic graphs. In Chapter 2, we begin by examining some basic results on distance magic graphs. We next look at results on different graph structures including regular graphs, multipartite graphs, graph products, join graphs, and splitting graphs. We conclude with other perspectives on distance magic graphs including embedding theorems, the matrix representation of distance magic graphs, lifted magic rectangles, and distance magic constants. In Chapter 3, we study graph labelings that retain the same labels as distance magic labelings, but alter the definition in some other way. These labelings include balanced distance magic labelings, closed distance magic labelings, D-distance magic labelings, and distance antimagic labelings. In Chapter 4, we examine results on neighborhood magic labelings, group distance magic labelings, and group distance antimagic labelings. These graph labelings change the label set, but are otherwise similar to distance magic graphs. In Chapter 5, we examine some applications of distance magic and distance antimagic labeling to the fair scheduling of tournaments. In Chapter 6, we conclude with some open problems

Neuronal Effects of Listening to Entrainment Music Versus Preferred Music in Patients With Chronic Cancer Pain as Measured via EEG and LORETA Imaging

Previous studies examining EEG and LORETA in patients with chronic pain discovered an overactivation of high theta (6–9 Hz) and low beta (12–16 Hz) power in central regions. MEG studies with healthy subjects correlating evoked nociception ratings and source localization described delta and gamma changes according to two music interventions. Using similar music conditions with chronic pain patients, we examined EEG in response to two different music interventions for pain. To study this process in-depth we conducted a mixed-methods case study approach, based on three clinical cases. Effectiveness of personalized music therapy improvisations (entrainment music – EM) versus preferred music on chronic pain was examined with 16 participants. Three patients were randomly selected for follow-up EEG sessions three months post-intervention, where they listened to recordings of the music from the interventions provided during the research. To test the difference of EM versus preferred music, recordings were presented in a block design: silence, their own composed EM (depicting both “pain” and “healing”), preferred (commercially available) music, and a non-participant’s EM as a control. Participants rated their pain before and after the EEG on a 1–10 scale. We conducted a detailed single case analysis to compare all conditions, as well as a group comparison of entrainment-healing condition versus preferred music condition. Power spectrum and according LORETA distributions focused on expected changes in delta, theta, beta, and gamma frequencies, particularly in sensory-motor and central regions. Intentional moment-by-moment attention on the sounds/music rather than on pain and decreased awareness of pain was experienced from one participant. Corresponding EEG analysis showed accompanying power changes in sensory-motor regions and LORETA projection pointed to insula-related changes during entrainment-pain music. LORETA also indicated involvement of visual-spatial, motor, and language/music improvisation processing in response to his personalized EM which may reflect active recollection of creating the EM. Group-wide analysis showed common brain responses to personalized entrainment-healing music in theta and low beta range in right pre- and post-central gyrus. We observed somatosensory changes consistent with processing pain during entrainment-healing music that were not seen during preferred music. These results may depict top–down neural processes associated with active coping for pain

The 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Ngā mihi aroha ki ngā tangata katoa and warm greetings to you all. Welcome to Herenga Delta 2021, the Thirteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. It has been ten years since the Volcanic Delta Conference in Rotorua, and we are excited to have the Delta community return to Aotearoa New Zealand, if not in person, then by virtual means. Although the limits imposed by the pandemic mean that most of this year’s 2021 participants are unable to set foot in Tāmaki Makaurau Auckland, this has certainly not stopped interest in this event. Participants have been invited to draw on the concept of herenga, in Te Reo Māori usually a mooring place where people from afar come to share their knowledge and experiences. Although many of the participants are still some distance away, the submissions that have been sent in will continue to stimulate discussion on mathematics and statistics undergraduate education in the Delta tradition. The conference invited papers, abstracts and posters, working within the initial themes of Values and Variables. The range of submissions is diverse, and will provide participants with many opportunities to engage, discuss, and network with colleagues across the Delta community. The publications for this thirteenth Delta Conference include publications in the International Journal of Mathematical Education in Science and Technology, iJMEST, (available at https://www.tandfonline.com/journals/tmes20/collections/Herenga-Delta-2021), the Conference Proceedings, and the Programme (which has created some interesting challenges around time-zones), by the Local Organizing Committee. Papers in the iJMEST issue and the Proceedings were peer reviewed by at least two reviewers per paper. Of the ten submissions to the Proceedings, three were accepted. We are pleased to now be at the business end of the conference and hope that this event will carry on the special atmosphere of the many Deltas which have preceded this one. We hope that you will enjoy this conference, the virtual and social experiences that accompany it, and take the opportunity to contribute to further enhancing mathematics and statistics undergraduate education. Ngā manaakitanga, Phil Kane (The University of Auckland | Waipapa Taumata Rau) on behalf of the Local Organising Committ

Mathematicians’ beliefs, instruction, and students’ beliefs: how related are they?

This is an Accepted Manuscript of an article published by Taylor & Francis in the INTERNATIONAL JOURNAL OF MATHEMATICAL EDUCATION IN SCIENCE AND TECHNOLOGY on November 29, 2021, available online: http://www.tandfonline.com/10.1080/0020739X.2021.1998684It is generally accepted that teachers’ beliefs impact their instructional choices, but characterizations of that relationship are limited in college settings. Furthermore, examinations of instructor beliefs, instruction, and student beliefs together in one setting are rarely described. Based on interviews with two Abstract Algebra instructors, classroom video from three units of instruction, and survey and interview data from students in the classes, this paper examines instructors’ stated beliefs, ways these beliefs manifested in their teaching, and students’ beliefs across the course. Both instructors made curricular choices clearly aligned with their stated views of the nature of mathematics, learning, and teaching. Day-to-day instructional choices reflected these stated beliefs as well, but the difficulty of material and tensions with other beliefs like the importance of interactivity manifested. Characterizations of the interactivity of classes and placement of the mathematical authority in class are provided through descriptive and quantitative measures. These characterizations of instruction provide nuanced portrayals of classroom norms and changes in those norms throughout the semester. Furthermore, subtle shifts in student beliefs about teaching and learning are noticeable, suggesting students’ beliefs about teaching and learning mathematics can be influenced even by modest changes in instructional practice

Conceptual metaphors for isomorphism and homomorphism: Instructors’ descriptions for themselves and when teaching

Article has a 24-month embargoGroup isomorphism and homomorphism are topics central to abstract algebra, yet research on instructors’ views of these concepts is limited. Based on interviews from two instructors as well as classroom video from eight class periods, this paper examines the language used to discuss isomorphism and homomorphism. Language used by instructors in interviews and classroom settings are identified and classified into four main categories: formal definition, mapping, sameness, and combinations of sameness and mapping language. How the two instructors drew on language classified into those four categories in the interview and instruction settings are examined for isomorphism and homomorphism. Similarities and differences between the inter- view and instruction contexts reveal the wide variety of ways of understanding isomorphism and homomorphism as well as a research need to examine mathematicians’ content knowledge in more than one context.n/

Learning to notice important student mathematical thinking in complex classroom interactions

© 2017 Elsevier Ltd Noticing students\u27 mathematical thinking is a key element of effective instruction, but novice teachers do not naturally engage in this practice. Prospective secondary school mathematics teachers were engaged in an intervention grounded in analysis of minimally edited video from local secondary school mathematics classrooms; the goal was to support their ability to notice important student thinking within the complexity of instruction. Evidence of participants\u27 learning in five iterations of the intervention is discussed, including their focus on student mathematical thinking, their ability to discuss the mathematics in that thinking, and their ability to notice particular high-leverage instances of student thinking

How mathematicians assign homework problems in abstract algebra courses

Embargo of 24 months from article publicationWhile many aspects of the teaching and learning of advanced mathematics have been explored, the role, construction, and values of homework have been virtually ignored. This report draws on task-based interviews with six mathematicians to explore the relationship between an instructor’s learning goals and factors considered when selecting homework problems. All participants viewed homework as critical to student learning, and the majority of the participants’ claims focused on either the mathematics or how the problem would help students learn; no instructor gave primacy to evaluative reasons for homework. We highlight six themes used by participants to evaluate and select items for inclusion in homework. They are (1) knowing and recalling ax- ioms and definitions, (2) developing an arsenal of examples, (3) developing new problem ap- proaches, (4) remediating misconceptions, (5) making connections to prior and future material, and (6) valuing reading notes or text

A perturbed system: How tenured faculty responded to the COVID-19 shift to remote instruction

This document is the Accepted Manuscript version of a Published Work that appeared in final form in the Journal of Chemical Education, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://pubs.acs.org/articlesonrequest/AOR-8EVEWDJYHNJUDSQTHRIU.This study investigates six university professors’ reflections on the shift to remote instruction during the Spring 2020 semester in response to the COVID-19 global pandemic. The rapid shift in instructional platform presents an opportunity to learn from unresolved challenges that persisted through the semester. Here we present a qualitative study of how experienced (i.e., associate or full) chemistry professors report their teaching practices in light of the COVID-19 disruptions. We observed four major themes: personal factors, contextual factors of the structure and culture, teacher thinking, and teachers’ practice. These themes revealed that the professors in this study adapted quickly using institutionally offered platforms, modified their courses as minimally as possible, struggled with assessment, and held diverging beliefs about teaching and students. The outcomes of this study have implications for ongoing efforts to reform instructional practices at the institutional and departmental level. Specifically, we recommend similar studies to ascertain current faculty beliefs and instructional practices in other departments in order to identify shared visions for change and effective supports for enacting that change.Northern Illinois Universit