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This colorful and concise little book is uniquely tailored for those who write mathematical texts at any level and are eager to improve their English writing skills. The easy-to-read guide focuses on helping the writer avoid common English mistakes in mathematical writing. With just a few minutes of engaging, light reading each day, the reader will learn to create clearer, more readable, math texts. The book covers 23 crucial topics, ranging from correct article and preposition usage to proper usage of dashes, conjunctions, and prepositions. It also addresses the construction of direct sentences, effective introductory phrases for formulas, and more. As a bonus to the reader, ‘Practice makes perfect'exercises relating to each topic are freely accessible on this book's Springer website. Appendix A gives a quick tutorial on grammatical terms and constructs. Appendix B looks at ChatGPT and the positive aspects of its powerful capabilities. Additionally, Paul Halmos's article on ‘How to write mathematics'is included in Appendix C. It deals with the mathematical aspects of writing.

Mathematical science communication, as well as the field of science communication in general, has gained momentum over the last few decades. Mathematical science communication aims to inform the public about contemporary research, enhance factual and methodological knowledge, and foster a greater interest and support for the science of mathematics. This enables the public to apply it to their practical life, and to decision-making on a greater scale. These objectives are met in the various formats and media through which mathematical science communication is brought to the public.The first 13 chapters of the book consist of best-practice examples from the areas of informal math education, museums and exhibitions, and the arts. The final 5 chapters discuss the structural aspects of mathematical science communication and contribute to the basis for its theoretical framework.

A personal, practical, and inspirational guide to written and oral STEM communications for scientists and technical professionals.In Sharing Our Science, scientist-turned-writing teacher Brandon Brown offers an eminently useful guidebook for STEM practitioners looking to communicate their technical work to either a technical or a broader audience. Professionals are increasingly required to communicate their work through blogs, podcasts, and newsletters and to submit to traditional media. After seeing his colleagues struggle to find a writing guide that tackled the unique challenges of writing and speaking about scientific topics, Brown set out to write the definitive handbook to assist STEM students, scientists, engineers, and tech workers alike.In this practical and relevant book, Brown uses his experience as a proven science communicator to cover three levels of writing: fundamental craft considerations, such as narrative tension, structure, sentences, and audience; unique scientific considerations, such as conveying numbers and utilizing metaphors; and finally, social considerations, such as public speaking and writing inside and outside of silos. In place of a reference manual, Brown's engaging narrative guide clarifies the fundamental principles that impact all scientific communication tasks, from white papers and slide decks to Zoom meetings and emails. Sharing Our Science represents the culmination of a lifetime of writing, research, and teaching that will enrich scientists'careers and illuminate the ways in which science is done and conveyed to the world.

In this book, Joanna Baumgart offers a detailed and innovative account of how a mixed methods approach, combining corpus linguistics and discourse analysis, can shed light on educational practice. Corpus Linguistics and Cross-Disciplinary Action Research is based on a 22,000-word corpus of mathematics lessons in a multicultural secondary school in Ireland with the analysis of classroom data supported by insights from reflective meetings with the participating teacher. It demonstrates how examination of video recordings of lessons and reflective conversations facilitate discursive changes in the classroom and increase teacher awareness of classroom interaction. Throughout, the role of teacher talk is used as a model in the subject-specific discourse into which students are socialized. Baumgart also relates the story of a successful interdisciplinary approach to action research, thereby providing an example of how talk and interaction can be examined within wider educational contexts.Building on the premise of the key role which language, and talk in particular, plays in teaching and learning processes, this book will be of keen interest to teacher-educators as well as researchers in the fields of corpus linguistics, discourse analysis and educational linguistics.

Why mathematics is not merely formulaic: an argument that to write a mathematical proof is tantamount to inventing a story.In The Meaning of Proofs, mathematician Gabriele Lolli argues that to write a mathematical proof is tantamount to inventing a story. Lolli offers not instructions for how to write mathematical proofs, but a philosophical and poetic reflection on mathematical proofs as narrative. Mathematics, imprisoned within its symbols and images, Lolli writes, says nothing if its meaning is not narrated in a story. The minute mathematicians open their mouths to explain something—the meaning of x, how to find y—they are framing a narrative. Every proof is the story of an adventure, writes Lolli, a journey into an unknown land to open a new, connected route; once the road is open, we correct it, expand it. Just as fairy tales offer a narrative structure in which new characters can be inserted into recurring forms of the genre in original ways, in mathematics, each new abstract concept is the protagonist of a different theory supported by the general techniques of mathematical reasoning. In ancient Greece, there was more than an analogy between literature and mathematics, there was direct influence. Euclid's proofs have roots in poetry and rhetoric. Mathematics, Lolli asserts, is not the mere manipulation of formulas.

A clear, practical, first-of-its-kind guide to communicating and understanding numbers and data—from bestselling business author Chip Heath.How much bigger is a billion than a million? Well, a million seconds is twelve days. A billion seconds is…thirty-two years. Understanding numbers is essential—but humans aren't built to understand them. Until very recently, most languages had no words for numbers greater than five—anything from six to infinity was known as “lots.” While the numbers in our world have gotten increasingly complex, our brains are stuck in the past. How can we translate millions and billions and milliseconds and nanometers into things we can comprehend and use? Author Chip Heath has excelled at teaching others about making ideas stick and here, in Making Numbers Count, he outlines specific principles that reveal how to translate a number into our brain's language. This book is filled with examples of extreme number makeovers, vivid before-and-after examples that take a dry number and present it in a way that people click in and say “Wow, now I get it!” You will learn principles such as: -SIMPLE PERSPECTIVE CUES: researchers at Microsoft found that adding one simple comparison sentence doubled how accurately users estimated statistics like population and area of countries. -VIVIDNESS: get perspective on the size of a nucleus by imagining a bee in a cathedral, or a pea in a racetrack, which are easier to envision than “1/100,000th of the size of an atom.” -CONVERT TO A PROCESS: capitalize on our intuitive sense of time (5 gigabytes of music storage turns into “2 months of commutes, without repeating a song”). -EMOTIONAL MEASURING STICKS: frame the number in a way that people already care about (“that medical protocol would save twice as many women as curing breast cancer”). Whether you're interested in global problems like climate change, running a tech firm or a farm, or just explaining how many Cokes you'd have to drink if you burned calories like a hummingbird, this book will help math-lovers and math-haters alike translate the numbers that animate our world—allowing us to bring more data, more naturally, into decisions in our schools, our workplaces, and our society.

Classroom interaction has a significant influence on teaching and learning. It is through interaction that we solve problems, build ideas, make connections and develop our understanding. Patterns in Mathematics Classroom Interaction describes, exemplifies and considers the implications of patterns and structures of mathematics classroom interaction. Drawing on a Conversation Analytic approach, the book examines how the structures of interactions between teachers and students influence, enable, and constrain the mathematics that students are experiencing and learning in school. In particular, it considers the handling of difficulties or errors and the consequences on both the mathematics students are learning, and the learning of this mathematics. The various roles of silence and the treatment of knowledge and understanding within everyday classroom interactions also reveal the nature of mathematics as it is taught in different classrooms. Examples of students explaining, reasoning and justifying as they interact are also drawn upon to examine how the structures of classroom interaction support students to develop these discursive practices. The approach taken in Patterns in Mathematics Classroom Interaction enables the identification of not only what structures exist and pervade classroom discourse, but also how these structures influence teaching and learning. It is the understanding of how these structures affect students'experiences in the classroom that permits the use and development of practices that can support students'learning. This reflexive relationship between these structures of interactions and student actions and learning is central to the issues explored in this book, alongside the implications these may have for teachers'practice, and students'learning.

This book offers an international perspective on the current and future state of the research, focusing, in particular, on the role and use of language in mathematics school teaching and learning. It focuses on the development of a unified view of the languages of the learners, of the teachers and of mathematics by considering the role of language in the learning, teaching and doing of mathematics in the classroom, and the current richness and plurality of language and culture.The contributions in this volume combine to show how views of language and of language research in mathematics education have changed significantly in recent decades, and how they will continue to change and become even more complex and challenging in the era of diversity. All of these contributions by leading scholars are grouped into two sections for emphasis on issues of:• Theorising the complexity of language in mathematics teaching and learning• Opening spaces of learning with mathematics classroom research on languageThis book will be of great interest to mathematics teachers, teacher educators, curriculum developers and mathematics education researchers who deal with the study and implementation of pedagogies of mathematics teaching and learning, specifically in regions of the world which are culturally and sociolinguistically diverse.

The articles in this volume grew out of a 2019 workshop, held at Johns Hopkins University, that was inspired by a belief that when mathematicians take time to reflect on the social forces involved in the production of mathematics, actionable insights result. Topics range from mechanisms that lead to an inclusion-exclusion dichotomy within mathematics to common pitfalls and better alternatives to how mathematicians approach teaching, mentoring and communicating mathematical ideas. This collection will be of interest to students, faculty and administrators wishing to gain a snapshot of the current state of professional norms within mathematics and possible steps toward improvements.

The book contains self-contained descriptions of existing models, accompanied by critical analyses of their properties both from a theoretical and practical standpoint. It aims to develop'modeling skills'within the readers, giving them the ability to develop their own models and improve existing ones. Written in connection with a full, open source Python Library, this project also enables readers to run the simulations discussed within the text.

Students learning math are expected to do more than just solve problems; they must also be able to demonstrate their thinking and share their ideas, both orally and in writing. As many classroom teachers have discovered, these can be challenging tasks for students. The good news is, mathematical communication can be taught and mastered.In Teaching Students to Communicate Mathematically, Laney Sammons provides practical assistance for K–8 classroom teachers. Drawing on her vast knowledge and experience as a classroom teacher, she covers the basics of effective mathematical communication and offers specific strategies for teaching students how to speak and write about math. Sammons also presents useful suggestions for helping students incorporate correct vocabulary and appropriate representations when presenting their mathematical ideas.This must-have resource will help you help your students improve their understanding of and their skill and confidence in mathematical communication.

Beyond Answers: Exploring Mathematical Practices with Young Children, author Mike Flynn provides teachers with a clear and deep sense of the Standards for Mathematical Practice and shares ideas on how to best implement them in K-2 classrooms.Each chapter is dedicated to one of the eight common core standards. Using examples from his own teaching and vignettes from many other K-2 teachers, Flynn does the following: Invites you to break the cycle of teaching math procedurally Demonstrates what it means for children to understand not just do math Explores what it looks like when young children embrace the important behaviors espoused by the practices The book's extensive collection of stories from K-2 classroom provides readers with glimpses of classroom dialogue, teacher reflections, and examples of student work. Focus questions at the beginning of each vignette help you analyze the examples and encourage further reflection. Beyond Answers is a wonderful resource that can be used by individual teachers, study groups, professional development staff, and in math methods courses.

Whether you are a new or an experienced teacher, Communication and Creativity in the Math Classroom provides you with classroom-tested activities and ideas which are motivating, engaging, and meaningful to students. Traditional textbooks commonly feature conventional, un-engaging, and somewhat boring problems and activities. Communication and Creativity in the Math Classroom provides you with activities and ideas which stress life skills such as communicating more effectively, being creative, analyzing a variety of problems, following directions, and working cooperatively with others. These skills are very valuable but are rarely addressed in the traditional math curriculum. The materials and ideas in this book allow you to interject these skills into your daily lessons while covering various mathematical topics. Many of the easily reproducible activities can be used as assessments; consequently, suggested scoring rubrics are included as well as helpful strategies and observations.

El texto que aquí presentamos busca profundizar el estudio de algunas nociones desarrolladas en el marco de la teoría de las situaciones didácticas, con frecuencia utilizada en investigaciones y documentos de apoyo a docentes en diferentes idiomas. En español, en el año 2007, Libros del Zorzal difundió un texto de Guy Brousseau cuyo título es Iniciación al estudio de la teoría de las situaciones didácticas. La noción de medio es particularmente interesante y productiva desde el punto de vista teórico, ya que permite abordar diversas cuestiones específicas sobre la enseñanza y el aprendizaje de la matemática. Asimismo, el estudio teórico que la noción posibilita, permite enriquecer las interpretaciones que se tienen de lo que sucede en un aula, sea en el marco de un estudio experimental o de investigación, como en una clase común.'Lo que sucede en un aula'no es una descripción de los hechos'reales'en el ámbito escolar, ni tampoco un prototipo de cómo debe ser la enseñanza. La teoría es una modelización sobre los procesos de producción de conocimientos matemáticos según las condiciones creadas por el docente para que el alumno se encuentre con un conocimiento bien determinado (el medio); es un modo de representar las interacciones entre los alumnos y el medio, y las interacciones entre docente y alumnos.

Why narrative is essential to mathematicsCircles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier—'Don't disturb my circles'—words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds—stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities.A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of'myths of origins'in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.

Do word problems and math vocabulary confuse students in your mathematics classes? Do simple keywords like'value'and'portion'seem to mislead them? Many words that students already know can have a different meaning in mathematics. To grasp that difference, students need to connect English literacy skills to math. Successful students speak, read, write, and listen to each other so they can understand, retain, and apply mathematics concepts. This book explains how to use 10 classroom-ready literacy strategies in concert with your mathematics instruction. You'll learn how to develop students who are able to explain to themselves - and communicate to others - what problems mean and how to attack them. Embedding these strategies in your instruction will help your students gain the literacy skills required to achieve the eight Common Core State Standards for Mathematics. You'll discover the best answer to their question,'When am I ever going to use this?'The 10 Strategies: 1. Teaching mathematical words explicitly 2. Teaching academic words implicitly 3. Reinforcing reading comprehension skills that apply to mathematics 4. Teaching mathematics with metaphor and gesture 5. Unlocking the meaning of word problems 6. Teaching note-taking skills for mathematics 7. Using language-based formative assessment in mathematics 8. Connecting memorization to meaning in mathematics 9. Incorporating writing-to-learn activities in mathematics 10. Preparing students for algebraic thinking

Improving Mathematics at Work questions the mathematical knowledge and skills that matter in the twenty-first century world of work, and studies how the use of mathematics in the workplace is evolving in the rapidly-changing context of new technologies and globalisation. Through a series of case studies from the manufacturing and financial service sectors, the authors argue that there has been a radical shift in the type mathematical skills required for work – a shift not yet fully recognised by the formal education system, or by employers and managers. Examining how information technology has changed mathematical requirements, the idea of Techno-mathematical Literacies (TmL) is introduced to describe the emerging need to be fluent in the language of mathematical inputs and outputs to technologies and to interpret and communicate with these, rather than merely to be procedurally competent with calculations. The authors argue for careful analyses of workplace activities, looking beyond the conventional thinking about numeracy, which still dominates policy arguments about workplace mathematics. Throughout their study, the authors answer the following fundamental questions: What mathematical knowledge and skills matter for the world of work today? How does information technology change the necessary knowledge and the ways in which it is encountered? How can we develop these essential new skills in the workforce? With evidence of successful opportunities to learn with TmL that were co-designed and evaluated with employers and employees, this book provides suggestions for the development of TmL through the use of authentic learning activities, and interactive software design. Essential reading for trainers and managers in industry, teachers, researchers and lecturers of mathematics education, and stakeholders implementing evidence-based policy, this book maps the fundamental changes taking place in workplace mathematics.