This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.

News about this title: — Author Marty Weissman has been awarded a Guggenheim Fellowship for 2020. (Learn more here.) — Selected as a 2018 CHOICE Outstanding Academic Title — 2018 PROSE Awards Honorable Mention An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.

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.

This book focuses on issues related to mathematics teaching and learning resources, including mathematics textbooks, teacher guides, student learning and assessment materials, and online resources. The book highlights various theoretical and methodological approaches used to study teaching and learning resources, and addresses the areas of resources, teachers, and students at an international level. As for the resources, the book examines the role textbooks and other curricular or learning resources play in mathematics teaching, learning, and assessment. It asks questions such as: Could we consider different types of textbooks and roles they play in teaching and learning? How does the digitalization of information and communication affect these roles? What are defining features of e-textbooks, and how could we characterize the differences between the traditional textbooks and e-textbooks? As for the teachers, the book discusses the relationships between teachers’ individual and collective resources, and the way in which we could model such relationships. Specific questions addressed are: What is the role of teachers in developing textbooks and other teaching and learning materials? What are the relationships between resource designers and users? What are the consequences of these changing roles and relationships for the teaching of mathematics, and for teacher knowledge and professional development? As for the students, the book explores how students, as well as their teachers, interact through resources. It raises and addresses questions such as: What are the effects of modern ICT (particularly internet) on students’ use and the design of resources? How do changing patterns of use and design affect student behaviour, learning, and relationships to the subject of mathematics?

This volume is based on lectures delivered at the 2022 AMS Short Course “3D Printing: Challenges and Applications” held virtually from January 3–4, 2022. Access to 3D printing facilities is quickly becoming ubiquitous across college campuses. However, while equipment training is readily available, the process of taking a mathematical idea and making it into a printable model presents a big hurdle for most mathematicians. Additionally, there are still many open questions around what objects are possible to print, how to design algorithms for doing so, and what kinds of geometries have desired kinematic properties. This volume is focused on the process and applications of 3D printing for mathematical education, research, and visualization, alongside a discussion of the challenges and open mathematical problems that arise in the design and algorithmic aspects of 3D printing. The articles in this volume are focused on two main topics. The first is to make a bridge between mathematical ideas and 3D visualization. The second is to describe methods and techniques for including 3D printing in mathematical education at different levels— from pedagogy to research and from demonstrations to individual projects. We hope to establish the groundwork for engaged academic discourse on the intersections between mathematics, 3D printing and education.

Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.

This timely volume raises issues concerning the nature of school mathematics and mathematics at work, and the challenges of teaching valuable mathematics in school and providing appropriate training for a variety of careers. It offers lively commentaries on important `hot' topics: transferring knowledge and skill across contexts; ‘authentic mathematics’; comparability of different types of assessment; and analyses of research methods.

This maths scheme is written specifically for Scotland to help implement the recommendations from "Improving Mathematics Education 5-14". It provides an increasing pace of progression; end of level assessment; oral and mental calculation; integral homework; and support for planning.

Research-based strategies to reach English learners – now aligned with the Common Core! Instead of just watching your English learners struggle, ensure that they develop high-level math skills and gain greater fluency in English. Debra Coggins’ bestselling book has helped many teachers achieve these intertwined goals by offering strategies that support mathematics learning along with language acquisition for English Learners. Now in its second edition, English Learners in the Mathematics Classroom addresses Common Core requirements, enabling your students to build 21st century skills that will serve them well into the future. Through this trusted resource, you’ll develop specialized teaching strategies that can be adapted across grade levels for students at all stages of English language acquisition. You’ll discover Mathematics lesson scenarios in every chapter, directly connected to the Common Core Standards and the Standards for Mathematical Practice Instructional approaches that promote participation, hands-on learning, and true comprehension of mathematics concepts that benefit all students Sample lessons, visuals, and essential vocabulary that connect mathematical concepts with language development Whether you are rediscovering this book or picking it up for the first time, you’ll find standards-based strategies that will enable your English learners to enjoy and master mathematics. "The ideas and strategies in this book, supported by research and field experiences, will benefit ALL students because they are addressing learning challenges that are common for many learners." Trudy Mitchell, Middle School Math Consultant San Diego, CA "This is by far the best book on designing mathematics instruction for English learners. The short but thorough research reviewed in each chapter gives background for why the teaching tips are so important in developing mathematically literate students." Dan Battey, Associate Professor Rutgers University

First Peoples living in remote Australia are educated in two worlds. The future of bush food enterprises in outstations in Utopia depends on the successful transfer of intergenerational knowledge. High school girls respectfully inquire about how to harvest and process important cultural materials from country. Students, senior women and young men strengthen their connections to self, kinship and culture and share responsibility to care for country. Careful collaboration with First Nations people creates opportunities to provide mathematics education which complements and is informed by the work that already exists in the local school community. Consultation with assistant teachers, students, and other community members creates opportunities to validate Indigenous pedagogies in mathematics education. Decolonising Mathematics Education explores and responds to student interest in managing and harvesting akatyerr (desert raisin). Transforming pedagogy enables the students to respond more broadly to the needs of Utopia Eastern Anmatyerr and Alyawarr people to price and sell this important bush food. Income generated from the enterprise is modest, however the skills of a small start-up business have been applied to many learning opportunities that exist in the local community.