The 50 most-cited articles in The Mathematics Enthusiast, 2022

Have you ever struck up a conversation with a stranger in a coffee shop and been surprised to learn that you were born in the same week, but in different years? Or maybe you have that one annoying friend who always seems to win raffles and lotteries even though you never win anything, and you just can’t figure out how they always get so lucky? Or perhaps, just for fun, you visited a psychic one day, and you were shocked by how much they were able to tell you about yourself. In The Improbability Principle, David J. Hand explains that, despite how unlikely these and other events may seem, they are in fact much more probable than we may think.

With its bright yellow cover and its ominous title, this book attracts attention. The subtitle, “How big data increases inequality and threatens democracy” signals very strongly that the “math” in question in the title is primarily that which relates to the statistical and computational means of collecting, analysing and using data. For some readers, the title might be surprising, because it challenges the typical understanding of mathematics as an objective and value-neutral discipline. Worse, it claims that mathematics is significantly involved in creating inequality and compromising democracy. If it is true, then the answer to the perennial student question, “when am I ever going to use this?” has now become, “when will it use you?”

At the outset, Dr. Hannah Fry’s book Hello World: Being Human in the Age of Algorithms is an engaging survey of how algorithms are being used in modern life. The book is written for a general audience with a focus on concepts and principles. As such, the narrative does not dig deeply into the details of any particular topic but instead offers a snapshot of how algorithms reside within a variety of contexts in the modern world. Through relatable examples, Dr. Fry builds a narrative that explains how algorithms are used as tools to predict, influence, augment, and mimic human behavior. Woven throughout the narrative are stories that reveal the power and pitfalls of algorithms. We learn about algorithms used by advertisers, data brokers, judges, chess masters, and healthcare workers. Along the way, Dr. Fry reveals how algorithms are being used to identify cancerous cells, build driverless vehicles, influence an online behavior, and create art. After reading the book, I was left asking practical questions such as, did that recent grocery store advertisement arrive by chance or is it…

Considerable research has been conducted on the constraints to recreation that traditionally underrepresented communities in the United States confront; however, there remains a lack of synthesis concerning constraints to visitation to federally designated wilderness areas. This scoping review of the current available literature seeks to reveal what constraints have been identified to visitation to federally designated wilderness in the United States and what groups are experiencing them. Constraints identified include discomfort and safety concerns specific to wilderness settings, cultural expectations, and issues of time, cost, and access. Additionally, constraints are explored with reference to the influence of management actions focused on preserving wilderness character, and directions of future research are discussed.

As statistics educators, our overarching goal is to instill in our students an appreciation for the stories that can be told from data. Storytelling, however, is never straightforward. Surely, we can remember times where we have been in the thrall of an experienced raconteur with a penchant to up-sell narratives with a healthy sprinkling of imagination and exaggeration in order to pique the interest of their readers or listeners. Given we are living in a “post-truth” world, where “alternative facts” and “fake news” permeate the airwaves, equipping students with the skills to distinguish fact from fiction is more important than ever (Ridgway, Nicholson, & Stern, 2017).

Broadly speaking, school mathematics has been placed in a double bind. From state policymakers, there is the culmination of decades of increasing requirements to teach more mathematics, which now often means a requirement of four full years of mathematics in high school or every student progressing through at least a second course in algebra (Remillard et al., 2017). From the mathematics education community, there is growing consensus around the call to ban tracking (e.g., National Council of Teachers of Mathematics, 2018; National Council of Supervisors of Mathematics & TODOS, 2016) because of the known harms of identifying and segregating students based on mathematical “ability.” But tracking is one of the primary strategies that schools (and communities) conceive of when trying to meet the demand for all students to complete more mathematics courses.

Agenda and meeting minutes from the December 14, 2022 meeting of the University of Montana Staff Senate.

Student newspaper of the University of Montana, Missoula.

Student newspaper of the University of Montana, Missoula.

GLI Study Abroad Mixer -- Franke GLI Internship: Social Media and Communications -- Mansfield Dialogues: "The Path to Delivering Real Solutions: A Conversation with Senator Bill Cassidy, M.D." -- English Language Institute: Volunteers Needed: Virtual Conversation Partners -- Holiday Helpers!

Old hand cut Japanese stencil in frame. Stencil depicts two flowers with buds and a vine pattern. Brown paper stencil. "An Original hand cut Japanese stencil used in the process of applying design to Kimono fabric. From the Tom and Frances Blakemore Collection of Stencils, costumes, and textiles shown on tour at leading museums. The accompanying book, Japanese Design through Textile Patterns explains the process and the symbolism expressed in the designs."

GLI Study Abroad Mixer -- Franke GLI Internship: Social Media and Communications -- Baucus Leaders: DC, Climate Scholars, and Baucus Leaders Montana -- Happy Thanksgiving

Student newspaper of the University of Montana, Missoula.

In the Blackfeet Tribal Court of Appeals, the Court clarified that when the Court, in review of an appellate case, directs parties to submit a detailed summary of the status of the case, within a limited time period, and the partied do not provide that status update, the Court will dismiss that case, without prejudice.

GLI Coffee Talk: Inequality and Human Rights -- Study Abroad Application Deadlines -- International Education Week -- Careers in Humanitarian Organizations -- Mansfield Dialogues: "U.S.-Taiwan Relations: Past, Present, and Future" -- Can the Cats Food Drive

Student newspaper of the University of Montana, Missoula.

Agenda and minutes from the November 9, 2022 meeting of the Associated Students of the University of Montana (ASUM). The following resolutions were discussed: SB06-22/23-Resolution Generally Amending Article IV of the Bylaws Note: Article IV pertains to the processes and purview of the Interview Committee

Congratulations to Franke GLI student Sophia Rodriguez -- Mansfield Dialogues: "Can Civility Prevail in the Montana State Legislature" -- "The Dharma of Justice in the Sanskrit Epics: Debates on Gender, Varna & Species" with Dr. Ruth Vanita -- GLI Coffee Talk: Inequality and Human Rights -- Study Abroad Application Deadlines -- Wilderness and Civilization Program

“Nil”, “Nunca”, “Nada”, “Nil”, “Nothing”, “Zero”. Sounds of a multilingual class of mathematics, perhaps. No, it is the sounds around the family table card game as we all declare the number of tricks that we would like to take in a card game called Wizard. The speaker is telling the scorekeeper that they would not like to take any tricks. They would like to take “zero” tricks as if they could gather the zero cards. We all know that we do not want any tricks and we do our best not to take any if we declare that we want zero tricks.

Indigenous scholar Richard van Camp of the Dogrib Nation shares how “a great story reminds us of what it means to be human” (van Camp in Galloway, 2020). Keith Devlin’s book, Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World, does just that – reminding us what it means to be human, but in this case through mathematics. In Finding Fibonacci, Devlin shares his story and journey to learn more about mathematician Leonardo Pisano (Fibonacci) and Leonardo’s manuscript Liber Abbaci (Book of Calculation), one of the first manuscripts written on practical arithmetic in Western Europe, and what Devlin argues “would change the world” (p. 17).

In the 2003 Pixar animation Finding Nemo, a clownfish named Marlin is an overprotective father, and for good reason: he has recently gone through the trauma of losing both his wife and all their fertilized eggs save one. Nemo is his only remaining offspring, a son. On Nemo’s first day of school, he gets caught in a fishing net and is taken far away. Marlin spends the rest of the movie looking for Nemo. He gets to know a variety characters in his search, some providing comic relief, some providing leads. But in each interaction Marlin learns a more about himself, in particular, that he is too fearful and too protective. For some, Finding Nemo is about Nemo; for others, it is about Marlin. That is, instead of Marlin providing a subplot, he provides the central story. Finding Nemo is about Marlin’s personal journey of overcoming the trauma of losing his wife and almost-children. To give even more of a twist to a seemingly benign movie, there is a theory bouncing around on the Internet that Marlin imagines Nemo and everything that happens in the movie is only imagined. That is, he makes…

In the book Birth of a Theorem: A Mathematical Adventure, Cédric Villani paints a portrait of himself, from the (dare I say) obsessed mathematician who works until the wee hours of the night, to the ordinary citizen, enjoying an impressive variety of music, to the slightly odd man sporting an ornamental spider daily. From Lyon to Paris, through the despair of not being able to eat quality cheese, Villani takes us on a journey, revisiting the path that led him to win the Fields Medal. He takes us back in time and punctuates his account with anecdotes or stories of mathematicians. We recognize well-known names (Nash, Poincaré, etc.) through stories that are less well-known. He lets us in his adventure, and we jump in with both feet (e.g., see Figure 1).

Bellos’s (2010) Grapes of Math is not a book about the history of mathematics, although he includes maths histories. It is not a math textbook, although he leads the reader through a variety of mathematical concepts. It does not follow the life of a great mathematician, scientist, or philosopher, although they make their presence known throughout the book. Rather, Grapes of Math it lies at the intersection of these concepts. It is a book of stories, stories of mathematical ideas and the cultures that informed their development. And Bellos is a gifted storyteller.

Daniel Tammet’s Thinking in Numbers: On Life, Love, Meaning, and Math (2012) is composed of 25 essays that share his views and experiences of mathematics, connections he makes between mathematics and poetry, and biographical stories. He is a writer, a linguist and a tutor who was born in London, England and lives in Paris, France.

From cover to cover, Ben Orlin’s Math with Bad Drawings is modest. By this we do not mean to suggest that the book underwhelms in its contributions to the popularization of mathematics. In fact, we take the exact opposite as true, and the commendations from prominent popularizers of mathematics such as Steven Strogatz, Hannah Fry, and John Urschel that are printed on the book jacket provide us ample evidence. By modest we mean the book cloaks its potent insights on mathematics and mathematics education in self-effacement. Of course, this modesty is entirely intentional, and employed by Orlin with pinpoint precision. As a result of his winsome trope, which developed from its early days on his blog, he manages to take a subject ignored by a large subsection of the population and unfurl it through his unique mixture of self-proclaimed “bad” drawings, quippy narrative, and acute insight into the intersections of mathematics, mathematics teaching, and society.

I found that Loving + Hating Mathematics: Challenging the Myths of Mathematical Life ended up being an interesting choice for me to write a review on from the perspective of a mathematics educator. My research has focused on the perceptions that individuals bring about mathematics to a teacher education program. I have found it interesting that every year the majority of the future teachers either focus on the negatives of mathematics or the rules and formulas that they see as the foundation (Holm, 2018). Rarely am I told about the beauty and elegance of the subject that seems to drive the mathematicians to live and breathe this field. For this review, I have chosen to focus on how the teaching of mathematics could be conceptualized in a way that allows the learners to experience what seems to drive the mathematicians whose stories are told in this book. Through the words of Hersh and John-Steiner as well as my observations of the book, I will also discuss some of the inequities that are a struggle in the field of mathematics as a whole in order to ponder why there seems to be a…

A feeling emerges from reading McGrayne’s book expressed as a paraphrase of a verse from Hamlet: There are more things behind Bayes’ theorem, Horatio, than dreamt of in your philosophy. The book tells a story of the birth and survival of an idea around which social enterprises, personal odysseys, and human passions are masterfully woven by the author. The book has 17 chapters distributed in five parts and two annexes. These parts reveal a narrative structure worthy of Propp: The hero of the story (Bayes’ theorem) is born and raised normally but rejected later. It is forced to act in secret but returns to the light and is submitted to several tests. The hero emerges triumphant from all of them. The above is just an outline of a complex but accessible chronicle that includes many brilliant and fascinating figures and extraordinary situations. We recommend the following three reviews that undoubtedly motivate you to immerse yourself in reading the book: Paulos (2011), Wainer & Savage (2012) and McGrayne (2015).

The goal of this review is to explore The Art of Statistics using a mathematics education perspective and to illuminate the ways that it can be used as a resource in math instruction by students, preservice teachers, and math educators in general. I take the approach that the teaching and learning of mathematics is a part of the complex system comprising of many “interacting agents” (Davis, 2018, p. 77), such as students, teacher, curricula, and technology. The content of the book is a potential resource in the classroom, a potential part of the complex network. Echoing Jorge Louis Borges’ claim that a book is not an isolated entity, but that it contains infinite narratives brought by readers (Borges, 2007), I would like to examine the potential role of the content of this book in the learning ecosystem, including how the elements of this book could be used, and repurposed to fit our pedagogical goals.

If anything, it was a few years of teaching grade eight home economics classes that made the situation very clear to me. There were the spectacular cooking disasters, like the group that while making a chocolate cake from scratch somehow switched the measurements for the salt and the sugar. Not only did they end up with a product that even a growing grade eight boy wouldn’t eat, but the cake actually erupted in the oven while it was baking. But there were also the smaller, more telling moments. I’d see a group from across the room that had come to a standstill. I’d approach and discover that kids who had been acing their math tests all year long found themselves unable to agree on the result of halving 1¾ cups of flour and were now all staring at their measuring cups in silence. Put a fraction calculation out of context on a piece of paper, these students were golden; faced with actual ingredients and tools under the flickering fluorescent lights of our home economics lab, they were flummoxed. While the Great Cake Explosion was a once-in-acareer lowlight (although it’s a good story,…

In “Love and Math” the author intertwines his personal experiences as a student of mathematics and as a research mathematician with an exposition of modern mathematics, focusing on its elegance and beauty. Much is said in previous reviews (e.g., Grosholz, 2015) of this New York Times bestseller and winner of the Euler Book Prize from the Mathematical Association of America. All praise the author for his fascinating narratives in which he reveals the joy of intellectual discovery and provides a passionate account of exciting ideas of modern mathematics. There is no need in repetition, so this review is rather personal. I start with my personal encounters with “Love and Math” and then share what I learned from the book as a teacher and mathematics educator, focusing on issues that are often overlooked in acclaimed accounts of Frenkel’s mathematical expositions.

How Not to Be Wrong is a wonderful and entertaining romp through a field of intriguing and thought-provoking anecdotes and social conundrums in which mathematical thinking and mathematics are revealed in all their messiness and power. While reading Jordan Ellenberg’s weave of stories for the first time, I found myself retelling them to as many individuals in my social circles as I could. Though the intent of the book is quite serious, [its goal is to show that mathematical thinking is accessible and useful to those who have not mastered complex mathematics, that mathematical thinking can lead to profound insights about the world around us, and perhaps, to reify mathematics as a foundation for truth] I found its tone light and engaging, and I really enjoyed retelling the stories as they sparked thoughtful conversations amongst friends and family. Talking about slime mold decision making helped stave off the feelings of dread and the awareness of crumbling social foundations around us. Ellenberg makes the case for the power of mathematical thinking to open a variety of phenomena to…

In the field of probability instruction, much has been written about the increasingly important role of uncertainty and probability in our everyday lives. This work similarly highlights the key role that probability plays in a growing number of professional areas.

The book The Signal and The Noise; Why So Many Predictions Fail - But Some Don’t is, as its name implies, a book about predictions in a wide range of fields including weather, sports-betting, elections, and economic predictions. Rather than focus solely on the mathematics of prediction in each field, it places just as much emphasis on the role of people that make predictions. Thus, the book is about the human process of making predictions, the many factors that affect their accuracy, and how these factors interact with each other. Silver’s (2012) approach highlights that because the person making predictions is an indispensable part of the prediction process, the fallibility of people leads to the fallibility of predictions. He takes great care to describe approaches to mitigating these biases and describes them thoroughly in the context of prediction.

In addition to the title’s cheeky play on the famous words God does not play dice with the universe (famously attributed to Einstein), Ian Stewart’s Do Dice Play God is a fascinating tour de force that embeds the discipline of statistics and probability within an informative and insightful socio-historical account of its development. Stewart characterizes the science of statistics and probability as the mathematical quantification of uncertainty—a very useful and productive way to think about a discipline with a reputation for being notoriously difficult and often counter-intuitive for people to understand. But his account goes beyond merely providing such an apt characterization of the discipline; he follows through by providing penetrating and clearly presented examples and analyses of the mathematics at play throughout the book’s 18 chapters. One cannot help but think that Stewart—a renowned mathematician and retired mathematics professor—is a gifted teacher! All of this is presented in an informal conversational style, infused with occasional humor, and usually in sufficient…

The biggest problem I have with reviewing The Black Swan: The Impact of the Highly Improbable (Taleb, 2010) is deciding from what perspective to write. There are a number of lenses through which I considered this work in relation to mathematics education: the Associate Professor, always searching for new resources for mathematics education classes; the teacher, always looking for new messages and ways of speaking to students (including pre-service teachers) about what mathematics is, what purposes it serves, and what limitations it inherently carries; the learner-teacher, always looking for a greater depth of understanding of the mathematics we are charged with teaching; the curriculum and pedagogy researcher and theorist, always looking for new ideas that might be applied to or impact education within and beyond the mathematics classroom; and the learning ally, always critiquing what is included or not for diversity of voice and ways of knowing. In the review that follows, I will speak to what I “saw” in looking through these various lenses.

I have always enjoyed games, especially when incorporated into the classroom. I can still remember the game my fifth-grade teachers had us play to explore colonizing a new world. One of the most impactful games I’ve played is SET®, which has become a go-to for mathematics teachers as a means for exploring geometry, combinatorics, probability, statistics, and vector spaces (Larson Quinn et al., 1999; Waddell Jr., 2017). I first learned the game in the seventh grade and continue to play the game today. How many sets do you see in Figure 1?

I hate calculus. Which is a lie: I secretly love it. I enjoy teaching it, drawing intricate diagrams of where the definition of the derivative comes from, stumping my students on convoluted trigonometric integrals with solutions dependent on partial fractions, hammering mnemonics for the derivative rules—all the joys of teaching calculus. And I enjoyed learning it, too. Well, not failing it the first time, but after that. I long for my undergraduate time spent in the reading room of Rutherford South re-arranging integrals à la Fubini’s Theorem, the massive lecture halls of anxious engineering students copying every stroke of chalk from the front, and the arithmetic errors costing me scores of marks from my tests. A calculus course presents the liturgy of undergraduate mathematics: students and instructors alike gather, willfully or otherwise, to engage in the ritualistic celebration of the mysteries of the infinite.

Dr. Francis Su uses an autobiography (or a dual autobiography) to discuss an issue in mathematics: it is often non-flourishing. When crafting this Euler Book Prize winner, Su and his co-author, Christopher Jackson, drew on their own personal experiences to educate and inspire readers to want to do (and teach) mathematics.

A common, widespread view on the field of mathematics entails that “mathematics is dry as dust [and] as exciting as a telephone book” (Davis & Hersh, 1981, p. 169), and that the professional mathematician is merely “a kind of calculator” (Krull, 1987, p. 48). Even more provocatively, mathematics is conceived by many of the general public as a “deadend” discipline in which all questions have already been answered, where nothing worthwhile is left for further investigation (Movshovitz-Hadar, 2008). However, mathematics is an active, growing, open-ended field – a fact which can be illustrated, amongst others, by the exponential growth in the number of new articles that are published per year (Dunne, 2019). Furthermore, the common perception of the subject by the people who are working within the field – the mathematicians themselves – is that mathematical work is creative in nature and often driven by its intrinsic aesthetic dimension (e.g., Brinkmann & Sriraman, 2009; Gadanidis, 2012; Sinclair, 2004).

Mathematics – the word alone can strike fear into the hearts of students, parents, and educators alike. This emotional response seems to be not only acceptable, but almost expected and, should you differ, then you are considered either a genius or a bit insane. “How could someone like math?”, they think.

Paul Lockhart is a former computer programmer, elementary teacher, research mathematician, university professor, and somewhat more recently a K-12 mathematics teacher and author. Lockhart’s first written composition appeared two decades ago in 2002. All of 25 pages, his essay A Mathematician's Lament began like this: A musician wakes from a terrible nightmare. In this dream he finds himself in a society where music education has been made mandatory ... Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made—all without the advice or participation of a single working musician or composer.” (p. 1)

I am a mathematics educator working in a Faculty of Education, at a mid-sized university. I have degrees in mathematics, teaching, and education related to the teaching and learning of mathematics. I also have twenty years of experience with school boards as a secondary school mathematics teacher and department head. It is from these experiences, knowledge, and professional practice that I approached this book review—from a place of how I see the world around me and work to understand it. I love thinking about and working to understand teachers’ beliefs, problem solving, and professional learning in problem solving contexts, and thus my secondary school teacher ‘self’, or identity, is quite interconnected to my mathematics education researcher ‘self, or identity.

Framed calligraphy called "Stars" by Seiran Yanagida. One of the foremost Japanese calligraphers. His works hang at museums of Hawaii and in Congressional Library in Washington D.C. among places. Black ink on white paper. Framed in a blue wood frame with a white matt.

Student newspaper of the University of Montana, Missoula.

Ceramic teacup. The base clay is a brown red in color with numerous inclusions. The overglaze is a mottled cream and grey coloring with pink undertones. The cup flares out at the base then narrows before flaring to the rim again.

Karatsu-Yaki Sake Cup (pottery). Ceramic sake cup made from a beige clay. Clear gloss overglaze and a brown grass image on the front of the cup. Gold sticker with black characters on it on the back of the cup.

Congratulations to GLI and UM alumnus Nick Mills -- Beyond the Classroom Experience proposals deadline and GLI Scholarship applications due -- 17th Annual Diversity Symposium -- GLI Coffee Talk: Inequality and Human Rights

This week’s episode is the October edition of Incentives & Instincts, a recurring series in which Justin speaks with economist and friend, Bryce Ward, about some of the broader problems facing our society. It is election season here in Montana and across the country. To navigate some big questions, Justin asks Bryce and guest Rob Saldin, University of Montana political science professor, if our democracy is really at risk. After Rob says yes, Justin goes on to ask how we can solve our problems, what the importance of civics education is and how to get more people to participate in democracy.