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| examples of reflection in math: Nurturing Reflective Learners in Mathematics Berinderjeet Kaur, 2013 This annual volume focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reflection among students and teachers in mathematics classrooms. Published jointly with the Association of Mathematics Educators in Singapore. |
| examples of reflection in math: Reflection Groups and Invariant Theory Richard Kane, 2013-03-09 Reflection groups and invariant theory is a branch of mathematics that lies at the intersection between geometry and algebra. The book contains a deep and elegant theory, evolved from various graduate courses given by the author over the past 10 years. |
| examples of reflection in math: Teaching Numeracy Margie Pearse, K. M. Walton, 2011-03-23 Transform mathematics learning from “doing” to “thinking” American students are losing ground in the global mathematical environment. What many of them lack is numeracy—the ability to think through the math and apply it outside of the classroom. Referencing the new common core and NCTM standards, the authors outline nine critical thinking habits that foster numeracy and show you how to: Monitor and repair students’ understanding Guide students to recognize patterns Encourage questioning for understanding Develop students’ mathematics vocabulary Included are several numeracy-rich lesson plans, complete with clear directions and student handouts. |
| examples of reflection in math: University Physics OpenStax, 2016-11-04 University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result. The text and images in this textbook are grayscale. |
| examples of reflection in math: Guided Math Workshop Laney Sammons, Donna Boucher, 2017-03-01 This must-have resource helps teachers successfully plan, organize, implement, and manage Guided Math Workshop. It provides practical strategies for structure and implementation to allow time for teachers to conduct small-group lessons and math conferences to target student needs. The tested resources and strategies for organization and management help to promote student independence and provide opportunities for ongoing practice of previously mastered concepts and skills. With sample workstations and mathematical tasks and problems for a variety of grade levels, this guide is sure to provide the information that teachers need to minimize preparation time and meet the needs of all students. |
| examples of reflection in math: Reflection Groups and Coxeter Groups James E. Humphreys, 1992-10 This graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications. |
| examples of reflection in math: College Algebra Jay Abramson, 2018-01-07 College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they've learned. Coverage and Scope In determining the concepts, skills, and topics to cover, we engaged dozens of highly experienced instructors with a range of student audiences. The resulting scope and sequence proceeds logically while allowing for a significant amount of flexibility in instruction. Chapters 1 and 2 provide both a review and foundation for study of Functions that begins in Chapter 3. The authors recognize that while some institutions may find this material a prerequisite, other institutions have told us that they have a cohort that need the prerequisite skills built into the course. Chapter 1: Prerequisites Chapter 2: Equations and Inequalities Chapters 3-6: The Algebraic Functions Chapter 3: Functions Chapter 4: Linear Functions Chapter 5: Polynomial and Rational Functions Chapter 6: Exponential and Logarithm Functions Chapters 7-9: Further Study in College Algebra Chapter 7: Systems of Equations and Inequalities Chapter 8: Analytic Geometry Chapter 9: Sequences, Probability and Counting Theory |
| examples of reflection in math: Combinatorics of Coxeter Groups Anders Bjorner, Francesco Brenti, 2006-02-25 Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups |
| examples of reflection in math: Advanced Mathematical Thinking David Tall, 2006-04-11 This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator. |
| examples of reflection in math: What's Math Got to Do with It? Jo Boaler, 2008 Discusses how to make mathematics for children enjoyable and why it is important for American children to succeed in mathematics and choose math-based career paths in the future. |
| examples of reflection in math: Becoming a Reflective Mathematics Teacher Alice F. Artzt, Eleanor Armour-Thomas, Frances R. Curcio, 2008 Artzt, Armour-Thomas and Curcio supply detailed observation instruments that preservice teachers can use when observing other teachers. They also offer reflective activities that provide a structure through which beginning teachers can think about their teaching in an insightful, thorough and productive manner. |
| examples of reflection in math: Precalculus Jay P. Abramson, Valeree Falduto, Rachael Gross (Mathematics teacher), David Lippman, Melonie Rasmussen, Rick Norwood, Nicholas Belloit, Jean-Marie Magnier, Harold Whipple, Christina Fernandez, 2014-10-23 Precalculus is intended for college-level precalculus students. Since precalculus courses vary from one institution to the next, we have attempted to meet the needs of as broad an audience as possible, including all of the content that might be covered in any particular course. The result is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text. Many chapters of OpenStax College Precalculus are suitable for other freshman and sophomore math courses such as College Algebra and Trigonometry; however, instructors of those courses might need to supplement or adjust the material. OpenStax will also be releasing College Algebra and Algebra and trigonometry titles tailored to the particular scope, sequence, and pedagogy of those courses.--Preface. |
| examples of reflection in math: Mathematical Reflections Peter Hilton, Derek Holton, Jean Pedersen, 2012-12-06 A relaxed and informal presentation conveying the joy of mathematical discovery and insight. Frequent questions lead readers to see mathematics as an accessible world of thought, where understanding can turn opaque formulae into beautiful and meaningful ideas. The text presents eight topics that illustrate the unity of mathematical thought as well as the diversity of mathematical ideas. Drawn from both pure and applied mathematics, they include: spirals in nature and in mathematics; the modern topic of fractals and the ancient topic of Fibonacci numbers; Pascals Triangle and paper folding; modular arithmetic and the arithmetic of the infinite. The final chapter presents some ideas about how mathematics should be done, and hence, how it should be taught. Presenting many recent discoveries that lead to interesting open questions, the book can serve as the main text in courses dealing with contemporary mathematical topics or as enrichment for other courses. It can also be read with pleasure by anyone interested in the intellectually intriguing aspects of mathematics. |
| examples of reflection in math: International Reflections on the Netherlands Didactics of Mathematics Marja van den Heuvel-Panhuizen, 2019-08-13 This open access book, inspired by the ICME 13 Thematic Afternoon on “European Didactic Traditions”, takes readers on a journey with mathematics education researchers, developers and educators in eighteen countries, who reflect on their experiences with Realistic Mathematics Education (RME), the domain-specific instruction theory for mathematics education developed in the Netherlands since the late 1960s. Authors from outside the Netherlands discuss what aspects of RME appeal to them, their criticisms of RME and their past and current RME-based projects. It is clear that a particular approach to mathematics education cannot simply be transplanted to another country. As such, in eighteen chapters the authors describe how they have adapted RME to their individual circumstances and view on mathematics education, and tell their personal stories about how RME has influenced their thinking on mathematics education. |
| examples of reflection in math: Reflective Primary Mathematics Elizabeth Jackson, 2015-08-20 ‘This original book shows the crucial importance of personal philosophies of mathematics. Using current research it guides us to reflect on our attitudes and beliefs. Essential reading for anybody interested in mathematics and its teaching.’ Paul Ernest, Emeritus Professor of Mathematics Education, University of Exeter Teaching mathematics can be challenging, and returning to a mathematics classroom yourself may not inspire you with confidence. This book can help you to become an assured teacher who can give young learners the high quality mathematics education that they deserve, by exploring the philosophy that lies behind good mathematics teaching and its application in the classroom. Throughout the book you are encouraged to put your own thoughts on mathematics learning and teaching under the microscope and examine your perceptions and understanding in order to develop as a critically reflective teacher, aware of potential challenges and what underpins effective mathematics teaching in primary schools. Coverage includes: · developing your own philosophy towards mathematics teaching · understanding links between confidence and learning · the importance of subject knowledge · common beliefs and attitudes among mathematics learners · how to develop your relationship with the subject. This is essential reading for all students studying primary mathematics on initial teacher education courses, including undergraduate (BEd, BA with QTS), postgraduate (PGCE, School Direct, SCITT, Teach First) and NQTs. Elizabeth Jackson has over thirty years’ experience of mathematics education through primary and secondary school teaching, lecturing in initial teacher education and supervising mathematics Master’s dissertations, as well as conducting research into mathematics and writing. |
| examples of reflection in math: The Geometry and Topology of Coxeter Groups Michael Davis, 2008 The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are CAT(0) groups. The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures. |
| examples of reflection in math: Guided Math AMPED Reagan Tunstall, 2021-03-31 In today's classrooms, the instructional needs and developmental levels of our students are highly varied, and the conventional math whole-group model has its downsides. In contrast to the rigid, one-size-ts-all approach of conventional whole-group instruction, guided math allows us to structure our math block to support student learning in risk-free, small-group instruction. Guided math goes beyond just reorganizing your math block; it also gives you an opportunity to approach math instruction with a renewed sense of perspective and purpose. Drawing on two decades of experience, Reagan Tunstall oers step-by-step best practices to help educators revolutionize their math blocks with a student-centered approach. Whether you're a new teacher who's curious about guided math or a veteran educator looking to hone your methodology, Guided Math AMPED will transform your math block into an exciting and engaging encounter that encourages your students to see themselves as genuine mathematicians. Most educators have come to realize that the magic happens at the teacher table or during small-group instruction. If that's the case, Guided Math AMPED is the spell book. -JENNIFER SALYARDS, M.Ed., principal, Chamberlin Elementary, Stephenville ISD Guided Math AMPED provides educators with a practical framework for enhancing math instruction in a way that provides research-based practices, differentiated instruction, and fun, all while strengthening relationships with students and developing math mindsets. No matter your experience or tenure in education, Guided Math AMPED will give you tips and tricks to implement in your classroom. -MATT BERES, district administrator, Wooster, OH Guided math is one of the best things you can implement in your classroom, and Reagan Tunstall is the best to learn from, thanks to her perfect framework and step-by-step instructions. She has thought through every potential roadblock and offers concise solutions because she's experienced it all in her own classroom. -HALEE SIKORSKI, educator, A Latte Learning Don't you dare let another teacher borrow this book . . . you may never get it back! From the rst page to the end, this book is lled with practical ideas and guidelines guaranteed to take your guided math block to the next level. -LORI MCDONALD, M.Ed., retired educator |
| examples of reflection in math: CK-12 Calculus CK-12 Foundation, 2010-08-15 CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration. |
| examples of reflection in math: Geometry with an Introduction to Cosmic Topology Michael P. Hitchman, 2009 The content of Geometry with an Introduction to Cosmic Topology is motivated by questions that have ignited the imagination of stargazers since antiquity. What is the shape of the universe? Does the universe have and edge? Is it infinitely big? Dr. Hitchman aims to clarify this fascinating area of mathematics. This non-Euclidean geometry text is organized intothree natural parts. Chapter 1 provides an overview including a brief history of Geometry, Surfaces, and reasons to study Non-Euclidean Geometry. Chapters 2-7 contain the core mathematical content of the text, following the ErlangenProgram, which develops geometry in terms of a space and a group of transformations on that space. Finally chapters 1 and 8 introduce (chapter 1) and explore (chapter 8) the topic of cosmic topology through the geometry learned in the preceding chapters. |
| examples of reflection in math: Maximizing Self-Reflections in the Classroom Ellen Richard, 2022-11-22 What if we could guide children to self-reflect on their level of understanding, to learn what concepts they truly grasp and to identify those concepts with which they still struggle—before and after being assessed on these concepts? What if they could take this information and produce a plan to help themselves master material before an assessment? This practical book will enable you to work with students more effectively so they can evaluate their own levels of understanding, and determine strategies to get them from where they are academically to where they need to be. You’ll also find out how to involve families, since self-reflection works better when students, teachers, and families partner in the learning process. Appropriate for K-8 teachers and curriculum coordinators, the book is perfect for teamwide book studies and teacher training. Examples are included throughout, and the appendix tools can be downloaded for classroom use. |
| examples of reflection in math: Activating Math Talk Paola Sztajn, Daniel Heck, Kristen Malzahn, 2020-09-24 Achieve High-Quality Mathematics Discourse With Purposeful Talk Techniques Many mathematics teachers agree that engaging students in high quality discourse is important for their conceptual learning, but successfully promoting such discourse in elementary classrooms—with attention to the needs of every learner—can be a challenge. Activating Math Talk tackles this challenge by bringing practical, math-specific, productive discourse techniques that are applicable to any lesson or curriculum. Framed around 11 student-centered discourse techniques, this research-based book connects purposeful instructional techniques to specific lesson goals and includes a focus on supporting emergent multilingual learners. You will be guided through each technique with Classroom examples of tasks and techniques spanning grades K–5 Reflection moments to help you consider how key ideas relate to your own instruction Classroom vignettes that illustrate the techniques in action and provide opportunities to analyze and prepare for your own implementation Group discussion questions for engaging with colleagues in your professional community Achieving high-quality mathematics discourse is within your reach using the clear-cut techniques that activates your math talk efforts to promote every student’s conceptual learning. |
| examples of reflection in math: PISA Learning Mathematics for Life A Perspective from PISA OECD, 2010-03-04 Learning Mathematics for Life examines the link between the PISA test requirements and student performance. It focuses specifically on the proportions of students who answer questions correctly across a range of difficulty. The questions are classified by content, competencies, context and format. |
| examples of reflection in math: Teaching Math to Multilingual Students, Grades K-8 Kathryn B. Chval, Erin Smith, Lina Trigos-Carrillo, Rachel J. Pinnow, 2021-01-07 Using strengths-based approaches to support development in mathematics It’s time to re-imagine what’s possible and celebrate the brilliance multilingual learners bring to today’s classrooms. Innovative teaching strategies can position these learners as leaders in mathematics. Yet, as the number of multilingual learners in North American schools grows, many teachers have not had opportunities to gain the competencies required to teach these learners effectively, especially in disciplines such as mathematics. Multilingual learners—historically called English Language Learners—are expected to interpret the meaning of problems, analyze, make conjectures, evaluate their progress, and discuss and understand their own approaches and the approaches of their peers in mathematics classrooms. Thus, language plays a vital role in mathematics learning, and demonstrating these competencies in a second (or third) language is a challenging endeavor. Based on best practices and the authors’ years of research, this guide offers practical approaches that equip grades K-8 teachers to draw on the strengths of multilingual learners, partner with their families, and position these learners for success. Readers will find: • A focus on multilingual students as leaders • A strength-based approach that draws on students’ life experiences and cultural backgrounds • An emphasis on maintaining high expectations for learners’ capacity for mastering rigorous content • Strategies for representing concepts in different formats • Stop and Think questions throughout and reflection questions at the end of each chapter • Try It! Implementation activities, student work examples, and classroom transcripts With case studies and activities that provide a solid foundation for teachers’ growth and exploration, this groundbreaking book will help teachers and teacher educators engage in meaningful, humanized mathematics instruction. |
| examples of reflection in math: Transformational Plane Geometry Ronald N. Umble, Zhigang Han, 2014-12-01 Designed for a one-semester course at the junior undergraduate level, Transformational Plane Geometry takes a hands-on, interactive approach to teaching plane geometry. The book is self-contained, defining basic concepts from linear and abstract algebra gradually as needed. The text adheres to the National Council of Teachers of Mathematics Principles and Standards for School Mathematics and the Common Core State Standards Initiative Standards for Mathematical Practice. Future teachers will acquire the skills needed to effectively apply these standards in their classrooms. Following Felix Klein’s Erlangen Program, the book provides students in pure mathematics and students in teacher training programs with a concrete visual alternative to Euclid’s purely axiomatic approach to plane geometry. It enables geometrical visualization in three ways: Key concepts are motivated with exploratory activities using software specifically designed for performing geometrical constructions, such as Geometer’s Sketchpad. Each concept is introduced synthetically (without coordinates) and analytically (with coordinates). Exercises include numerous geometric constructions that use a reflecting instrument, such as a MIRA. After reviewing the essential principles of classical Euclidean geometry, the book covers general transformations of the plane with particular attention to translations, rotations, reflections, stretches, and their compositions. The authors apply these transformations to study congruence, similarity, and symmetry of plane figures and to classify the isometries and similarities of the plane. |
| examples of reflection in math: Studying Classroom Teaching as a Medium for Professional Development National Research Council, Policy and Global Affairs, Board on International Scientific Organizations, U.S. National Commission on Mathematics Instruction, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematical Sciences Education Board, 2002-08-09 The Mathematical Sciences Education Board (MSEB) and the U.S. National Commission on Mathematics Instruction (USNCMI) took advantage of a unique opportunity to bring educators together. In August 2000, following the Ninth International Congress on Mathematics Education (ICME-9) in Makuhari, Japan, MSEB and USNCMI capitalized on the presence of mathematics educators in attendance from the United States and Japan by holding a two and a half-day workshop on the professional development of mathematics teachers. This workshop used the expertise of the participants from the two countries to develop a better, more flexible, and more useful understanding of the knowledge that is needed to teach well and how to help teachers to obtain this knowledge. A major focus of the workshop was to discuss teachers' opportunities in both societies-using teaching practice as a medium for professional development. Another focus of the workshop addressed practice by considering the records of teaching, including videos of classroom lessons and cases describing teachers and their work. These proceedings reflect the activities and discussion of the workshop using both print and video to enable others to share in their experience |
| examples of reflection in math: Statistical Mechanics of Lattice Systems Sacha Friedli, Yvan Velenik, 2017-11-23 A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail. |
| examples of reflection in math: The Impact of Identity in K-8 Mathematics Learning and Teaching Julia Aguirre, Danny Bernard Martin, 2013 Each teacher and student brings many identities to the classroom. What is their impact on the student’s learning and the teacher’s teaching of mathematics? This book invites K–8 teachers to reflect on their own and their students’ multiple identities. Rich possibilities for learning result when teachers draw on these identities to offer high-quality, equity-based teaching to all students. Reflecting on identity and re-envisioning learning and teaching through this lens especially benefits students who have been marginalized by race, class, ethnicity, or gender. The authors encourage teachers to reframe instruction by using five equity-based mathematics teaching practices: Going deep with mathematics; leveraging multiple mathematical competencies; affirming mathematics learners’ identities; challenging spaces of marginality; and drawing on multiple resources of knowledge. Special features of the book: Classroom vignettes, lessons, and assessments showing equity-based practices Tools for teachers’ self-reflection and professional development, including a mathematics learning autobiography and teacher identity activity at nctm.org/more4u Suggestions for partnering with parents and community organisations End-of-chapter discussion questions |
| examples of reflection in math: Mathematical Problem Solving ALAN H. SCHOENFELD, 2014-06-28 This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople with an interest in higher-order thinking skills in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, rules of thumb for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior. |
| examples of reflection in math: Mathematics for Human Flourishing Francis Su, 2020-01-07 Winner of the Mathematics Association of America's 2021 Euler Book Prize, this is an inclusive vision of mathematics—its beauty, its humanity, and its power to build virtues that help us all flourish“This is perhaps the most important mathematics book of our time. Francis Su shows mathematics is an experience of the mind and, most important, of the heart.”—James Tanton, Global Math ProjectA good book is an entertaining read. A great book holds up a mirror that allows us to more clearly see ourselves and the world we live in. Francis Su’s Mathematics for Human Flourishing is both a good book and a great book.—MAA Reviews For mathematician Francis Su, a society without mathematical affection is like a city without concerts, parks, or museums. To miss out on mathematics is to live without experiencing some of humanity’s most beautiful ideas.In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, an award‑winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires—such as for play, beauty, freedom, justice, and love—and cultivates virtues essential for human flourishing. These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother’s, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher’s letters to the author appear throughout the book and show how this intellectual pursuit can—and must—be open to all. |
| examples of reflection in math: Productive Math Struggle John J. SanGiovanni, Susie Katt, Kevin J. Dykema, 2020-03-09 All students face struggle, and they should—it is how they learn and grow. The teacher’s job is not to remove struggle, but rather to value and harness it, helping students develop good habits of productive struggle. But what’s missing for many educators is an action plan for how to achieve this, especially when it comes to math. This book guides teachers through six specific actions—including valuing, fostering, building, planning, supporting, and reflecting on struggle—to create a game plan for overcoming obstacles by sharing · Actionable steps, activities, and tools for implementation · Instructional tasks representative of each grade level · Real-world examples showcasing classroom photos and student work |
| examples of reflection in math: A First Course in Linear Algebra Kenneth Kuttler, Ilijas Farah, 2020 A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook.--BCcampus website. |
| examples of reflection in math: Physically Based Rendering Matt Pharr, Greg Humphreys, 2010-06-28 This updated edition describes both the mathematical theory behind a modern photorealistic rendering system as well as its practical implementation. Through the ideas and software in this book, designers will learn to design and employ a full-featured rendering system for creating stunning imagery. Includes a companion site complete with source code for the rendering system described in the book, with support for Windows, OS X, and Linux. |
| examples of reflection in math: Conferring in the Math Classroom Gina Picha, 2023-10-10 All students enter our math classrooms with ideas worthy of discussion. Some of the most effective breakthroughs come from short, intentional conversations between students and teacher, yet planning for these moments can seem daunting. In her innovative book, Conferring in the Math Classroom: A Practical Guidebook to Using 5-Minute Conferences to Grow Confident Mathematicians, Gina Picha focuses on simple and transformative ways teachers can use math conferences, short conversations between teachers and small groups of students at work, to guide instruction, assess understanding, and build strong math thinkers. Inside you will learn to: Facilitate math conferences to listen to students, identify and build on their strengths, and encourage them to share their math thinking Build a positive math identity that will help nurture student-centered math classrooms Ask exploratory questions to gain data-driven insight into their math reasoning and plan the next steps for instruction Provide differentiated math instruction based on the individual or small group needs Drive fun and interactive math talk in the classroom Picha includes teacher questioning guides, If-Then charts organized by grade level and math topic, and note-taking templates to help you get started with math conferring right away. This practical and highly accessible approach can help students deepen their math understanding, build confidence in their math abilities, and connect learnings between math subjects. |
| examples of reflection in math: The Five Practices in Practice [Elementary] Margaret (Peg) Smith, Victoria Bill, Miriam Gamoran Sherin, 2019-08-14 Take a deep dive into the five practices for facilitating productive mathematical discussions Enhance your fluency in the five practices—anticipating, monitoring, selecting, sequencing, and connecting—to bring powerful discussions of mathematical concepts to life in your elementary classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively. • Video excerpts vividly illustrate the five practices in action in real elementary classrooms • Key questions help you set learning goals, identify high-level tasks, and jumpstart discussion • Prompts guide you to be prepared for and overcome common challenges Includes planning templates, sample lesson plans and completed monitoring tools, and mathematical tasks. |
| examples of reflection in math: Math That Matters Marian Small, 2019-05-17 In this insightful math resource for grades 3–8, popular professional developer Marian Small helps teachers understand and facilitate meaningful assessments to advance student understandings. Small shows new and veteran teachers how to do three fundamental things well: identify the most important math to assess; construct meaningful assessments—both formative and summative—to measure student understanding; and provide students with feedback that is clear, timely, and specific. Examples for each grade level are provided, along with details on how to pose questions, analyze errors, and help students understand and learn from their mistakes. The book provides specific guidance for when and how to offer feedback on both correct and incorrect answers in order to advance students’ mathematical thinking. Like other Marian Small bestsellers, Math That Matters combines her special brand of lucid explanation of difficult concepts with fresh and engaging activities. “Our understanding of the power of assessment to improve learning has deepened significantly in the past two decades. . . . Marian Small draws upon the critical research behind this understanding to explain what effective practice looks like. It is essential reading for all elementary educators and has the potential to profoundly affect the quality of mathematics assessment in our schools.” —From the Foreword by Damian Cooper, president, Plan Teach Assess “Teachers are often clamoring for concise classroom assessments that can capture students’ conceptual understanding. Clamor no more! Math That Matters is a timely response to that need. Marian Small removes the mystery of how to engage students in learning while collecting assessment data that drive next instructional plans.” —Karen Karp, Johns Hopkins University “The beauty of this book is that it is simple enough for brand new teachers and complex enough for experienced teachers. The author offers an amazing gift by linking assessment ideas directly to common state standards.” —Felicia Darling, Santa Rosa Junior College |
| examples of reflection in math: The Four Pillars of Geometry John Stillwell, 2005-08-09 This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises |
| examples of reflection in math: Handbook of International Research in Mathematics Education Lyn D. English, David Kirshner, 2015-07-30 This third edition of the Handbook of International Research in Mathematics Education provides a comprehensive overview of the most recent theoretical and practical developments in the field of mathematics education. Authored by an array of internationally recognized scholars and edited by Lyn English and David Kirshner, this collection brings together overviews and advances in mathematics education research spanning established and emerging topics, diverse workplace and school environments, and globally representative research priorities. New perspectives are presented on a range of critical topics including embodied learning, the theory-practice divide, new developments in the early years, educating future mathematics education professors, problem solving in a 21st century curriculum, culture and mathematics learning, complex systems, critical analysis of design-based research, multimodal technologies, and e-textbooks. Comprised of 12 revised and 17 new chapters, this edition extends the Handbook’s original themes for international research in mathematics education and remains in the process a definitive resource for the field. |
| examples of reflection in math: How to Teach Mathematics, Second Edition Steven George Krantz, 1999 This expanded edition of the original bestseller, How to Teach Mathematics, offers hands-on guidance for teaching mathematics in the modern classroom setting. Twelve appendices have been added that are written by experts who have a wide range of opinions and viewpoints on the major teaching issues. Eschewing generalities, the award-winning author and teacher, Steven Krantz, addresses issues such as preparation, presentation, discipline, and grading. He also emphasizes specifics--from how to deal with students who beg for extra points on an exam to mastering blackboard technique to how to use applications effectively. No other contemporary book addresses the principles of good teaching in such a comprehensive and cogent manner. The broad appeal of this text makes it accessible to areas other than mathematics. The principles presented can apply to a variety of disciplines--from music to English to business. Lively and humorous, yet serious and sensible, this volume offers readers incisive information and practical applications. |
| examples of reflection in math: The Best Writing on Mathematics 2014 Mircea Pitici, 2015 An anthology of the year's finest writing on mathematics from around the world, featuring promising new voices as well as some of the foremost names in mathematics. |
| examples of reflection in math: Revisiting Mathematics Education Hans Freudenthal, 2005-12-08 This book is a product of love and respect. If that sounds rather odd I initially apologise, but let me explain why I use those words. The original manuscript was of course Freudenthal’s, but his colleagues have carried the project through to its conclusion with love for the man, and his ideas, and with a respect developed over years of communal effort. Their invitation to me to write this Preface e- bles me to pay my respects to the great man, although I am probably incurring his wrath for writing a Preface for his book without his permission! I just hope he understands the feelings of all colleagues engaged in this particular project. Hans Freudenthal died on October 13th, 1990 when this book project was well in hand. In fact he wrote to me in April 1988, saying “I am thinking about a new book. I have got the sub-title (China Lectures) though I still lack a title”. I was astonished. He had retired in 1975, but of course he kept working. Then in 1985 we had been helping him celebrate his 80th birthday, and although I said in an Editorial Statement in Educational Studies in Mathematics (ESM) at the time “we look forward to him enjoying many more years of non-retirement” I did not expect to see another lengthy manuscript. |
Examples - Apache ECharts
Apache ECharts，一款基于JavaScript的数据可视化图表库，提供直观，生动，可交互，可个性化定制的数据可视化图表。
Examples - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code …
Examples - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code …
Apache ECharts
ECharts: A Declarative Framework for Rapid Construction of Web-based Visualization. 如果您在科研项目、产品、学术论文、技术报告、新闻报告、教育、专利以及其他相关活动中使用了 …
Events - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code …
Examples - Apache ECharts
Apache ECharts，一款基于JavaScript的数据可视化图表库，提供直观，生动，可交互，可个性化定制的数据可视化图表。
Examples - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing …
Examples - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing List; How to Contribute; Dependencies; Code Standard; Source Code (GitHub) Issues …
Apache ECharts
ECharts: A Declarative Framework for Rapid Construction of Web-based Visualization. 如果您在科研项目、产品、学术论文、技术报告、新闻报告、教育、专利以及其他相关活动中使用了 Apache ECharts，欢迎引用本论文。
Events - Apache ECharts
Examples; Resources. Spread Sheet Tool; Theme Builder; Cheat Sheet; More Resources; Community. Events; Committers; Mailing …
