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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Book Review: Algebra The Beautiful: An Ode To Math’S Least-Loved Subject By G. Arnell Williams, Judith V. Grabiner
Book Review: Algebra The Beautiful: An Ode To Math’S Least-Loved Subject By G. Arnell Williams, Judith V. Grabiner
Journal of Humanistic Mathematics
In his book Algebra the Beautiful, G. Darnell Williams has undertaken a challenging job – to show the importance, deep structure, intellectual connections, and sheer beauty of classroom algebra. This review describes some of the questions the book raises, the historical and cultural context it provides, and the intellectual apparatus it deploys.
Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur
Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur
Journal of Humanistic Mathematics
Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …
The Nothing That Really Matters, Szilárd Svitek
The Nothing That Really Matters, Szilárd Svitek
Journal of Humanistic Mathematics
Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, that of natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state …
Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos
Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos
Journal of Humanistic Mathematics
We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …
The Fractal Geometry Of Mathematics Classrooms: Navigating Classroom Environments In Factory-Model Schools, Cacey L. Wells
The Fractal Geometry Of Mathematics Classrooms: Navigating Classroom Environments In Factory-Model Schools, Cacey L. Wells
Journal of Humanistic Mathematics
Mathematics education has a diverse and complex history. After decades of national reform, mathematics classrooms today are still in desperate need of change. This article examines the current state of factory-model schooling through the lens of Mandelbrot's The Fractal Geometry of Nature in order to rethink pedagogic practices.
The Problem Of Words: Learning To Teach Mathematics When Numbers And Languages Mix, Gladys Krause
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.
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 …
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 …
Got Books? A Story Of Creative Mathematics Children's Book Writing, Maria G. Fung, Pamela Hollander
Got Books? A Story Of Creative Mathematics Children's Book Writing, Maria G. Fung, Pamela Hollander
Journal of Humanistic Mathematics
In this report, we describe a joint project between a mathematics content course and literacy methods course for pre-service elementary teachers that resulted in our students writing children's mathematically themed books. Out report then focuses first on the creative process of combining mathematical knowledge and ideas for teaching with the craft of writing for children, and second on the creative connection between mathematics and literacy education at the elementary school level.
On "Animals", Ql Converts, And Transfer - An Interview, Gizem Karaali, H. L. Vacher
On "Animals", Ql Converts, And Transfer - An Interview, Gizem Karaali, H. L. Vacher
Journal of Humanistic Mathematics
In March 2017, Gizem Karaali interviewed Len Vacher, the editor in chief of Numeracy, the flagship journal of the National Numeracy Network. This is the extended transcript of this conversation, which ranges from quantitative literacy to computational geology, from transfer of learned content and skills to interdisciplinary collaboration.
Students Studying Students And Reasoning About Reasoning: A Qualitative Analysis, Salvatore J. Petrilli, Grant Clark, Nicholas Demarco, Jack Esposito, Brianne Giuliano, Sara Greiss, Emily Harris, Alessia Merritts, Kyle Murray, Mateusz Piekut, Brian Seidl, Scott Shannon, Nicole Silva, Christina Sullivan, Brittany Willoughby, Yile Zhou
Students Studying Students And Reasoning About Reasoning: A Qualitative Analysis, Salvatore J. Petrilli, Grant Clark, Nicholas Demarco, Jack Esposito, Brianne Giuliano, Sara Greiss, Emily Harris, Alessia Merritts, Kyle Murray, Mateusz Piekut, Brian Seidl, Scott Shannon, Nicole Silva, Christina Sullivan, Brittany Willoughby, Yile Zhou
Journal of Humanistic Mathematics
In this work, a faculty member takes a journey along with students as they enhance their understanding of how people solve mathematical problems through a mainly qualitative statistical project. Student authors of this paper registered for a problem solving seminar led by the faculty author, and then created and analyzed self-built assessment tools to explore problem solving techniques. Here we share our findings and recommendations, which we hope will inspire others to explore novel pedagogical techniques in the teaching of mathematical problem solving. We incorporate into our presentation ur voices, reflecting on how we and others solve problems.
Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge
Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge
Journal of Humanistic Mathematics
Parents and educators have powerful opportunities to introduce children to big mathematical ideas, when those ideas become necessary. Children are capable and curious. They don’t need to be sheltered from big mathematical ideas. Bring out mathematical ideas when kids are ready, or when they are needed. This article describes one such instance, when I helped my six-year-old son move beyond zero in the negative direction when subtracting.
Visual Teaching Of Geometry And The Origins Of 20th Century Abstract Art, Stephen Luecking
Visual Teaching Of Geometry And The Origins Of 20th Century Abstract Art, Stephen Luecking
Journal of Humanistic Mathematics
As a group, the artists educated near the turn of the 19th and 20th centuries possessed greater mathematical knowledge than expected of artists today, especially regarding constructive skills in Euclidean geometry. Educational theory of the time stressed such skills for students in general, who needed these to enter the workplace of the time. Mathematics teaching then stressed the use of manipulatives, i.e., visual and interactive aids thought to better fix the student’s acquisition of mathematical skills. This visual training, especially in geometry, significantly affected the early development of abstraction in art. This paper presents examples of this visual …
Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily Cilli-Turner, Gail Tang, Gulden Karakok, Houssein El Turkey
Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily Cilli-Turner, Gail Tang, Gulden Karakok, Houssein El Turkey
Journal of Humanistic Mathematics
The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Creativity in Mathematics. Please send your abstract submissions via email to the guest editors by March 1, 2019. Initial submission of complete manuscripts is due August 1, 2019. The issue is currently scheduled to appear in July 2020.
Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois
Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois
Journal of Humanistic Mathematics
Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry …
The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli
The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli
Journal of Humanistic Mathematics
In this article I describe Adelphi University's Mathematics Orientation Seminar, a new course that was introduced into the mathematics major to help students find their passion in mathematics and to strengthen the educational community within our department. I discuss quantitative and qualitative results of surveys among students in the Mathematics Orientation Seminar in Fall 2016 and Fall 2017, which suggest that this might be a useful course for other institutions to utilize within any major. Finally, I explore faculty perspectives and describe what I believe to be the final version of this course.
College Dropout To College Professor, Deborah L. Gochenaur, Rose I. Verbos
College Dropout To College Professor, Deborah L. Gochenaur, Rose I. Verbos
Journal of Humanistic Mathematics
Being a college dropout wasn’t something to be proud of; it just happened. Life doesn’t always turn out the way we want or expect. Yet, it is often how we deal with defeat that defines us – figuring out when to lick our wounds and when to come back fighting. It took a few years to redefine my dream, start a family, and seem to move forward, but the ache for more was always in the back of my mind. Could I succeed at something at which I had already failed? Going back to school at a community college at …
Ways Of Relating To The Mathematics Of The Past, Michael N. Fried
Ways Of Relating To The Mathematics Of The Past, Michael N. Fried
Journal of Humanistic Mathematics
Historians of mathematics, by definition, look at mathematics of the past. But mathematicians, too, often look at mathematics of the past; mathematicians of the past themselves often looked very closely at mathematics of their own past. Is their relationship to the past the same as that of the historians? Is every view of the past an historical view? Indeed, is every historical view historical in the same way? Or is it possible that there are different kinds of relationships to the mathematics of the past? This paper will suggest that there are in fact a variety of such relationships. It …
Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan
Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan
Journal of Humanistic Mathematics
This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.
What If?: Mathematics, Creative Writing, And Play, Emily Clader
What If?: Mathematics, Creative Writing, And Play, Emily Clader
Journal of Humanistic Mathematics
Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.
The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker
The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker
Journal of Humanistic Mathematics
In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
Journal of Humanistic Mathematics
While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …
A Mathematician Weighs In On The Evolution Debate, Kris H. Green
A Mathematician Weighs In On The Evolution Debate, Kris H. Green
Journal of Humanistic Mathematics
There are a variety of reasons underlying the lack of public acceptance for the theory of evolution in the United States. An overlooked cause is related to problems with the mathematics curriculum in the K-12 setting. In this essay, we examine this relationship and propose changes to the mathematics curriculum that could improve mathematical thinking while also providing a basis for understanding theories, like evolution, that are poorly understood.