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Articles 61 - 79 of 79
Full-Text Articles in Mathematics
In Search Of Star Clusters: An Introduction To The K-Means Algorithm, Marcio Nascimento
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.
A Note On A Mathematician-Cyclist: Anna Kiesenhofer, Man Keung Siu
A Note On A Mathematician-Cyclist: Anna Kiesenhofer, Man Keung Siu
Journal of Humanistic Mathematics
This short note offers some reflections on the teaching and learning of mathematics inspired by the news about a feat accomplished by the Austrian mathematician-cyclist Anna Kiesenhofer in the Summer Olympic Games held in Tokyo in 2021.
Extremal Mathematicians, Carlos A. Alfaro
Extremal Mathematicians, Carlos A. Alfaro
Journal of Humanistic Mathematics
We report on the top ten mathematicians with the highest number of articles, citations, and students, based on data from MathSciNet and the Mathematics Genealogy Project.
Navigating A Calculus Course During A Pandemic: A Usma Perspective, Shane K. Smith, Tyson H. Walsh, Lee Evans
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 …
On The Mathematics Of Social Distancing, Robert Haas
On The Mathematics Of Social Distancing, Robert Haas
Journal of Humanistic Mathematics
Early in the COVID-19 pandemic, when spring began to make itself felt, photos showed New Yorkers enjoying the outdoors, while properly socially distanced, by sitting on the grass in a square lattice of circles. But the planners should have consulted a mathematician for the design, because significantly more people (over 15% more) could enjoy the same area safely if the circles were closer packed into a hexagonal lattice.
Covid-19, Vaccines, And Decision Theory, Michael A. Lewis
Covid-19, Vaccines, And Decision Theory, Michael A. Lewis
Journal of Humanistic Mathematics
In this piece, I delve into some thoughts I've had about decision theory. These have been inspired by the vaccine rollout phase of the COVID-19 Pandemic. I focus on decision making under uncertainty, as it relates to the decision to get vaccinated or not.
The Hamster Diaries, Pamela B. Pierce
The Hamster Diaries, Pamela B. Pierce
Journal of Humanistic Mathematics
When the pandemic hits, the author acquires a hamster, who provides some humorous anecdotes and some much-needed inspiration.
Mindfully Navigating The Wind And Water: Defining The Currents Of Metaphors That Interfere With Excellence In Mathematics Education, Rob Blom, Olivia Lu, Chunlei Lu
Mindfully Navigating The Wind And Water: Defining The Currents Of Metaphors That Interfere With Excellence In Mathematics Education, Rob Blom, Olivia Lu, Chunlei Lu
Journal of Humanistic Mathematics
We bring to the forefront of educational thought a specific attitude toward the COVID-19 crisis that harnesses the symbolism of wind and water to navigate the cultural storm interfering upon our mathematical and pedagogical craft. The purpose of our paper is to open up space for opportunities in mathematics education using integral mindfulness as the rudder to readjust our bearings. More specifically, through conceptual analyses and making explicit the currents of change, disorder, and technology, we can apply discernment to these metaphors that intersect our pedagogy to re-align efforts and attitudes toward an integrated (aperspectival) culture of mathematics education. Through …
Unmotivated, Depressed, Anxious: Impact Of The Covid-19 Emergency Transition To Remote Learning On Undergraduates’ Math Anxiety, Melinda Lanius, Tiffany Frugé Jones, Samantha Kao, Tynan Lazarus, Alex Farrell
Unmotivated, Depressed, Anxious: Impact Of The Covid-19 Emergency Transition To Remote Learning On Undergraduates’ Math Anxiety, Melinda Lanius, Tiffany Frugé Jones, Samantha Kao, Tynan Lazarus, Alex Farrell
Journal of Humanistic Mathematics
In summer 2020, we invited the 6761 undergraduate students who took a Spring 2020 math course at the University of Arizona to participate in a survey, with 13% responding. We asked about their experience with the emergency transition to remote learning and measured their math anxiety before and after the transition using the well-established Abbreviated Math Anxiety Scale(AMAS). “Unmotivated, depressed, anxious” are the words one undergraduate used to describe their emergency transition to remote learning. Our results indicate that limited access to quality technology and inadequate communication with an instructor were the two greatest predictors for an increase in math …
Nilpotents Leave No Trace: A Matrix Mystery For Pandemic Times, Eric L. Grinberg
Nilpotents Leave No Trace: A Matrix Mystery For Pandemic Times, Eric L. Grinberg
Journal of Humanistic Mathematics
Reopening a cold case, Inspector Echelon, high-ranking in the Row Operations Center, is searching for a lost linear map, known to be nilpotent. When a partially decomposed matrix is unearthed, he reconstructs its reduced form, finding it singular. But were its origins nilpotent?
A Mother-Mathematician Meets The Covid-19 Era, Bonnie Jacob
A Mother-Mathematician Meets The Covid-19 Era, Bonnie Jacob
Journal of Humanistic Mathematics
Just ask the family cat: we are not all in this together, and never were. In this piece, I describe my journey as a mother and mathematician in the United States during the COVID-19 pandemic. Even though I am one of the lucky ones, we could do so much better.
Teiresias, Proportions, And Sexual Pleasure, Spyros Missiakoulis
Teiresias, Proportions, And Sexual Pleasure, Spyros Missiakoulis
Journal of Humanistic Mathematics
In this short article, I claim that Teiresias, the blind prophet of Apollo, in order to answer the question of whether “in sexual intercourse the woman had a larger share of pleasure than the man did”, measured the abstract concept of sexual pleasure and acted as a present-day scholar. With the help of numerical, not geometrical, proportions, he ended up with the conclusion “a man enjoyed one-tenth of the pleasure and a woman nine-tenths”.
Happiness In Mathematics Education: The Experiences Of Preservice Elementary Teachers, Jeffrey Pair, Kent Dinh
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
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 …
Makers Do Math! Legitimizing Informal Mathematical Practices Within Making Contexts, Amber Simpson, Signe Kastberg
Makers Do Math! Legitimizing Informal Mathematical Practices Within Making Contexts, Amber Simpson, Signe Kastberg
Journal of Humanistic Mathematics
In this paper, we argue that making activities within non-formal learning environments (e.g., museums, libraries) provide opportunities to engage youth in what we define as mathematical practices for making, everyday mathematical practices within the context of making activities. The mathematical practices identified from two non-formal school-based contexts highlighted three mathematical practices for making: informal measurement, spatial reasoning, and curiosity. These practices are identified in prior scholarship as being beneficial and foundational for the understanding of mathematical concepts. As educators and researchers turn to non-formal and informal contexts, with an eye toward understanding ways youth engage in the activity of making, …
Plane Figurate Number Proofs Without Words Explained With Pattern Blocks, Gunhan Caglayan
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.
Intersection Cographs And Aesthetics, Robert Haas
Intersection Cographs And Aesthetics, Robert Haas
Journal of Humanistic Mathematics
Cographs are complete graphs with colored lines (edges); in an intersection cograph, the points (vertices) and lines (edges) are labeled by sets, and the line between each pair of points is (or represents) their intersection. This article first presents the elementary theory of intersection cographs: 15 are possible on 4 points; constraints on the triangles and quadrilaterals; some forbidden configurations; and how, under suitable constraints, to generate the points from the lines alone. The mathematical theory is then applied to aesthetics, using set cographs to describe the experience of a person enjoying a picture (Mu Qi), poem (Dickinson), play (Shakespeare), …
Seeing Mathematics And Seeing Mathematicians, Mark Huber, Gizem Karaali
Seeing Mathematics And Seeing Mathematicians, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.