Education Commons^™

Book Review: Reckonings: Numerals, Cognition, And History By Stephen Chrisomalis, Milton Rosa, Daniel Clark Orey

Journal of Humanistic Mathematics

This review of Reckonings shares our thoughts on the diverse insights presented by Stephen Chrisomalis’s version of the history of numerical notation. Chrisomalis suggests that members of distinct cultural groups write numbers as an active choice in accordance with their own sociocultural contexts, which reflect the influences of historical, cognitive, social, economic, political, environmental, and cultural factors. This book integrates comparative, cognitive, and evolutionary understandings on numerical cognition with historical and linguistic evidence on the use and transformation of numeral systems through the historical advancement of numeracy. Chrisomalis offers an interesting historical perspective on numbers that builds upon three main …

An Urgent Plea For More Graduate Programs In Statistics Education, David Eli Drew, Sam Behseta, Cherie L. Ichinose

Journal of Humanistic Mathematics

Lately, much has been written about the importance of amplifying statistics-related content in the K-12 curricula. This can be viewed in parallel or as an addendum to the existing mathematics curricula in the United States. Nevertheless, a key component of this debate is the lack of robust and cutting-edge academic programs in statistics education. In this piece, we emphasize the urgent need for investing in creating strong statistics education programs, which would significantly contribute to nurturing quantitative literacy as well as preparing a more informed citizenry in the 21^st century.

The Problem Of Words: Learning To Teach Mathematics When Numbers And Languages Mix, Gladys Krause

Journal of Humanistic Mathematics

In this piece I propose a perspective shift, from a simplified view of mathematics story problems to a more academically rigorous perspective that integrates mathematical proficiency and language practices crucial for educating bilingual students. The data presented in this article provide a window into what preparing bilingual pre-service teachers to teach mathematics might involve. I discuss issues that arise in the context of preparing Spanish-English bilingual pre-service teachers in a way that can inform their practice in linguistically and culturally diverse classrooms.

Lessons Learned From The Disorder Of Operations, Egan J. Chernoff

Journal of Humanistic Mathematics

The purpose of this article, in general, is to explore certain possible outcomes associated with an underaged gambler attempting to collect his rightful winnings. More specifically, this article is a thought experiment investigating the union of (1) skill testing questions, (2) the equation that recently broke/divided the internet, and (3) how different outcomes render different elements of the thought experiment moot. For example, when the final arbiter has total dominion over a particular outcome, the mathematics of a skill testing question is rendered moot. The article concludes with a discussion revealing how disorder of operations could be considered the teaching …

In Search Of Star Clusters: An Introduction To The K-Means Algorithm, Marcio Nascimento

Journal of Humanistic Mathematics

This article is a gentle introduction to K-means, a mathematical technique of processing data for further classification. We begin with a brief historical introduction, where we find connections with Plato’s Timæus, von Linné’s binomial classification, and the star clustering concept of Mary Sommerville and collaborators. Artificial intelligence algorithms use K-means as a classification methodology to learn about data in a very accurate way, because it is a quantitative procedure based on similarities.

Navigating A Calculus Course During A Pandemic: A Usma Perspective, Shane K. Smith, Tyson H. Walsh, Lee Evans

Journal of Humanistic Mathematics

In this article we analyze publications written about different teaching modalities and evaluate how each applies to a calculus class during the on-going COVID-19 pandemic. We focus on the positives and negatives of teaching and learning in a virtual, classroom, or HyFlex environment. Although arguments could be made for each environment, especially given different institutional objectives, this work aims to explain why we eventually preferred teaching our Fall 2020 multivariable calculus course in a face-to-face classroom setting at the United States Military Academy at West Point. We also offer measures of performance to compare the current COVID-19 semester with previous …

Middle School Students Generating Mathematical Problems From A Real-Life Situation, David Coffland, Ying Xie

Journal of Humanistic Mathematics

In this study, we examined the effect of different presentation formats of a realistic situation on students’ mathematical problem-posing behavior. We divided thirty-six middle school students into two groups, gave them a pretest, and then showed them a realistic, problem-posing situation in Artifact or Video format. We used Silver’s core dimensions of creativity, namely fluency, flexibility, and originality, to measure participants’ problem-posing activity. The results for the fluency measures showed that the Artifact group wrote more questions than the Video group but the same number of mathematics problems. The Video group posed problems in more mathematical domains than the Artifact …

Plane Figurate Number Proofs Without Words Explained With Pattern Blocks, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on an artistic interpretation of pattern block designs with primary focus on the connection between pattern blocks and plane figurate numbers. Through this interpretation, it tells the story behind a handful of proofs without words (PWWs) that are inspired by such pattern block designs.

First Year College Experiences Of California’S Central Valley Latina/O/X Students, Alonzo Campos

CGU Theses & Dissertations

Making the decision to attend and pursue college as a means of social mobility is an option students in the state of California make every year when graduating high school. Scholars have contributed extensively to understand how students prepare and transition into their first year of college, as well as the benefits and outcomes that allows students to acclimate and succeed. The multiple factors that contribute to students’ acclimation into higher education has been a central point. The aim of this study was to explore how Latina/o/x students from California’s Central Valley navigated their college transition in the first year …

The Subtle Distinctions Of Memoir: Reclassifying Jeannette Wall’S The Glass Castle, Anna Cornelia Salvati

Scripps Senior Theses

In this paper, I will begin by exploring the history of memoir, the rise of the “misery memoir,” and I intend to challenge the generalized use of the term. Though the cultural rise of trauma memoirs is real, the genre cannot be a blanket term for memoirs that discuss trauma. I have selected The Glass Castle as my evidence because although it includes disturbing details, Walls effortfully tries to reorient the reader’s focus. The term misery memoir is inadequate to describe The Glass Castle because it is not about misery. It obscures Walls’s message that in order to achieve self-acceptance …

The Heirloom As Evidence: Investigating The Colonial Trace Preserved Within My Family’S Sandalwood Box, Olivia Meehan

Pitzer Senior Theses

This paper accompanies my senior art exhibition Picturing the Colonial Trace. Pulling from a wide range of interdisciplinary scholars, I theorize the practice of critical white auto-ethnography through visual interrogations of family heirlooms. The heirloom as evidence holds within its form a colonial trace. I investigate this trace through my creative practice, revealing the environmental, economic, and interpersonal histories of the British colonization of the Indian subcontinent. My art disrupts my family’s narrative of a benevolent British Empire and redirects attention to the silences of my family archive. This thesis proposes a potential model for white scholars of Environmental …

Fourth Voices Conference On Teaching Stem With Song, Lawrence M. Lesser

Journal of Humanistic Mathematics

The fourth VOICES (Virtual Ongoing Interdisciplinary Collaborations on Educating with Song) conference will be held September 26, 2021, with its Sunday date especially targeting those whose teaching schedule precludes attendance on a weekday. This online-only conference explores the use of song to teach STEM content at the college or secondary school level and will include reviewed interactive sessions, video-posters, and discussions of interest to both practitioners and researchers.

Can We Science The Poop, Too?, Nat Banting

Journal of Humanistic Mathematics

This article describes how an innocuous question from a primary schooler taught me to pay attention to the dynamic meaning making activities of children—particularly, those of my young daughter. Through this lens, I examine how the verb-based world of children might compel us to think differently about the largely nominalized project of schooling and, more specifically, about the craft of teaching mathematics.

The Math Games Seminar: A Mathematical Learning Community, Anthony Delegge, Ellen Ziliak

Journal of Humanistic Mathematics

Learning communities can be an effective means of engaging university students across disciplines. Games have always been a source of both enjoyment and interesting mathematics. Based on our own interest in games, and the deep, strategic discussions we found ourselves having with students when we played games with them, we decided to design a learning community around the mathematics of games. We hoped in particular that such a community could be a great pathway to introducing mathematical thinking to students not majoring in mathematics, and that they would gain a greater appreciation for our field. In this paper, we describe …

An Interdisciplinary Rendezvous Between Mathematics And Literature: Reflections On Beauty As A Perspective In Comparative Disciplinary Didactics And A Thematic Approach To Interdisciplinary Work In Upper Secondary School, Uffe Thomas Jankvist, Helle Rørbech, Jesper Bremholm

Journal of Humanistic Mathematics

In this paper we propose a thematic focus on aesthetics in the context of an interdisciplinary collaboration between mathematics and literature (Language Arts) as a way to further students’ reflections on and deeper understanding of what characterizes the two subjects. Furthermore, we argue that approaching aesthetics through the perspective of literacy can potentially strengthen students’ understanding of ways of thinking particular to specific (academic) disciplines; ways of thinking that are otherwise often hidden when teaching focuses on more pragmatic aspects. G. H. Hardy’s A Mathematician’s Apology from 1940 serves as the recurring illustrative example in our discussions of the pedagogical …

“You Will Remain Unwavering In Your Determination To Succeed No Matter How Long It Takes”: A Mathematico-Emotional Analysis Of A Guide To Higher Learning, Kathleen M. Clark, Oksana M. Rubis

Journal of Humanistic Mathematics

In this article we present an analysis of the multi-fold artist’s book, A Guide to Higher Learning (Chen, 2009). In our analysis, we propose different perspectives from which to view the mathematical and philosophical aspects found within the book. We explore aspects of “higher learning” by analyzing the complex mathematical equations and textual elements that readers meet in the book. Chen challenges the reader with: “This is a test. You will not be given any assistance or instructions on how to proceed. You will not be told when to begin or when to stop” (Chen, 2009). Thus, in our exploration …

Response To Steven Colbert: Spicing Up The Exposition Of Differential Equations Via Engaging With Relevant History Of Algebra, Isaac Elishakoff

Journal of Humanistic Mathematics

This paper deals with some problems that can be incorporated in the exposition of ordinary differential equations in courses on Differential Equations and System Dynamics or Intermediate Strength of Materials, with a view to promote more interest and excitement by the attendees, both students and lecturers.

Using Mathematical Equations To Communicate And Think About Karma, Kien H. Lim, Christopher Yakes

Journal of Humanistic Mathematics

Two equations are presented in this article to communicate a particular understanding of karma. The first equation relates future experiences to past and present actions. Although the equation uses variables and mathematical symbols such as the integral sign and summation symbol, it reads more like a literal translation of an English sentence. Based on the key idea in the first equation, a second equation is then created to highlight the viability of using math to communicate concepts that are not readily quantifiable. Analyzing such equations can stimulate thinking, enhance understanding of spiritual concepts, raise issues, and uncover tensions between our …

Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza

Journal of Humanistic Mathematics

Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners' creativity, first, we combined cognitive and creative spirals and mathematical …

Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski

Journal of Humanistic Mathematics

Students have a complex relationship with mathematics. Some love it, but more often than not, the feelings are less favorable. These feelings can lead to decreased motivation which makes it difficult for students to engage with the subject as the semester progresses. Instructors also have difficulty addressing this waning motivation. In this paper, we claim peers are better able to connect with the students and this can be leveraged to better motivate students. We present an approach to having peers motivate their students. These peer interactions integrated with a mandatory mathematics course might improve students’ motivation.

Raise The (Proportion) Bar!, Michael Waters

Journal of Humanistic Mathematics

This article, drawing mainly on references to teacher preparation textbooks, proposes proportion bars as a somewhat novel graphical approach to solving simple (direct) proportion problems and to illustrate the advantages of such an approach, which include accessibility with materials at early grade levels, allowance of students to better develop number sense and estimation, facilitation of setting up proportions, allowance for conceptual understanding and motivation of the procedure for solving direct proportions, assistance with part-to-part and part-to whole comparisons, and drawing of connections among mathematical topics. The emphasis is on teaching with understanding, rather than procedural knowledge.

Authoring Self And Redefining Luck: Pathways To Arts Degrees And Professions For College Students Of Color, Shirlie Mae Mamaril Choe

CGU Theses & Dissertations

Educators and researchers have consistently championed the value of arts education in helping to foster greater creativity and innovative thought in students. Despite the apparent social value of arts and creativity, there is a growing negative public perception of the utility of arts education and degrees in the competitive job market. In addition to decreases in arts education funding at the elementary and secondary school levels, the proportion of students pursuing arts-related majors have decreased over the years. This is unsurprising since media outlets like the U.S. News & World Report regularly highlight the top majors for students to pursue …

Caratacus, The Remembered Warrior: The Legacies Of Caratcaus In Roman Histories And The British Victorian Era, Isabella Kearney

Pomona Senior Theses

This study will explore the origins of the historical figure of Caratacus and analyze its reception in Victorian and Edwardian Britain. This work will begin by providing an overview of Caratacus’ context in the first century in Britannia. Then, looking at the reception of Caratacus, the study will chronologically analyze the portrayal of Caratacus in the ancient sources of Tacitus and Cassius Dio. As the first textual evidence of Caratacus, this will provide insights into Caratacus’ history and the origins of Caratacus’ transformation into an icon of Roman and British history. This work will then analyze the receptions of Caratacus …

Remote Learning In The Era Of Covid-19: Accounting For Students' Personal Verve, Marissa Langley

Scripps Senior Theses

This study focuses on accommodating remote academic lessons for students’ personal verve levels. Personal verve is defined as the ability to adapt to and concentrate in environments with high levels of stimulation. The sociocultural psychologists Boykin discerned higher verve levels in Black communities compared to White communities. Boykin found that many Black students tend to learn best in high verve conditions, which incorporate aspects of African American culture like group work, varied activities, movement and noise, as opposed to traditional low verve conditions which consist of sitting quietly at a desk during lectures. White students tend to have low personal …

Drawing Parallels In Art Science For Collaborative Learning: A Case Study, Karen Westland

The STEAM Journal

This research paper explores drawing as a tool to facilitate interdisciplinary practice. Outlined is the personal experience of PhD researcher [name removed] in their physics/craft research project, combined with thoughts and opinions from collaborators gathered through group discursive interviews. Interdisciplinary projects face interpersonal and conceptually ambiguous challenges which can be addressed through adopting drawing techniques for educational purposes. Findings highlight that drawing can assist across a breadth of applications as a learning tool for everyone, regardless of drawing ability, to improve the functionality of collaborative projects. Specifically, drawing combined with other communication techniques develops a performative communicative approach that enriches …

Visual Arts Enhance Instruction In Observation And Analysis Of Microscopic Forms In Developmental And Cell Biology, Max Ezin, Christina Noravian, Amira Mahomed, Adam Lyle, Aveleen Gill, Tamira Elul

The STEAM Journal

Two important skills for scientists in developmental and cell biology, as well as in fields such as neurobiology, histology and pathology, are: 1) observation of features and details in microscopic images of cells, and 2) quantification of cellular features observed in microscopic images. However, current training in developmental and cell biology does not emphasize observation and quantitative analysis of microscopic images, and it is unclear how best to teach students these skills. Here, we describe our experiences applying visual artistic approaches to instruct undergraduate and graduate students in how to observe and analyze cellular forms in microscopic images. At Loyola …

Music In Steam: Beyond Notes, Hao Huang

The STEAM Journal

Given current debates about STEAM, it would be well to remember that more than five centuries before STEM was conceived, the original Renaissance man, Leonardo da Vinci, wrote in one of his notebooks that "To develop a complete mind, study the science of art, study the art of science. Learn how to see. Realize that everything connects to everything else." (Spong 2006) A discussion of the effectiveness of teaching music and its accompanying technology in conjunction with math and the science education follows. .Given the recent shift from in-classroom teaching to online instruction compelled by the Covid 19 pandemic, an …

Picking Up Steam: The Role Of Languages And Linguistics, Keith Mason

The STEAM Journal

Languages and linguistics are powerful skills that enhance STEAM curricula and careers. A variety of approaches and methods to language teaching and learning inform educators how to proceed with the enhancement of STEAM programs. Linguistics, the science of language, can help STEAM students, especially within the science and mathematics components, because of its reliance on hypothesis formulation for scientific inquiry and data collection and analysis. Language, an important aspect of the human experience, elevates or picks up the STEAM experience.

The International Conference On Creative Mathematical Sciences Communication: Online Event (Cmsc'20) And Cmsc'21, Frances Rosamond

Journal of Humanistic Mathematics

You are warmly invited to register now for the 5th International Conference on Creative Mathematical Sciences Communication (CMSC’21) which will be held at Adam Mickiewicz University in Poznań, Poland, 2–6 July, 2021.

The International Conference on Creative Mathematical Sciences Communication (CMSC) is a unique gathering of computer scientists and mathematicians, teachers, musicians, dancers, dramatists, game designers, educators and communicators of all sorts.

Due to the pandemic, the in-person event scheduled for 2020 has been post- poned and a short CMSC Online Event was organized as a “teaser” or trailer in order to feel the spirit of the full 5th CMSC …

Changes And Deltas, Jim Wolper

Journal of Humanistic Mathematics

Lecturing about Mathematics is like playing Jazz.