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In this note we explain the importance of clarity and give other tips for mathematical writing. Some of it is mildly opinionated, but most is just common sense and experience. [ABSTRACT FROM AUTHOR]

The article offers the author's insights on guides for research papers including in organizing principles, imagery and metaphors, and story of the development. Topics discussed include the research literature management, the meta-data analysis, and the project management. Also mentioned are the modes of reasoning, the human expression, and the mathematics education management.

According to a widely held view, mathematical proofs are essentially (indications of) formal derivations, and thus in principle mechanically checkable (this view is defended, for example, by Azzouni [3]). This should in particular hold for the kind of simple proof exercises typically given to students of mathematics learning to write proofs. If that is so, then automated proof checking should be an attractive option for math education at the undergraduate level. An opposing view would be that mathematical proofs are social objects and that what constitutes a mathematical proof can thus not be separated from the social context in which it arises. In particular, such “sociomathematical norms” play a role in teaching situations, see, for example, Stephan [37]. There thus seems to be a tension between the inherent social nature of “natural” mathematical proofs and attempts at their automated verification. In this paper, we explore this tension both theoretically and on the basis of our experiences with developing the Diproche system, a program for the automated verification of natural language proofs in college-level introduction to proof classes (modelled after the example of the Naproche system by Cramer, Koepke et al. [14]) and its use at the Europa-Universit¨at Flensburg during the winter term 2020/2021. [ABSTRACT FROM AUTHOR]

In this paper, we, a group of graduate students in mathematics education, discuss some of the metacognitive benefits of the non-traditional teaching methods we observed employed by one of our professors. This professor's methods challenge the common belief that well-managed class time is key for positive learning outcomes. Instead, he orients his teaching to share the exploration and sense-making phases of doing mathematics. The goal of his teaching is to share the idea that learning mathematics is a process of "refining our mathematical thinking". We argue that this approach to teaching helps students see that mathematics is a human endeavor, appreciate the cycles of learning mathematics and the importance of struggle throughout the process, and gain some insight on what it means to be an expert in mathematics. We encourage teachers and professors to move away from obsessing about structured, well-organized class time, and to instead move towards having flexible and risk-oriented class time. [ABSTRACT FROM AUTHOR]

This paper investigates creativity in students' constructions of everyday examples about basis in Linear Algebra. We analyze semi-structured interview data with 18 students from the United States and Germany with diverse academic and social backgrounds. Our analysis of creativity in students' everyday examples is orga- nized into two parts. First, we analyze the range of students' creative products by investigating the mathematical variability in the more commonly mentioned examples. Second, we unpack some of the collective processes in the construc- tion of students' examples. We examine how creativity was distributed through the interactions among the student, the interviewers, and other artifacts and ideas. Thus, in addition to contributing to the process vs. product discussion of creativity, our work also adds to the few existing studies that focus on collec- tive mathematical creativity. The paper closes with connections to anti-deficit perspectives in mathematics education and some recommendations for individual and collective creativity in the classroom. [ABSTRACT FROM AUTHOR]

The text is an invitation to the 7th International Conference on Creative Mathematical Sciences Communication (CMSC'24), which will take place from October 7-10, 2024, at the University of Trier in Germany. The conference aims to bring together mathematicians and computer scientists from around the world to explore innovative ways of communicating computational thinking and research. The conference will feature a variety of activities, including a sorting network demonstration, a math dance performance, a glass bead game, and a presentation on quantum computing. The conference proceedings will be published by Springer LNCS, and participants have the option to submit articles for publication. The CMSC conference series began in 2013 and focuses on developing hands-on computational thinking materials and activities. The conference website provides more information about the event and the submission guidelines. [Extracted from the article]

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 shared responsibility during these tumultuous times, we can once again strive toward the pursuit of excellence in mathematics education. [ABSTRACT FROM AUTHOR]

This is a review of What is a Mathematical Concept? edited by Elizabeth de Freitas, Nathalie Sinclair, and Alf Coles (Cambridge University Press, 2017). In this collection of sixteen chapters, philosophers, educationalists, historians of mathematics, a cognitive scientist, and a mathematician consider, problematise, historicise, contextualise, and destabilise the terms 'mathematical' and 'concept'. The contributors come from many disciplines, but the editors are all in mathematics education, which gives the whole volume a disciplinary centre of gravity. The editors set out to explore and reclaim the canonical question 'what is a mathematical concept?' from the philosophy of mathematics. This review comments on each paper in the collection. [ABSTRACT FROM AUTHOR]

In this paper I describe an activity based on a 1903 Sherlock Holmes murder mystery, in which a substitution cipher is used to encrypt secret messages. The story provides a fun and interesting way to talk about frequency analysis, and can be used as a segue into mathematical constructs such as modular arithmetic and computation. The activity is accessible to ages twelve and above, and has been successfully used in mathematics outreach and popularization efforts as well as in general education and mathematics courses. [ABSTRACT FROM AUTHOR]

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 mathematics within and beyond the typical K-16 curriculum. We share practical outreach methods inspired by real mathematics, and our experience with a liberal-arts 'math for poets' course which aims to develop math appreciation without losing its rigor or depth. While many of us are not comfortable doing live performances or making fancy videos, we all can use these methods to encourage a more positive mindset about mathematics in our communities. [ABSTRACT FROM AUTHOR]

A steward of the discipline was originally defined as an individual to whom "we can entrust the vigor, quality, and integrity of the field", and more specifically, as "someone who will creatively generate new knowledge, critically conserve valuable and useful ideas, and responsibly transform those understandings through writing, teaching, and application" [8]. Originally articulated for doctoral education, in 2019 the construct of stewardship was expanded so that it can also be applied to non-academic practitioners in any field, and can be initiated earlier than doctoral education [18]. In this paper we apply this construct to the context of mathematics and argue that even for those early in their training in mathematics, stewardly practice of mathematics can be introduced and practiced. Postsecondary and tertiary education in mathematics -- for future mathematicians as well as those who will use math at work -- can include curriculum-spanning training, and documented achievement in stewardship. Even before a formal ethical practice standard for mathematics is developed and deployed to help inculcate math students with a "tacit responsibility for the quality and integrity of their own work", higher education can begin to shape student attitudes towards stewardly professional identities. Learning objectives to accomplish this are described, to assist math instructors in facilitating the recognition and acceptance of responsibility for the quality and integrity of their own work and that of colleagues in the practice of mathematics. [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]

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]

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]

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]

I discuss the role of intuitive explanations in the learning, teaching, and popularization of mathematics. Several examples of such explanations are presented, related to linguistic explanations, perception, empirical models, and internal explanations inside mathematics itself. I emphasize the fact that intuitive explanations in a sense transgress mere mathematical arguments. I also discuss in brief the role of paradox resolution in mathematical education. [ABSTRACT FROM AUTHOR]

Teaching is widely considered one of the “caring professions,” but conceptualizations of care and how care is put into practice in education are not universal. In this article, we draw from a range of perspectives on care that integrate supportive interpersonal relationships, high expectations, and culturally relevant theories of critical care, as well as Queer Theory and Disability Justice, to explore the application of these ideas in mathematics education. We identify key elements for building communities of care in mathematics education contexts: co-constructing community agreements, redefining participation, shifting traditional power structures, collaborative problem solving, and building networks of care beyond the classroom. We share our experiences implementing these elements of communities of care and propose that the integration of these elements can serve as the starting point for a framework for building communities of care for equity, justice, and culturally responsive practice in mathematics education. [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]

Mathematics and aesthetics have a long history in common. In this relation however, the aesthetic dimension of mathematics largely refers to concepts such as purity, absoluteness, symmetry, and so on. In stark contrast to such a nexus of ideas, the Japanese aesthetic of wabi-sabi values imperfections, temporality, incompleteness, earthly crudeness, and even contradiction. In this paper, I discuss the possibilities of "wabi-sabi mathematics" by showing (1) how wabi-sabi mathematics is conceivable; (2) how wabi-sabi mathematics is observable; and (3) why we should bother about wabi-sabi mathematics. [ABSTRACT FROM AUTHOR]

Mathematicians, mathematics education researchers, and philosophers have written about mathematical beauty and many of the qualities commonly associated with it, such as simplicity, brevity, enlightenment, etc. One key theme that underlies many of these qualities is surprise or the unexpected. In this article, I discuss the integral role surprise plays in mathematical beauty. Through examples, I argue that simplicity alone is oftentimes not enough for a piece of mathematics to be considered beautiful, but rather it is unexpected simplicity that we seek. I propose, moreover, that surprise is necessary for enlightenment. The paper also reports results from an activity designed to elicit an appreciation of mathematical beauty from elementary preservice teachers; the majority reaction was a feeling of surprise. Understanding the relevance of surprise to mathematical beauty may offer us a feasible way to create opportunities for students to experience mathematical beauty. [ABSTRACT FROM AUTHOR]

The article offers information on the nature of mathematical beauty with the philosophical discussions on mathematical explanation and aesthetics.

Little is known about instructional means by which the aesthetic experience of mathematics can be enhanced for undergraduate learners. This paper presents and discusses an iterative lesson design process towards creating an opportunity for students to appreciate the beauty of an unexpected solution to a challenging calculus problem. The lesson design draws on insights from both mathematics education research on aesthetics and research on aesthetic appreciation in music. The data were collected over the course of five lessons with different groups of calculus students in which the intended problem was presented in two different ways. In addition, stimulated-recall interviews were conducted with nine students who took part in the later lessons and exhibited strong emotions regarding the problem. The data suggest that the students' aesthetic response to the problem was essentially conditioned by the extent of their surprise as a result of revealing a clever solution to the problem after being exposed to repeated failed attempts. Implications for practice are drawn. [ABSTRACT FROM AUTHOR]

A link between proving and problem solving has been established in the literature [5, 21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribe pen data from a previous study [13]. I focus on two participants' proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the mathematician and that of the graduate student. This study suggests the feasibility of an expanded framework for the proving process that can encompass both the similarities and the differences found. [ABSTRACT FROM AUTHOR]

In this paper, I explore recreational mathematics from two perspectives. I first study how the concept appears in educational policy documents such as standards, syllabi, and curricula from a selection of countries to see if and in what way recreational mathematics can play a part in school mathematics. I find that recreational mathematics can be a central part, as in the case of India, but also completely invisible, as in the standards from USA. In the second part of the report, I take an educational historical approach. I observe that throughout history, recreational mathematics has been an important tool for learning mathematics. Recreational mathematics is then both a way of bringing pleasure and a tool for learning mathematics. Can it also be a tool for social empowerment? [ABSTRACT FROM AUTHOR]

Teaching to develop creativity often requires a shift in instructional tasks. In this paper, we first summarize the body of research related to instructors facilitat- ing and recognizing mathematical creativity. We then provide details as to how one graduate course, designed to help mathematics educators develop a sense of school mathematics from an advanced standpoint, provided opportunities for students to: recognize the difference between problems and exercises, pose prob- lems, reect on the quality of the tasks they created and review tasks created by others. This series of activities were designed to help the graduate students rec- ognize and appreciate mathematical creativity. We then review the instructional activities in light of the five overarching principles to maximize creativity in K-12 mathematics classrooms suggested by Sriraman [36] and discuss how these might relate to the post-secondary and graduate education of mathematics educators. [ABSTRACT FROM AUTHOR]

The goal of the Creativity in Mathematics and Science project, funded by the National Science Foundation's [NSF's] Improving Undergraduate STEM Educa- tion program, is to reconsider how we teach mathematics at the collegiate level. Over the last three years, we have developed interdisciplinary modules that seek to encourage students, including non-STEM majors, to see mathematics in un- expected places, make connections to their own interests and disciplines, and explore creativity in mathematics. Relying on traits of creativity such as the abil- ity to connect ideas, be inquisitive, question norms, and have exibility [1], we encouraged students to participate and understand mathematics in unconven- tional ways. The scheduling of a professional juggling company's performance at our on-campus theater inspired us to create a module connecting mathematics and juggling for both a general education mathematics course and a mechanics course. We drew from research on the mathematics of juggling [2, 3] to de- velop a module that encouraged students to explore the patterns, notations, and mathematical elements of juggling in a variety of ways. Their final projects, rep- resenting further explorations, were displayed in our theater's lobby and featured interactive displays and demonstrations. In this paper we describe our experi- ences developing and implementing this juggling module, students' experiences with the modules, and their development of final projects. [ABSTRACT FROM AUTHOR]

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 our voices, reflecting on how we and others solve problems. [ABSTRACT FROM AUTHOR]

The notion of d'epaysement 'epist'emologique (epistemological disorientation) aims to capture the sense of disorientation when a learner is led to question their prior assumptions and understandings, generating uncertainty in a context in which they thought they had certain knowledge. This article describes an activity used with a group of practicing mathematics teachers in Uruguay that integrates elements of the history of mathematics related to Gödel's incompleteness theorem, with the aim of provoking in the participants the experience of d'epaysement 'epist'emologique. Results show that several of the teachers participating in the activity felt d'epaysement 'epist'emologique, and this feeling triggered empathy towards their own students. The article ends with a discussion of the real possibilities of integrating the history of mathematics in secondary mathematics courses and in the training of teachers. [ABSTRACT FROM AUTHOR]

Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it-both raised to the level of resentment-run through the paper "A Critique of the Modern Consensus in the Historiography of Mathematics." My review of that paper, sent to me blind, became a response to it. In particular, this essay attempts to clarify the nature of the historical discipline and to show that author of the Critique ends up, in effect, wanting and not wanting history at the same time. [ABSTRACT FROM AUTHOR]

Here we revisit a paper which examined two theses regarding the roles of religion and language of instruction in mathematics education. The first thesis states that if values of mathematics education are incompatible with the value system of the mother culture, then mathematics will be "appended" to the culture as a "technology" rather than assimilated as a "mode of thinking". The second thesis states that as soon as mathematics is applied in problems and situations, the language of instruction and learning becomes a cultural carrier in terms of behaviors, social relations, habits, and values. In the original paper, the first thesis was examined in the context of Islamic-Arab culture, while the second thesis was developed in the context of Lebanon. Here the original paper is first presented in its complete form, with some minor modifications. Next I offer some reflections on the relevance of these two theses today. [ABSTRACT FROM AUTHOR]

The article introduces various papers published within the issue, including one on teaching mathematics using an ethnomodelling approach, another on how teachers may motivate students to learn college-level mathematics and a paper on strategies for teaching the Fundamental Theorem of Calculus.

In the viral New York Times essay \To Fall in Love with Anyone, Do This", Mandy Len Catron details an experience she and an acquaintance had as they shared responses to psychologist Arthur Aron's thirty-six questions intended to make participants fall in love. She notes that \we all have a narrative of ourselves that we over up to strangers and acquaintances, but Dr. Aron's questions make it impossible to rely on that narrative". In this paper, we claim that we also have narratives of our relationship to mathematics that we over up to ourselves and others. Following, we over a mathematical version on Aron's thirty-six questions, designed to break out of our personal mathematical narratives and foster intimacy with mathematics. [ABSTRACT FROM AUTHOR]

The goal of this paper is to review current research on Inquiry Based Learning (IBL) and shed some light, from a student's perspective, on the challenges and rewards of this pedagogy. The first part of the article provides an extensive review of the literature on IBL. The second part focuses on one student's experiences in an IBL classroom. In particular, a graduate secondary mathematics student reflects upon his experiences in a college mathematics class where the instructor implemented an Inquiry Based Learning model. His experience is validated by current research on IBL educational methodology which structures the classroom environment for student centered learning. This student reported increased critical thinking skills, higher levels of motivation and engagement, and more retention of content than in other mathematics courses taken. Furthermore, this student believes that he was more invested in his learning, experienced improved conceptual understanding of content, and had higher levels of confidence in mathematics as a result of the IBL experience. As a preservice teacher candidate, he hopes to integrate IBL practices into his future teaching career to improve student learning. [ABSTRACT FROM AUTHOR]

In the Fall of 2013 our team of three different generations of mathematicians launched the free, online E-Brock Bugs mathematics computer game [5] which we developed from an original probabilistic board game, Brock Bugs, and its digital learning object version. We constructed E-Brock Bugs using Devlin's [9] mathematics computer game design principles for games that prompt players' development of mathematical thinking. As we created E-Brock Bugs we found it necessary to go through an evolving cyclic process of design, implementation, and analysis. In this paper we reect upon the main struggles we faced in this process and the unexpected personal growth that ensued in terms of our views and beliefs as mathematics educators. [ABSTRACT FROM AUTHOR]

Anneli Lax (1922-1999) was my mentor and thesis advisor at New York University in the late 1980s. I was fortunate to be included among her circle of friends and collaborators in the ensuing years. Dr. Lax made important contributions to mathematics and mathematics education. This article describes her pioneering work in promoting good exposition of elementary mathematics in support of mathematics and its pedagogy. The design and implementation of her views illustrate her indefatigable spirit and impressive work ethic for causes she championed. [ABSTRACT FROM AUTHOR]

Inspired by Brent Davis' conceptualization of listening and conversation in his book Teaching Mathematics: Toward a Sound Alternative, we propose how we as a mathematics education community may move forward by continuing in the conversation that emerged from COVID. We encourage all involved to listen rather than assume a discussion-oriented stance. Using an enactivist lens, we look at the pandemic learning space, give an overview of the education conversation that emerged in Ontario, and offer a way to rethink Mathematics Education within the frame of a conversation. We believe that if mathematics education is to engage learners in a meaningful way, sustaining the progress made in mathematics education, all stakeholders should embrace the changing context of our network within the environment and interact through listening. [ABSTRACT FROM AUTHOR]

The history of contemporary mathematical education is the history of a struggle against computers and IT. As a result specially selected simplified math problems are used while teaching. Just as it was a hundred years ago, contemporary students are forced to memorize a lot of rules and theorems in order to solve math problems. But we know that today they can get the same results using simple computer calculations. Information technologies can (and in this paper we argue that they should) change the traditional methods of solving mathematical problems. Here we share some simple problems that helped engineering students learn the basics of mathematics and computer science and even enjoy the learning process. In particular we point out that the ability to visualize solutions is very important in most contexts, and modern mathematical software packages offer users convenient and simple tools of visualization and even animation. Including them on our pedagogical team, we can significantly increase our students' understanding of the basic concepts and theorems of mathematics. [ABSTRACT FROM AUTHOR]

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

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 society. Embracing dystopia rather than trying to circumvent it generates new questions and pathways. [ABSTRACT FROM AUTHOR]

Erlwanger [18] shook the mathematics education world when he introduced Benny, a student who successfully worked through a behavioristic curriculum. Erlwanger showed how far removed Benny's understanding of mathematics was from expectations. Erlwanger's legacy is the basis for this comparative case study which explores students' actions in the modern, in-class computer-centered emporium classroom. Many striking similarities are found between Pearson's My- MathLabs (MML) and Benny's Individually Prescribed Instruction curriculum. In this case study we meet Barbara, a student who succeeds in MML but shows little understanding of mathematical concepts and demonstrates that the legacy of Benny is his continued appearance in our current students. However, what differentiates Benny and Barbara is more than time; it's the inequities resulting from imposing a pedagogy with well-known problematic characteristics to developmental mathematics students. Most of these developmental students are members of marginalized communities. As such, the social justice and ethical implications of using such a course structure are explored. [ABSTRACT FROM AUTHOR]

In this paper, we advocate the writing of mathematical fiction (i) as an aid for students in learning mathematics, and (ii) to engage students in doing mathematics. [ABSTRACT FROM AUTHOR]