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In peer instruction [12], students engage with core course concepts and then explain those concepts to one another in small groups. Unlike in lecture format, peer instruction involves every student in the class. In Spring 2019, the first author began using a modified version of peer instruction in Calculus III classes. He started each class by discussing important Calculus III concepts from three standpoints (the formula, the geometry behind the formula, and the physics behind the formula). During the last 20 minutes of each 50-minute class session, he polled the students using questions in the "Goldilocks Zone" -- not too hard and not too easy, but just right for Calculus III students. These questions ignited student-to-student discussions. Students' attendance and achievement have improved. The paper also describes how peer instruction has influenced the first author's own instructional practices. [ABSTRACT FROM AUTHOR]

When our students enter the workforce, be it in academia or in business, industry, government, they will be forced to make decisions about various ethical dilemmas. Once in a while, the scandalous stories like that of Enron, the three German auto-makers' diesel fuel pact, and the Equifax data breach make the headlines. However, employees at every workplace are faced with small to large-scale ethical situations almost daily. In our majors' future careers, a manager can be using an inappropriate graphic to display data to make the numbers look better, or the data collection processes used in a large public policy project can be completely skewed to support one conclusion that the client desires vs. another more reasonable conclusion. How well are our students prepared for dealing with these dilemmas? Can they even recognize an ethical dilemma? Do we provide them with the tools to be more vigilant about these situations and to make the appropriate decisions when the difficult choices have to be made? In this paper, I would like to invite us all to think about possible ways we can incorporate ethical decision making frameworks and case studies into our classes, particularly if our university does not have an ethics requirement for all majors. Even if there is a general ethics requirement, it is especially important for our students to be exposed to scenarios that are more relevant to the use of mathematics in the workforce since a general ethics course will not necessarily prepare them well for identifying subtle abuses of data processing and mathematical modeling. [ABSTRACT FROM AUTHOR]

Creativity is a broad phenomenon that scholars have interpreted in a multitude of ways. We notice that a majority of the views describe creativity as something innate. This paper aims to verge from this perspective and explore creativity in terms of the constant mutual interaction of a person and their environment. Using the theoretical framework, enactivism, and the notion of emergence, we investigate the creative processes involved in musical improvisations of south In- dian classical or Carnatic music and mathematical proof generation. Interview excerpts from professional Carnatic musicians and research mathematicians on their respective creative processes during musical improvisation and proof gen- eration are analyzed. This study gives a perspective to think about creativity, with an emphasis on emergence. This paper has been partly informed by self- reections on musical improvisations and mathematical proof generation by the first author, who is a performing Carnatic vocalist and a mathematician. [ABSTRACT FROM AUTHOR]

In this paper, I raise an issue often neglected in Project Based Learning (PBL) literature. What academic benefits, if any, does the teacher or the student gain by adopting PBL pedagogy in college? I argue that PBL by its structure yields little academic benefit for the teacher or the students, and this could affect motivation as well. I present some examples from my personal teaching experience in mathematics. And thus, as I explain, a more "traditional" project-based approach could be better for both teacher and students. [ABSTRACT FROM AUTHOR]

In teaching algebra, extra-mathematical word problems can bridge the gap between questions about abstract numbers and questions about everyday life. Thus, more than other aspects of elementary algebra, we would expect word problems to have changed in the recent past. This paper documents the findings of a collective research project that examined the content of such word problems over the past century. Alongside amusing and provocative examples, this paper shows how students can participate in exploratory research with primary sources from the history of mathematics. [ABSTRACT FROM AUTHOR]

In this paper we report our findings of college students' images of mathematicians and we reflect on different methodologies used to assess this information. The study reported in this paper was conducted in two stages. During the first stage, we asked 179 college students to "draw a mathematician" and also asked them to list five characteristics and five careers for a mathematician. In the second stage of the study, we conducted four focus group interviews with a total of twelve college students. During the focus group interviews, we showed the students 16 photos of real people and asked them to determine which they think are mathematicians and which are not. We found that college students do hold certain stereotypic images of mathematicians and that different perspectives arose based on the different research methodologies. In this paper, we argue for the need to go beyond relying solely on the "draw a mathematician" test and we conclude with a discussion on the implications that stereotypic images of mathematicians have on the mathematical workforce. [ABSTRACT FROM AUTHOR]

In this paper we discuss the happiness of preservice elementary teachers (PSTs). 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 understanding. [ABSTRACT FROM AUTHOR]

This paper describes a methodology for analyzing X chromosome data to establish biogeographical contributions to the author’s X chromosome. We present an exposition of how Hidden Markov Modeling (HMM) can be used as a black box for ancestry analysis and focus on a set of conditions that are not universal but fairly common. The first condition is that the ancestral populations are drawn from regions that have had very little or no contact with each other since prehistoric times. The second condition is that the number of possible ancestral populations is small. In this analysis, we assume that the ancestral populations are Native North American, Northwestern European, and West African. We compare the result of our analysis with the analyses carried out by the companies 23andMe and deCODEme for the same data. Finally, we point to a mechanism for reducing noise by adjusting the data before applying HMM. [ABSTRACT FROM AUTHOR]

Predictive policing has its roots in crime hotspot modeling. In this paper we give an example of what goes into mathematical crime hotspot modeling and show that the modeling assumptions perpetuate systemic racism in policing. The goal of this paper is to raise objections to this field of research, not on its mathematical merit, but on the scope of the problem formation. We do not make any suggestions about how to incorporate race into predictive policing models in order to make them less biased. [ABSTRACT FROM AUTHOR]

On May 12th, 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, and military. In this paper we pay homage to Ubiratan D’Ambrosio, sharing our thoughts related to his personal, professional, and academic life. [ABSTRACT FROM AUTHOR]

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 our Math Games Seminar learning community, from its origins in 2016, to its organization and to its impact on our students through the years. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model. [ABSTRACT FROM AUTHOR]

We present some aspects of the genesis of a geometric construction, which can be carried out with compass and straightedge, from the original idea to the published version (Fern'andez Gonz'alez 2016). The Midpoint Path Construction makes it possible to multiply the length of a line segment by a rational number between 0 and 1 by constructing only midpoints and a straight line. In the form of an interview, we explore the context and narrative behind the discovery, with first-hand insights by its author. Finally, we discuss some general aspects of this case study in the context of philosophy of mathematical practice. [ABSTRACT FROM AUTHOR]

As mathematics teachers, we hope our students will approach problems with a spirit of creativity. One way to both model and encourage this spirit | and, at the same time, to keep ourselves from getting bored | is through creative ap- proaches to problem design. In this paper, we discuss TACTivities, mathematical activities with a tactile component, as a creative outlet for those of us who teach mathematics, and as a resource for stimulating creative thinking in our students. We use examples, such as our derivative fridge magnets TACTivity, to illustrate the main ideas. We emphasize that TACTivities can be engaging, to teachers and learners alike, at any level of mathematics, by including examples from dif- ferent mathematics courses (calculus and mathematics for elementary teachers). As an example, our derivative fridge magnets have moving pieces of words that look like small refrigerator magnets. These small pieces can be combined to make true mathematical statements, of the form d=dx (some function) = some other function. There was creativity involved in the creation of these magnets, as the mathematics had to be challenging enough not to bore students yet have an easy entry for students to be successful. The students working with the magnets can use their creativity along with their mathematical knowledge while learning and/or reviewing a mathematical concept|in this case derivatives. We will ex- pand on the creative side of the creation and implementation of TACTivities in this paper. Note that our definition of tactile only means moving pieces (usually pieces of paper), as this is different than work from others that involves tactile props such as pipe cleaners, yarn, Spirographs, building blocks, and so on. This other work is invaluable, and we use props like these ourselves at times, but we believe that our TACTivities add a different dimension to tactile learning. [ABSTRACT FROM AUTHOR]

Although much creativity research has suggested that creativity is inuenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in the mathematics classroom, with fallibilist and social constructivist perspectives arguably being most conducive for conceiving of creativity as a type of action for all students. Thus, this paper proposes a framework of creative mathematical action that is based in these epistemologies and explains key aspects of the framework by drawing connections between it and research in the field of creativity. [ABSTRACT FROM AUTHOR]

In this paper we contribute an alternative conceptualization of creativity by high- lighting movement as creating spatial and temporal dimensions that are impor- tant to make sense of creativity in children mathematical thinking. Using data from an international collaboration between two teaching-research teams from the United States and Chile, we trace how children mobilized their social bodies, materials, tools, images, metaphors, languages, and improvisations in order to make sense of the concept of fractions. Based on these findings we offer a num- ber of discussion points that highlight the importance of creating these kinds of learning spaces, the role of tasks in promoting different kinds of movement, and implications for thinking about alternative conceptualization and operationaliza- tion of creativity as responding to issues of cultural and linguistic diversity and inclusivity. [ABSTRACT FROM AUTHOR]

In March 2017, Gizem Karaali interviewed Len Vacher, at the time the lead editor of Numeracy, the flagship journal of the National Numeracy Network. What follows 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. The interview was first published in Shifting Contexts Stable Core: Advancing Quantitative Literacy in Higher Education, edited by Luke Tunstall, Gizem Karaali, and Victor Piercey, and published in 2019 as MAA Notes Volume 88. It is reprinted here with the permission of the publisher. [ABSTRACT FROM AUTHOR]

This paper takes a mathematical analysis technique derived from the Interrogator's Fallacy (in a legal context), expands upon it to identify a set of three interrelated probabilistic tools with wide applicability, and demonstrates their ability to assess hypothesis-evidence relationships associated with important problems. [ABSTRACT FROM AUTHOR]

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 [16, 19], 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. It is argued that with a better understanding of the temporal dimension of mathematical beauty, educational experiences with mathematics can be designed to captivate attention and nurture interest and positive disposition by students toward mathematics. [ABSTRACT FROM AUTHOR]

This paper concerns the relation between a proof's beauty and its explanatory power -- that is, its capacity to go beyond proving a given theorem to explaining why that theorem holds. Explanatory power and beauty are among the many virtues that mathematicians value and seek in various proofs, and it is important to come to a better understanding of the relations among these virtues. Mathematical practice has long recognized that certain proofs but not others have explanatory power, and this paper offers an account of what makes a proof explanatory. This account is motivated by a wide range of examples drawn from mathematical practice, and the account proposed here is compared to other accounts in the literature. The concept of a proof that explains is closely intertwined with other important concepts, such as a brute force proof, a mathematical co-incidence, unification in mathematics, and natural properties. Ultimately, this paper concludes that the features of a proof that would contribute to its explanatory power would also contribute to its beauty, but that these two virtues are not the same; a beautiful proof need not be explanatory. [ABSTRACT FROM AUTHOR]

In this paper, I introduce teaching activities about Ramanujan's cab numbers and related software that can inspire people and help them enjoy these beautiful mathematical creations. [ABSTRACT FROM AUTHOR]

Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and geometric patterns. [ABSTRACT FROM AUTHOR]

Stereotypes about mathematicians that conflict with “traditionally feminine” identities are widely held by people from middle-school-age onwards, and can influence their participation in mathematics and related fields. Simply being exposed to women in mathematics is not enough to change students’ perceptions of mathematicians, and may even decrease girls’ interest in mathematics. This paper proposes a storytelling strategy to help change students’ perceptions of mathematicians. It includes several activities for intentionally incorporating women’s stories into the post-secondary classroom and a list of resources for finding existing powerful stories. The diverse stories of women mathematicians, including details of their personal lives and the barriers to success they faced, can relieve potential discord between students’ identities and those they see participating in mathematics. [ABSTRACT FROM AUTHOR]

As mathematicians, we often fail to appreciate the opportunities open to us when we teach developmental mathematics. One such opportunity is that we may deepen our understanding of mathematics that we have taken for granted. This paper contains a brief case study concerning what we have learned about operations, inverses, and exponents in the process of teaching beginning algebra. Our inquiry takes us from student questions about signed numbers, through the category of rings, to the world of Lie groups and Lie algebras. [ABSTRACT FROM AUTHOR]

Maths comes to life in human interaction. This has consequences for the mathematics itself. This paper discusses how this “coming to life” of mathematics in different social arenas influences the foundations of maths. We will argue that this influence is profound, to the extent that it is hard to upkeep the idea that there is or should be one foundation on which all mathematics can be built. [ABSTRACT FROM AUTHOR]

In this paper, simple ordinary differential equations are discussed against the background of William Shakespeare’s Romeo and Juliet. In addition, a version of this relationship in a somewhat opposite setting is considered. It is proposed that engineering mathematics courses include this topic in order to promote additional interest in differential equations. In the final section it is shown that vibration of a single-degree-of-freedom mechanical system can be cast as a love-hate relationship between its displacement and velocity, and dynamic instability identified as a transition from trigonometric love to hyperbolic. [ABSTRACT FROM AUTHOR]

“BEWARE and WARNING! This book is different from other books. You and YOU ALONE are in charge of what happens in this story.” This is the captivating introduction to every book in the interactive novel series, Choose Your Own Adventure (CYOA). Our project uses the mathematical field of graph theory to analyze forty books from the CYOA book series for ages 9-12. We first began by drawing the digraphs of each book. Then we analyzed these digraphs by collecting structural data such as longest path length (i.e. longest story length) and number of vertices with outdegree zero (i.e. number of endings). In this paper we discuss the results of statistical analyses we used to compare books by author, year, and reader preference. We also discuss numerous errors we found in the description of certain books and the publication of others. [ABSTRACT FROM AUTHOR]

Mathematics has often been referred to as an art. For some it is “the purest of the arts”, where the mathematicians’ art is “asking simple and elegant questions about our imaginary creations, and crafting satisfying and beautiful explanations”. Yet with classroom time given primarily to “covering the curriculum”, testing, and practicing problem-solving procedures, students’ opportunities to appreciate the aesthetic dimension of mathematics are often limited. To promote a responsive environment in an effort to enable students to become artists of their own mathematics experience, I consider in this paper two facets of the mathematics classroom. Content-wise I make the argument that students need to see problem-clarifying strategies in conjunction with problem-solving techniques, as the former are essential for making progress when engaging a mathematics problem where an explicit solution is not apparent. The other facet aiming to promote student agency is providing them opportunities to work with their own practical/professional concerns as students so as to become more creative and productive artists of their mathematics experience. [ABSTRACT FROM AUTHOR]

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 hold- ers, 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 and measuring provide a systematic and integrative way to teach the foundations of mathematical thinking? We illustrate how the fundamental structures of sym- metry, measuring, and comparison-of-quantities, starting with the embodied or- thogonal axes, form a basis for properties of equality, aspects of numbers and operations (including place value), geometry and number line representations, functions, algebraic reasoning, and measurement. We conclude by embedding the earlier geometric constructions of triangles and squares within the unit circle and making explicit connections to trigonometric functions. [ABSTRACT FROM AUTHOR]

When we teach mathematics, we strive to teach students to think like mathematicians. In this paper we discuss one particular mathematical habit of mind that students do not naturally display. More specifically our study of voting patterns in data collected from classroom voting questions indicates that the undergraduate students who were in the classes using these questions did not understand the significance of counterexamples to statements, or lacked the ability to construct them, or both. Searching for counterexamples to disprove statements is a natural habit of mind for professional mathematicians. In this paper we give examples, and make some recommendations. We believe that if our students get used to routinely seeking out counterexamples, as they play with various mathematical ideas, they may also end up enjoying their mathematical experiences more. [ABSTRACT FROM AUTHOR]

Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker's naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers. [ABSTRACT FROM AUTHOR]

Progress is possible. When I graduated from college, only 5% of the new U.S. doctorates in mathematics went to women; now it is about 30%. There is of course room (and need) for more progress. This paper begins with an account of my research about women and black mathematicians. The latter group claimed that racial equality can be achieved only when better elementary school mathematics education is available to all children in this country. That motivated me to lead a seven-year, grant-supported program to work with elementary school teachers and children in nine New Jersey districts, including Newark, Paterson, and Passaic. I share some disturbing, startling stories about this time as well as some stories of remarkable success. Recent admonitions to "raise standards for all" motivate a personal story about my mentally retarded brother; he and I needed and were given very different types of education. I then offer nine reasons for promoting mathematics education for all, three things good teachers need, and a few more suggestions for improving equity and education. The paper includes photographs and references to important books. [ABSTRACT FROM AUTHOR]

The phenomenon of twins, triplets, quadruplets, and other higher order multiples has fascinated humans for centuries and has even captured the attention of mathematicians who have sought to model the probabilities of multiple births. However, there has not been extensive research into the phenomenon of polyovulation, which is one of the biological mechanisms that produces multiple births. In this paper, I describe how my own experience becoming a mother to twins led me on a quest to better understand the scientific processes going on inside my own body and motivated me to conduct research on polyovulation frequencies. An overview of the previous mathematical research on multiple births, as well as my own contributions involving polyovulation, is presented. Furthermore, I discuss more generally how motherhood can inuence and enrich the research agendas of mathematicians. [ABSTRACT FROM AUTHOR]

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 will try to catalog some of these, without judgment as to whether they are necessarily correct or legitimate. It will also raise the question as to whether mathematics educators interested in the history mathematics have their own distinct relationship with the mathematics of the past or are aligned with one type or another. [ABSTRACT FROM AUTHOR]

The characters encounter high-stakes, life-or- death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have diverent reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book. [ABSTRACT FROM AUTHOR]

Thursday, November 8, 2018, is the twenty-fifth anniversary of the death of the celebrated Professor A. N. Tikhonov, one of my most favorite mathematicians. The idea of writing this paper to honor his life and scientific activities came to me as I was reading many of his works; I was impressed by his knowledge, amazing research, profound scholarship, perspicuity and eloquence of expression, painstaking accuracy, and big ideas. My aim is to be clear and evocative, for in this way I feel more in touch with my subject that is very interesting. [ABSTRACT FROM AUTHOR]

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, descriptions of mathematical practices for making build upon prior everyday mathematical practices and open up a new landscape of inquiry. [ABSTRACT FROM AUTHOR]

In 2009, a literature scholar, Melanie Bayley, proposed that Lewis Carroll’s famous books about Alice visiting the magical and illogical Wonderland were attempts to mock and critique the modern mathematics of the day. In this short paper, I aim to support Bayley’s thesis and expound upon Lewis Carroll’s artful use of symbolism to criticize excessive use of symbolism in mathematics. [ABSTRACT FROM AUTHOR]

In this paper, we give a comprehensive summary of the discussion on the Epicurean critique of mathematics and in particular of Euclid's geometry. We examine the methodological critique of the Epicureans on mathematics and we assess whether a "mathematical atomism" was proposed, and its implications. Finally, we examine the Epicurean philosophical stance on mathematics and evaluate whether it was on target or not. [ABSTRACT FROM AUTHOR]

Topological concepts arise naturally in young children's spatial reasoning yet topology is not part of our current K-12 education. In this paper, we extend the van Hiele model of spatial reasoning using Piaget's theory of representational space. By merging these two existing theories, we are able to place topological concepts in a context that is age appropriate. [ABSTRACT FROM AUTHOR]

Mathematical identity is an individual's concept of who he or she is mathematically. In this paper, metaphors for mathematics from elementary education majors are compared to metaphors created by secondary mathematics teaching majors. The analysis demonstrates a basic difference in the mathematical identity of the two groups, with the latter group having more holistic conceptions of mathematics than the first group. Elementary education majors describe mathematics as an ongoing struggle in which the mathematics is active, and they are the victims. The secondary teaching mathematics majors describe mathematics as an ongoing struggle in which they are active. [ABSTRACT FROM AUTHOR]

Good mathematics stands the test of time. As culture changes, we often ask different questions, bringing new perspectives, but modern mathematics stands on ancient discoveries. Isaac Newton’s discovery of calculus (along with Leibniz) may seem old but is predated by Archimedes’ findings. Current mathematics students should be familiar with parabolas and simple curves; in our introductory calculus courses, we teach them to compute the areas under such curves. Our modern approach derives its roots from Newton’s work; however, we have filled in many of the gaps in the pursuit of mathematical rigor. What many students may not know is that Archimedes solved the area problem for parabolas long before the use of algebraic expressions became mainstream. Archimedes used the geometry of the ancient Greeks, which gave him a vastly different perspective. In this paper, we provide both Archimedes’ and Newton’s proofs involving the quadrature of the parabola, trying to remain true to their original texts as much as feasible. [ABSTRACT FROM AUTHOR]

A “lost chapter” from Antoine de Saint-Exupéry’s Le Petite Prince about the Little Prince visiting a mathematician, written in French in the style of the original work, is presented along with several translations. [ABSTRACT FROM AUTHOR]

I share some of my adventures in mathematical research and homeschooling in the time of COVID-19. [ABSTRACT FROM AUTHOR]

This article, titled "Variations on a Meme: Thoughts and Responses to Isaac Elishakoff's 'Differential Equations of Love and Love of Differential Equations'," explores the concept of memes and their relationship to differential equations and love. The author discusses how memes, as cultural touchstones, can be used to express complex ideas in a concise way, similar to how differential equations are used in poetry. The article also includes brief comments on three poems related to the topic. Overall, the article examines the intersection of mathematics, poetry, and human relationships. [Extracted from the article]

This article chronicles the journey of an immigrant female mathematician in the United States. The chronicle encompasses early training, encouragements received, road-blocks encountered and the background while growing up which shaped the core of her being. The loving, supportive and educative background she received early in life provided the strength to withstand the hurdles thrown in the path of her career advancement. These hurdles are not unique to the author; many immigrant professionals face similar situations. The purpose of the article is to bring awareness to these challenges such professionals face and how they still persevere with discipline and focus. [ABSTRACT FROM AUTHOR]

Data science can contribute valuable predictions in diverse fields. But I write to express some concerns and red flags. I suggest that data science is being oversold. This article contains three questions that I believe data science must address as this new discipline matures. Is data science significantly different from statistics? This is a question that has haunted the field since the term first was introduced. By creating algorithms based on current societal decision rules that may be biased, even bigoted, does data science lock in and exacerbate inequality? Scholars have identified a continuum from data to information to knowledge to wisdom, with the ultimate goal being wisdom. Data scientists seem to be acting as though data alone are enough. The big data systems are mathematically complex and have predictive power, but can data science contribute significantly to our body of knowledge? [ABSTRACT FROM AUTHOR]