Education Commons^™

Violence In Mathematics Teaching. Reflections Inspired By Levinas’ Totality And Infinity, Adriano Demattè

Journal of Humanistic Mathematics

In mathematics class, violence is carried out in some usually not recognized situations. In this article, I share some reflections on the topic inspired by some passages of Totality and Infinity, work of the French-Lithuanian philosopher Emmanuel Levinas (1906-1995). I find violence by the teacher in not promoting students’ understanding of mathematics, in a distorted use of rhetoric, and in interrupting an ethical relation. This article analyses situations taken from class activities, focusing on the teacher’s presentation of mathematical content and students’ interventions. I also propose that the improvement of interventions in mathematics education is possible and suggest theoretical …

The Formal Presentation Language Of Mathematics And Communication Ethics, Marshall Gordon

Journal of Humanistic Mathematics

Mathematics employs a formal language where symbols, verbs, and nouns serve to express terms, concepts, and rules that concatenate to definitions, problem-solving procedures, and proofs. Taken together these constitute the expository language of mathematics found in journals, textbooks, and demonstrations. As a communication given to informing, there are epistemological and ethical considerations that deserve examination. For in keeping with the commitment to an aesthetic of concision promulgated by tradition, the formal presentation language and style of mathematics, while valuable in furthering the body of knowledge, provides only the conclusion of an inquiry, completely excluding the language of investigation that informed …

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.

A Reflection On Growth Mindset And Meritocracy, Rachel L. Petrik, Julianne Vega, Andrés R. Vindas-Meléndez

Journal of Humanistic Mathematics

As mathematicians working in higher education we reflect on meritocracy and growth mindset with a focus on the relationship between the two. We also note the subtle differences between growth mindset and grit. Our reflection ends with suggestions for how to move forward in the math classroom and throughout the collegiate level.

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 …

Teaching Preservice Teachers In The Time Of Covid: What’S Worth Keeping?, Kathy Liu Sun, Jennifer L. Ruef, Kathleen Jablon Stoehr, Madeline Ahearn

Journal of Humanistic Mathematics

As we begin to transition from online instruction to in-person, we (four mathematics teacher educators) reflect on how COVID-19 impacted our instruction and address the question: what will we take back to in-person instruction? This article includes our individual reflections and an analytical synthesis of them. Findings reveal that there were unanticipated ways that human connection and consideration arose from teaching online, much of which we want to maintain in some form when returning to brick and mortar classrooms. We conclude by highlighting the value and importance of reflection for our own well-being.

Happiness In Mathematics Education: The Experiences Of Preservice Elementary Teachers, Jeffrey Pair, Kent Dinh

Journal of Humanistic Mathematics

In this paper, we discuss preservice elementary teachers (PSTs) self-report of their happiness or unhappiness. Several times throughout a mathematics content capstone course, PSTs responded to prompts in which they described times from their past schooling experiences or during the course in which they experienced happiness or unhappiness in learning mathematics. Through thematic analysis, we examined their common experiences related to happiness and their mathematics learning. We found that PSTs’ happiness is related to expectations of themselves, their teachers, their peers, and mathematics itself. The study illuminates PST beliefs about mathematics teaching, collaborative group work, and the nature of mathematical …

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.

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.

Ubiratan D’Ambrosio: Celebrating His Life And Legacy, Milton Rosa, Daniel Clark Orey

Journal of Humanistic Mathematics

On May 12^th, Brazil and the world said goodbye to one of its biggest names in mathematics education, Ubiratan D’Ambrosio (December 8, 1932 – May 12, 2021). D’Ambrosio is recognized both throughout Brazil and internationally for having been the creator of ethnomathematics, a concept that acknowledges, values, and respects different mathematical ideas, procedures, and practices developed by the members of distinct cultural groups. D’Ambrosio analyzed the history of explanations of life and of natural evolution in different cultures. In the last years, his motivation had been the pursuit of peace, in all its four dimensions: individual, social, environmental, …

Teaching Mathematics: Heuristics Can And Ought To Lead The Way, Marshall Gordon

Journal of Humanistic Mathematics

In contrast to problem-solving procedures that are the “bricks and mortar” of demonstrations in mathematics textbooks, heuristics, defined by Polya as “the study of means and methods of problem solving”, are those mental actions that enable the practitioner to make progress when it is not clear how to solve problems directly. Yet, as essential as heuristic tools are, they tend not to be included in presentations in mathematics textbooks. The overarching problem can be understood in terms of students’ not developing productive means for engaging problems. A few mathematics problems are included to argue for the validity, if not the …

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.

Arithmetics, Interrupted, Matilde Lalín

Journal of Humanistic Mathematics

I share some of my adventures in mathematical research and homeschooling in the time of COVID-19.

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 …

How I First Heard About Calculus, Bradley J. Lucier

Journal of Humanistic Mathematics

An attempt to motivate a class of engineering students leads to insights both personal and pedagogical.

Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg

Journal of Humanistic Mathematics

How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and …

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 …

A Holistic Mathematics Curriculum Revision: An Adelphi University Case Study, Salvatore J. Petrilli

Journal of Humanistic Mathematics

Join me as I take you on a journey with the faculty of the Department of Mathematics and Computer Science at Adelphi University during our two-year re-envisioning and implementation of our mathematics curriculum. From the beginning this involved a data-driven initiative that naturally led to the revisions. Here I describe in detail the process that our department followed. In closing I end with some recommendations for interesting research directions in the field of mathematics education.

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.

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 …