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5 Strands of Mathematical Proficiency: Implications for Industry Success
By Dr. Evelyn Reed, PhD
Dr. Evelyn Reed is a Professor of Mathematics Education at the University of California, Berkeley, with over 20 years of experience researching and developing effective mathematics instruction. Her work focuses on bridging the gap between theoretical mathematical understanding and practical application in various industries.
Published by: The Institute for Advanced Studies in Mathematics (IASM) – A leading publisher of peer-reviewed research and educational materials in mathematics and related fields, known for its rigorous editorial process and commitment to disseminating high-quality knowledge.
Editor: Dr. Anya Sharma, PhD – A seasoned editor with extensive experience in mathematics education and publishing. Dr. Sharma has edited numerous publications on mathematics pedagogy and its applications in diverse sectors.
Introduction:
The ability to effectively apply mathematical concepts isn't simply about calculating numbers; it's about a deeper, more nuanced understanding that empowers individuals to solve complex problems and drive innovation. This comprehensive understanding is encapsulated in the widely recognized framework of the 5 strands of mathematical proficiency. This article delves into each strand, highlighting its significance and exploring its implications for various industries. Understanding and nurturing these five strands is crucial for fostering a mathematically literate workforce, capable of tackling the intricate challenges of the modern world.
1. Conceptual Understanding:
The first strand, conceptual understanding, involves grasping the big picture. It's about comprehending the underlying concepts, relationships, and principles that govern mathematical operations. For example, understanding the concept of "ratio" goes beyond knowing how to calculate it; it involves recognizing ratios in various contexts, from scaling recipes to analyzing financial data. In industries like finance, engineering, and data science, a strong conceptual understanding is paramount for interpreting complex models and making informed decisions. A lack of conceptual understanding can lead to misinterpretations of data, flawed designs, and ultimately, costly errors. Developing this strand through rigorous problem-solving and real-world application is critical for industry success.
2. Procedural Fluency:
Procedural fluency refers to the ability to accurately and efficiently perform calculations and apply algorithms. While not as important as conceptual understanding, it's a crucial supporting pillar of the 5 strands of mathematical proficiency. It's the ability to execute the mechanics of mathematics quickly and accurately. In fields like accounting, software development, and manufacturing, accurate and efficient computations are essential for productivity and precision. For instance, a programmer with strong procedural fluency can write efficient algorithms, while an accountant can process financial statements without errors. However, procedural fluency without conceptual understanding can be a recipe for mindless application, leading to errors when dealing with novel situations.
3. Strategic Competence:
Strategic competence represents the ability to formulate, represent, and solve mathematical problems. This involves selecting appropriate strategies, making connections between different mathematical concepts, and adapting to changing circumstances. It's the ability to approach a problem systematically, break it down into smaller, manageable parts, and find the most efficient solution. This strand is particularly critical in fields like engineering, operations research, and data analysis, where professionals are frequently faced with complex and ill-defined problems requiring creative solutions. Industry leaders need employees who can not only perform calculations but also develop novel approaches to address unique challenges.
4. Adaptive Reasoning:
Adaptive reasoning focuses on the ability to think logically, justify conclusions, and reflect on mathematical processes. It's about being able to explain your reasoning, identify and correct errors, and evaluate the reasonableness of solutions. This is the analytical engine that drives the other strands of the 5 strands of mathematical proficiency. This strand is crucial across all industries. In fields like scientific research, law, and medicine, the ability to construct rigorous arguments and evaluate evidence is paramount. A strong adaptive reasoning ability allows individuals to critique their own work, identify flaws in logic, and build robust and reliable solutions.
5. Productive Disposition:
The final strand, productive disposition, encompasses the attitudes and beliefs towards mathematics. It's about having a positive outlook, believing in one's ability to learn and solve problems, and persevering through challenges. This is often the overlooked element in the 5 strands of mathematical proficiency, but it's crucial for success. A positive disposition fuels motivation, encourages exploration, and promotes resilience in the face of difficulty. In every industry, problem-solving requires persistence and a growth mindset. Employees with a productive disposition are more likely to embrace challenges, seek out solutions, and contribute creatively to their organizations.
Implications for Industry:
The 5 strands of mathematical proficiency have significant implications for industries across the board. Organizations that prioritize the development of these strands in their employees are more likely to:
Improve problem-solving capabilities: Employees with strong mathematical proficiency can tackle complex challenges more effectively.
Enhance innovation: A deep understanding of mathematical concepts fuels creativity and the development of new solutions.
Reduce errors and improve accuracy: Proficiency leads to fewer mistakes and greater reliability in outcomes.
Boost productivity and efficiency: Efficient procedures and effective strategies lead to faster and more efficient work processes.
Increase competitiveness: A mathematically skilled workforce gives organizations a competitive edge in the marketplace.
Conclusion:
The 5 strands of mathematical proficiency—conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition—are not just academic concepts; they are fundamental skills for success in the modern workplace. Cultivating these strands through education and training is crucial for developing a workforce capable of driving innovation, solving complex problems, and ensuring the continued success of industries worldwide. By investing in the development of these essential mathematical proficiencies, organizations can unlock the full potential of their employees and gain a significant competitive advantage in today's rapidly evolving landscape.
FAQs:
1. How can the 5 strands of mathematical proficiency be assessed in the workplace? Through observation of problem-solving approaches, analysis of work products, and targeted assessments designed to measure specific skills.
2. What training programs are effective for developing these proficiencies in adults? Programs that emphasize real-world applications, collaborative learning, and problem-based approaches are most effective.
3. How can managers foster a productive disposition in their teams? By creating a supportive environment, encouraging risk-taking, celebrating successes, and providing constructive feedback.
4. Are certain industries more reliant on specific strands of mathematical proficiency? Yes, some industries (e.g., finance) rely heavily on procedural fluency and strategic competence, while others (e.g., research) emphasize adaptive reasoning and conceptual understanding.
5. How can these strands be integrated into existing employee training programs? By incorporating problem-solving activities, case studies, and simulations that require the application of mathematical concepts.
6. What are the long-term benefits of investing in developing these proficiencies? Improved employee performance, increased innovation, reduced errors, and a more competitive organization.
7. How can educational institutions better prepare students for the demands of the modern workplace in terms of mathematical proficiency? By emphasizing conceptual understanding, problem-solving skills, and real-world applications in their curriculum.
8. Are there specific technologies that can help develop these mathematical proficiencies? Yes, educational software, simulations, and online learning platforms can provide targeted practice and feedback.
9. How can companies measure the return on investment (ROI) of investing in developing these proficiencies? By tracking improvements in employee performance, error rates, problem-solving efficiency, and innovation output.
Related Articles:
1. Developing Conceptual Understanding in Mathematics: This article explores strategies for fostering a deep understanding of mathematical concepts, emphasizing connections and real-world applications.
2. The Importance of Procedural Fluency in Mathematical Problem Solving: This article discusses the role of efficient calculation in successful problem-solving, highlighting the need for a balance between fluency and conceptual understanding.
3. Strategic Competence: A Key to Effective Problem Solving: This article delves into the various strategies used in mathematical problem-solving and emphasizes the importance of selecting the most appropriate approach.
4. Adaptive Reasoning in Mathematics: Cultivating Critical Thinking Skills: This article focuses on developing the ability to reason logically, justify conclusions, and evaluate the reasonableness of solutions.
5. Fostering a Productive Disposition Towards Mathematics: This article explores strategies for cultivating positive attitudes and beliefs about mathematics, essential for perseverance and success.
6. The Role of Mathematical Proficiency in Data Science: This article examines the specific mathematical skills required for success in the field of data science, highlighting the importance of all five strands.
7. Applying Mathematical Proficiency in Financial Modeling: This article explores the application of mathematical proficiency in the financial industry, with a focus on risk management and investment strategies.
8. Mathematical Proficiency and Engineering Design: This article examines the role of mathematical proficiency in the engineering design process, emphasizing the importance of problem-solving and modeling.
9. Assessing Mathematical Proficiency: Methods and Techniques: This article discusses various methods for assessing the five strands of mathematical proficiency, including both formative and summative assessments.
| 5 strands of mathematical proficiency: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-07-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
| 5 strands of mathematical proficiency: Mathematical Proficiency for All Students: Toward a Strategic Research and Development Program in Mathematics Education Deborah Loewenberg, 2003-04-15 A clear need exists for substantial improvement in mathematics proficiency in U.S. schools. The RAND Mathematics Study Panel was convened to inform the U.S. Department of Education's Office of Educational Research and Improvement on ways to improve the quality and usability of education research and development (R&D). The panel identified three areas for focused R&D: development of teachers' mathematical knowledge used in teaching; teaching and learning of skills needed for mathematical thinking and problem-solving; and teaching and learning of algebra from kindergarten through the 12th grade. |
| 5 strands of mathematical proficiency: Assessing Mathematical Proficiency Alan H. Schoenfeld, 2007-05-21 Testing matters! It can determine kids' and schools' futures. In a conference at the Mathematical Sciences Research Institute, mathematicians, maths education researchers, teachers, test developers, and policymakers gathered to work through critical issues related to mathematics assessment. They examined: the challenges of assessing student learning in ways that support instructional improvement; ethical issues related to assessment, including the impact of testing on urban and high-poverty schools; the different (and sometimes conflicting) needs of the different groups; and different frameworks, tools, and methods for assessment, comparing the kinds of information they offer about students' mathematical proficiency. This volume presents the results of the discussions. It highlights the kinds of information that different assessments can offer, including many examples of some of the best mathematics assessments worldwide. A special feature is an interview with a student about his knowledge of fractions and a demonstration of what interviews (versus standardized tests) can reveal. |
| 5 strands of mathematical proficiency: Response to Intervention in Math Paul J. Riccomini, Bradley S. Witzel, 2010 Provides educators with instructions on applying response-to-intervention (RTI) while teaching and planning curriculum for students with learning disabilities. |
| 5 strands of mathematical proficiency: Principles to Actions National Council of Teachers of Mathematics, 2014-02 This text offers guidance to teachers, mathematics coaches, administrators, parents, and policymakers. This book: provides a research-based description of eight essential mathematics teaching practices ; describes the conditions, structures, and policies that must support the teaching practices ; builds on NCTM's Principles and Standards for School Mathematics and supports implementation of the Common Core State Standards for Mathematics to attain much higher levels of mathematics achievement for all students ; identifies obstacles, unproductive and productive beliefs, and key actions that must be understood, acknowledged, and addressed by all stakeholders ; encourages teachers of mathematics to engage students in mathematical thinking, reasoning, and sense making to significantly strengthen teaching and learning. |
| 5 strands of mathematical proficiency: Education and Learning to Think Division of Behavioral and Social Sciences and Education, Commission on Behavioral and Social Sciences and Education, Committee on Research in Mathematics, Science, and Technology Education, 1987-02-01 The economic and social challenges confronting the nation today demand that all citizens acquire and learn to use complex reasoning and thinking skills. Education and Learning to Think confronts the issues facing our schools as they take on this mission. This volume reviews previous research, highlights successful learning strategies, and makes specific recommendations about problems and directions requiring further study. Among the topics covered are the nature of thinking and learning, the possibilities of teaching general reasoning, the attempts to improve intelligence, thinking skills in academic disciplines, methods of cultivating the disposition toward higher order thinking and learning, and the integral role motivation plays in these activities. |
| 5 strands of mathematical proficiency: Teaching Mathematics Meaningfully David H. Allsopp, David Allsopp (Ph. D.), Maggie M. Kyger, LouAnn H. Lovin, 2007 Making mathematics concepts understandable is a challenge for any teacher--a challenge that's more complex when a classroom includes students with learning difficulties. With this highly practical resource, educators will have just what they need to teach mathematics with confidence: research-based strategies that really work with students who have learning disabilities, ADHD, or mild cognitive disabilities. This urgently needed guidebook helps teachers Understand why students struggle.Teachers will discover how the common learning characteristics of students with learning difficulties create barriers to understanding mathematics. Review the Big Ideas. Are teachers focusing on the right things? A helpful primer on major NCTM-endorsed mathematical concepts and processes helps them be sure. Directly address students' learning barriers. With the lesson plans, practical strategies, photocopiable information-gathering forms, and online strategies in action, teachers will have concrete ways to help students grasp mathematical concepts, improve their proficiency, and generalize knowledge in multiple contexts. Check their own strengths and needs. Educators will reflect critically on their current practices with a thought-provoking questionnaire. With this timely book--filled with invaluable ideas and strategies adaptable for grades K-12--educators will know just what to teach and how to teach it to students with learning difficulties. |
| 5 strands of mathematical proficiency: Proceedings of the 13th International Congress on Mathematical Education Gabriele Kaiser, 2017-10-31 This book is open access under a CC BY 4.0 license. The book presents the Proceedings of the 13th International Congress on Mathematical Education (ICME-13) and is based on the presentations given at the 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 brought together about 3.500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. Directly before the congress activities were offered for 450 Early Career Researchers. The proceedings give a comprehensive overview on the current state-of-the-art of the discussions on mathematics education and display the breadth and deepness of current research on mathematical teaching-and-learning processes. The book introduces the major activities of ICME-13, namely articles from the four plenary lecturers and two plenary panels, articles from the five ICMI awardees, reports from six national presentations, three reports from the thematic afternoon devoted to specific features of ICME-13. Furthermore, the proceedings contain descriptions of the 54 Topic Study Groups, which formed the heart of the congress and reports from 29 Discussion Groups and 31 Workshops. The additional important activities of ICME-13, namely papers from the invited lecturers, will be presented in the second volume of the proceedings. |
| 5 strands of mathematical proficiency: Principles and Standards for School Mathematics , 2000 This easy-to-read summary is an excellent tool for introducing others to the messages contained in Principles and Standards. |
| 5 strands of mathematical proficiency: Learning and Instruction National Research Council, Division of Behavioral and Social Sciences and Education, PANEL ON LEARNING AND INSTRUCTION., Strategic Education Research Partnership, 2003-12-04 The Strategic Education Research Partnership (SERP) is a bold, ambitious plan that proposes a revolutionary program of education research and development. Its purpose is to construct a powerful knowledge base, derived from both research and practice, that will support the efforts of teachers, school administrators, colleges of education, and policy officialsâ with the ultimate goal of significantly improving student learning. The proposals in this book have the potential to substantially improve the knowledge base that supports teaching and learning by pursuing answers to questions at the core of teaching practices. It calls for the linking of research and development, including instructional programs, assessment tools, teacher education programs, and materials. Best of all, the book provides a solid framework for a program of research and development that will be genuinely useful to classroom teachers. |
| 5 strands of mathematical proficiency: Math Curse Jon Scieszka, 1995-10-01 Did you ever wake up to one of those days where everything is a problem? You have 10 things to do, but only 30 minutes until your bus leaves. Is there enough time? You have 3 shirts and 2 pairs of pants. Can you make 1 good outfit? Then you start to wonder: Why does everything have to be such a problem? Why do 2 apples always have to be added to 5 oranges? Why do 4 kids always have to divide 12 marbles? Why can't you just keep 10 cookies without someone taking 3 away? Why? Because you're the victim of a Math Curse. That's why. But don't despair. This is one girl's story of how that curse can be broken. |
| 5 strands of mathematical proficiency: Cleverlands Lucy Crehan, 2016-12-01 As a teacher in an inner-city school, Lucy Crehan was exasperated with ever-changing government policy claiming to be based on lessons from ‘top-performing’ education systems. She resolved to find out what was really going on in the classrooms of countries whose teenagers ranked top in the world in reading, maths and science. Cleverlands documents Crehan’s journey around the world, weaving together her experiences with research on policy, history, psychology and culture to offer extensive new insights into what we can learn from these countries. |
| 5 strands of mathematical proficiency: Number Talks Sherry Parrish, 2010 A multimedia professional learning resource--Cover. |
| 5 strands of mathematical proficiency: Mathematical Understanding for Secondary Teaching Mary Kathleen Heid, Patricia S. Wilson, Glendon W. Blume, 2015 A perennial discussion about teacher development is the optimal content background for teachers. In recent years, that discussion has taken center stage in the work of mathematics education researchers, mathematicians, mathematics professional developers, and mathematics education policymakers. Much of the existing and prior work in this area has been directed toward mathematical knowledge for teaching at the elementary level. The work described in this volume takes a sometimes-neglected approach, focusing on the dynamic nature of mathematical understanding rather than on a stable description of mathematical knowledge, and on mathematics for secondary teaching rather than mathematics for teaching at the elementary level. The work reported in Mathematical Understanding for Secondary Teaching: A Framework and Classroom-Based Situations is a practice-based response to the question of what mathematical understandings secondary teachers could productively use in their teaching. For each of more than 50 events, our team of almost 50 mathematics educators who were experienced mathematics teachers developed descriptions of the mathematics that teachers could use-each of those descriptions (consisting of the event and the mathematics related to the event) is what we call a Situation. We developed our Framework for Mathematical Understanding for Secondary Teaching (MUST) based on an analysis of our entire set of Situations. We call the work practice-based because the MUST framework is based on actual events that we witnessed in our observations of secondary mathematics practice. Groups of mathematics teachers can use this volume to enhance their own understandings of secondary mathematics. School leaders and professional developers in secondary mathematics will find our MUST Framework and Situations useful as they work with teachers in enhancing and deepening their understanding of secondary mathematics. Mathematics teacher educators and mathematicians who teach mathematics to prospective and in-service secondary teachers will be able to couch their mathematical discussions in the Situations-examples that arise from secondary mathematics classrooms. They will be able to use this volume as they design courses and programs that enhance mathematics from the perspectives identified in the MUST framework. Policymakers and researchers can use our MUST framework as they consider the mathematics background needed by teachers. |
| 5 strands of mathematical proficiency: Ready, Set, SCIENCE! National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Board on Science Education, Heidi A. Schweingruber, Andrew W. Shouse, Sarah Michaels, 2007-11-30 What types of instructional experiences help K-8 students learn science with understanding? What do science educators, teachers, teacher leaders, science specialists, professional development staff, curriculum designers, and school administrators need to know to create and support such experiences? Ready, Set, Science! guides the way with an account of the groundbreaking and comprehensive synthesis of research into teaching and learning science in kindergarten through eighth grade. Based on the recently released National Research Council report Taking Science to School: Learning and Teaching Science in Grades K-8, this book summarizes a rich body of findings from the learning sciences and builds detailed cases of science educators at work to make the implications of research clear, accessible, and stimulating for a broad range of science educators. Ready, Set, Science! is filled with classroom case studies that bring to life the research findings and help readers to replicate success. Most of these stories are based on real classroom experiences that illustrate the complexities that teachers grapple with every day. They show how teachers work to select and design rigorous and engaging instructional tasks, manage classrooms, orchestrate productive discussions with culturally and linguistically diverse groups of students, and help students make their thinking visible using a variety of representational tools. This book will be an essential resource for science education practitioners and contains information that will be extremely useful to everyone �including parents �directly or indirectly involved in the teaching of science. |
| 5 strands of mathematical proficiency: Contemporary Debates in Childhood Education and Development Sebastian Suggate, Elaine Reese, 2012-06-14 What are the risks and benefits of non-parental care for young children? What are the short- and long-term effects of academically vs. play-focused environments for learning? How and when should we teach reading? What are the purposes of Education? What is the best way to teach mathematics to children, from preschool and beyond? Contemporary Debates in Childhood Education and Development is a unique resource and reference work that brings together leading international researchers and thinkers, with divergent points of view, to discuss contemporary problems and questions in childhood education and developmental psychology. Through an innovative format whereby leading scholars each offer their own constructive take on the issue in hand, this book aims to inform readers of both sides of a variety of topics and in the process encourage constructive communication and fresh approaches. Spanning a broad spectrum of issues, this book covers: Phonic and whole language reading approaches The developmental effect of non-parental childcare The value of pre-school academic skill acquisition The most effective methods of teaching mathematics Standardized assessment – does it work? The role of electronic media and technology The pedagogical value of homework The value of parents’ reading to children. This book combines breadth of vision with cutting edge research and is a ‘must have’ resource for researchers, students and policy makers in the fields of education and child development. |
| 5 strands of mathematical proficiency: 5 Principles of the Modern Mathematics Classroom Gerald Aungst, 2015-10-09 Students pursue problems they’re curious about, not problems they’re told to solve. Creating a math classroom filled with confident problem solvers starts by introducing challenges discovered in the real world, not by presenting a sequence of prescribed problems, says Gerald Aungst. In this groundbreaking book, he offers a thoughtful approach for instilling a culture of learning in your classroom through five powerful, yet straightforward principles: Conjecture, Collaboration, Communication, Chaos, and Celebration. Aungst shows you how to Embrace collaboration and purposeful chaos to help students engage in productive struggle, using non-routine and unsolved problems Put each chapter’s principles into practice through a variety of strategies, activities, and by incorporating technology tools Introduce substantive, lasting cultural changes in your classroom through a manageable, gradual shift in processes and behaviors Five Principles of the Modern Mathematics Classroom offers new ideas for inspiring math students by building a more engaging and collaborative learning environment. Bravo! This book brings a conceptual framework for K-12 mathematics to life. As a parent and as the executive director of Edutopia, I commend Aungst for sharing his 5 principles. This is a perfect blend of inspiring and practical. Highly recommended! Cindy Johanson, Executive Director, Edutopia George Lucas Educational Foundation Aungst ignites the magic of mathematics by reminding us what makes mathematicians so passionate about their subject matter. Grounded in research, his work takes us on a journey into classrooms so that we may take away tips to put into practice today. Erin Klein, Teacher, Speaker, and Author of Redesigning Learning Spaces |
| 5 strands of mathematical proficiency: The Elements of Creativity and Giftedness in Mathematics B. Sriraman, Kyeong Hwa Lee, 2011-07-23 The Elements of Creativity and Giftedness in Mathematics edited by Bharath Sriraman and KyeongHwa Lee covers recent advances in mathematics education pertaining to the development of creativity and giftedness. The book is international in scope in the “sense” that it includes numerous studies on mathematical creativity and giftedness conducted in the U.S.A, China, Korea, Turkey, Israel, Sweden, and Norway in addition to cross-national perspectives from Canada and Russia. The topics include problem -posing, problem-solving and mathematical creativity; the development of mathematical creativity with students, pre and in-service teachers; cross-cultural views of creativity and giftedness; the unpacking of notions and labels such as high achieving, inclusion, and potential; as well as the theoretical state of the art on the constructs of mathematical creativity and giftedness. The book also includes some contributions from the first joint meeting of the American Mathematical Society and the Korean Mathematical Society in Seoul, 2009. Topics covered in the book are essential reading for graduate students and researchers interested in researching issues and topics within the domain of mathematical creativity and mathematical giftedness. It is also accessible to pre-service and practicing teachers interested in developing creativity in their classrooms, in addition to professional development specialists, mathematics educators, gifted educators, and psychologists. |
| 5 strands of mathematical proficiency: Every Math Learner, Grades K-5 Nanci N. Smith, 2017-02-01 Differentiation that shifts your instruction and boosts ALL student learning! Nationally recognized math differentiation expert Nanci Smith debunks the myths surrounding differentiated instruction, revealing a practical approach to real learning differences. Theory-lite and practice-heavy, this book provides a concrete and manageable framework for helping all students know, understand, and even enjoy doing mathematics. Busy K-5 mathematics educators learn to Provide practical structures for assessing how students learn and process mathematical concepts Design, implement, manage, and formatively assess and respond to learning in a standards-aligned differentiated classroom; and Adjust current instructional materials to better meet students' needs Includes classroom videos and a companion website. |
| 5 strands of mathematical proficiency: Modeling Mathematical Ideas Jennifer M. Suh, Padmanabhan Seshaiyer, 2016-12-27 Modeling Mathematical Ideas combining current research and practical strategies to build teachers and students strategic competence in problem solving.This must-have book supports teachers in understanding learning progressions that addresses conceptual guiding posts as well as students’ common misconceptions in investigating and discussing important mathematical ideas related to number sense, computational fluency, algebraic thinking and proportional reasoning. In each chapter, the authors opens with a rich real-world mathematical problem and presents classroom strategies (such as visible thinking strategies & technology integration) and other related problems to develop students’ strategic competence in modeling mathematical ideas. |
| 5 strands of mathematical proficiency: Math Fact Fluency Jennifer Bay-Williams, Gina Kling, 2019-01-14 This approach to teaching basic math facts, grounded in years of research, will transform students' learning of basic facts and help them become more confident, adept, and successful at math. Mastering the basic facts for addition, subtraction, multiplication, and division is an essential goal for all students. Most educators also agree that success at higher levels of math hinges on this fundamental skill. But what's the best way to get there? Are flash cards, drills, and timed tests the answer? If so, then why do students go into the upper elementary grades (and beyond) still counting on their fingers or experiencing math anxiety? What does research say about teaching basic math facts so they will stick? In Math Fact Fluency, experts Jennifer Bay-Williams and Gina Kling provide the answers to these questions—and so much more. This book offers everything a teacher needs to teach, assess, and communicate with parents about basic math fact instruction, including The five fundamentals of fact fluency, which provide a research-based framework for effective instruction in the basic facts. Strategies students can use to find facts that are not yet committed to memory. More than 40 easy-to-make, easy-to-use games that provide engaging fact practice. More than 20 assessment tools that provide useful data on fact fluency and mastery. Suggestions and strategies for collaborating with families to help their children master the basic math facts. Math Fact Fluency is an indispensable guide for any educator who needs to teach basic math facts. |
| 5 strands of mathematical proficiency: Strength in Numbers Ilana Seidel Horn, 2012 Written by a seasoned teacher, researcher and teacher educator with over two decades of teaching experience, the goal of this book is to support teachers in developing tools for effective group work in their secondary mathematics classrooms. Effective group work engages children’s own thinking and allows them to work together to understand a concept. It can also address problems that often arise in typical mathematics instruction by providing a framework for teachers to create engaging learning environments. The book outlines ways to choose tasks, help students adjust to new ways of approaching schoolwork, and discusses the types of status problems that can impede the most earnest attempts at collaborative learning. This practical, useful book introduces tested tools and concepts for creating equitable collaborative learning environments that supports all students and develops confidence in their mathematical ability. |
| 5 strands of mathematical proficiency: Whose Math Is It? Joseph Michael Assof, 2024-07-31 Foster Confidence and Ownership in Every Math Student When it comes to math, does it feel like some students embrace problem-solving with agency and ownership while others are confused—or simply along for the ride? How do educators bridge that divide to develop competence, confidence, and ownership in every student? The answers lie in establishing clear and effective measures for success. Steeped in the principles of success criteria, Whose Math Is It? provides educators with everything they need to create a classroom environment where students feel empowered to step up and take the lead. Divided into two parts, this must-read guide first defines what success looks like for math students, then provides the research-based best practices teachers can use to help students take control of their learning. Learn how to: Define and establish effective success criteria in a mathematics classroom Implement a variety of strategies to support student ownership and success Develop class-wide social norms specific to math Promote metacognition through self-regulated learning, self-assessment, and feedback Reinforce student ownership through structured peer interactions and collaboration Whose Math Is It? is an essential resource for K-12 math teachers who want to empower their students to actively own their mathematics learning. By emphasizing the importance of success criteria, promoting self-regulated learning, and developing math-specific social norms, this book provides practical strategies for creating an environment where when asked, Whose math is it? every student can emphatically respond: My math! |
| 5 strands of mathematical proficiency: Transforming Primary Mathematics Mike Askew, 2012-02-07 What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in Transforming Primary Mathematics, a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings from the largest research programme into primary mathematics funded in recent years, it offers a clear, practical approach to implementing fundamental change in curriculum, classroom environment and teaching styles. Written by one of the top experts in mathematics education, it offers an inspiring, sometimes controversial, and often unconventional look at the subject of mathematics, by: - Endorsing the use of a 'new mathematics' - one based on problem solving, modelling and inquiry, not on abstract rules, memorising, and regurgitation - Arguing that there is more to maths teaching than 'death by a thousand worksheets' - Challenging norms, such as the practice of sorting children into sets based on their perceived mathematical ability - Asking whether this mathematical ability is innate or a result of social practices - Upholding the idea that mathematics teaching is an adaptive challenge, rather than a technical problem - Advocating an environment where teachers are encouraged to take risks - Looking at how best to prepare learners for an unknown future - Encouraging reflection on teachers' own beliefs and values about mathematics. Transforming Primary Mathematics is for all primary school teachers who want to make mathematics welcoming, engaging, inclusive and successful--Résumé de l'éditeur. |
| 5 strands of mathematical proficiency: Everything You Need for Mathematics Coaching Maggie B. McGatha, Jennifer M. Bay-Williams, Beth McCord Kobett, Jonathan A. Wray, 2018-04-02 Math coaches wear many hats. You think on your feet and have to invent, react, and respond—often without time to prepare—in a myriad of professional contexts. What’s your go-to resource for support? Plan, focus, and lead: Your toolkit for inspiring math teachers Meet Everything You Need For Mathematics Coaching: Tools, Plans, and a Process That Works for Any Instructional Leader. This one-stop, comprehensive toolkit for improving mathematics instruction and learning is designed for busy math coaches and teacher leaders who often have to rely on their own competencies. Using the Leading for Mathematical Proficiency Framework, the authors position student outcomes as the focus of all professional work and connect the Eight Mathematical Practices for students with NCTM’s Eight Effective Teaching Practices to help you guide teachers toward growing mathematics proficiency in their classrooms. This hands-on resource details critical coaching and teaching actions, and offers nearly a hundred tools for: Shifting classroom practice in a way that leads to student math proficiency and understanding of mathematical concepts. Honing in on key areas, including content knowledge and worthwhile tasks, student engagement, questioning and discourse, analysis of student work, formative assessment, support for emergent language learners and students with special needs, and more. Navigating a coaching conversation. Planning and facilitating professional learning communities. Finding a focus for professional development or a learning cycle. Making connections between professional learning activities, teaching, and student learning. Using the coaching cycle—plan, gather data, reflect—to build trust and rapport with teachers. With examples from the field, a comprehensive list of resources for effective coaching, and a plethora of tools you can download and share with teachers, this toolkit is your must-have guide to designing a professional learning plan and leading with clarity and purpose. |
| 5 strands of mathematical proficiency: Conceptual and Procedural Knowledge James Hiebert, 2013-08-21 First Published in 1986. This book is intended for those people who are interested in how mathematics is learned. It is intended especially for those who are interested in the mental processes involved in becoming mathematically competent and the mental processes that inhibit such competency from developing. The volume opens with an overview of the issue and then traces the relationships between conceptual and procedural knowledge in mathematics from preschool days through the years of formal schooling. Mathematics educators and cognitive psychologists from a variety of perspectives contribute theoretical arguments and empirical data to illuminate the nature of the relationships and, in tum, the nature of mathematics learning. |
| 5 strands of mathematical proficiency: Teaching by Design in Elementary Mathematics, Grades K1 Jennifer Stepanek, Melinda Leong, Linda Griffin, 2010-11-16 Strengthen your mathematics lessons through collaborative planning Teaching by Design in Elementary Mathematics is a series of comprehensive professional development guides that help teachers investigate how students learn. Grounded in the latest research, this book is one of three volumes focused on grade-appropriate number and operations topics aligned with the Common Core State Standards. The capstone activity of each book guides the group through the co-creation and implementation of a prototype lesson. The teacher teams then evaluate the impact of the lesson on student learning and work together to revise it for maximum effectiveness. Through the process, teachers develop: Deeper content knowledge of important mathematical concepts Improved understanding of how students learn these mathematical ideas A stronger foundation for developing effective lessons and improving instruction Enhanced collaboration skills Each volume includes a large assortment of reproducible handouts as well as built-in facilitation notes. Teachers will also find helpful resources that address the issue of finding time for school-based professional development and teacher collaboration. |
| 5 strands of mathematical proficiency: Teaching by Design in Elementary Mathematics, Grades 23 Jennifer Stepanek, Melinda Leong, Linda Griffin, 2010-11-19 This professional learning programme for Key Stage 2 mathematics teaching is grounded in the latest research on the characteristics of effective professional development. The materials help teachers: - deepen their content knowledge for important mathematical concepts in their grade - increase their understanding of how students learn these mathematical ideas - use their knowledge to develop effective lessons and improve instruction - enhance their collaboration skills. The mathematical content of Teaching by Design in Mathematics matches content topics in number and operations identified for each grade by the NCTM Curriculum Focal Points. The culminating activity of the programme is the co-creation of a prototype lesson which is taught to students by team members; the team then investigates the impact of the lesson on student learning. The cycle of investigating, planning, teaching, observing, debriefing, and revising a lesson together contributes to a climate of continuous professional learning. |
| 5 strands of mathematical proficiency: How Students Learn National Research Council, Division of Behavioral and Social Sciences and Education, Committee on How People Learn, A Targeted Report for Teachers, 2005-01-23 How do you get a fourth-grader excited about history? How do you even begin to persuade high school students that mathematical functions are relevant to their everyday lives? In this volume, practical questions that confront every classroom teacher are addressed using the latest exciting research on cognition, teaching, and learning. How Students Learn: History, Mathematics, and Science in the Classroom builds on the discoveries detailed in the bestselling How People Learn. Now, these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. Organized for utility, the book explores how the principles of learning can be applied in teaching history, science, and math topics at three levels: elementary, middle, and high school. Leading educators explain in detail how they developed successful curricula and teaching approaches, presenting strategies that serve as models for curriculum development and classroom instruction. Their recounting of personal teaching experiences lends strength and warmth to this volume. The book explores the importance of balancing students' knowledge of historical fact against their understanding of concepts, such as change and cause, and their skills in assessing historical accounts. It discusses how to build straightforward science experiments into true understanding of scientific principles. And it shows how to overcome the difficulties in teaching math to generate real insight and reasoning in math students. It also features illustrated suggestions for classroom activities. How Students Learn offers a highly useful blend of principle and practice. It will be important not only to teachers, administrators, curriculum designers, and teacher educators, but also to parents and the larger community concerned about children's education. |
| 5 strands of mathematical proficiency: Adding It Up National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2001-12-13 Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction. Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics. |
| 5 strands of mathematical proficiency: Mathematical Learning and Understanding in Education Kristie Newton, Sarah Sword, 2018-05-16 Mathematics holds an essential, ubiquitous presence in the education sector, as do ongoing explorations of its effective teaching and learning. Written by leading experts on mathematics and mathematics education, this book situates issues of student thinking and learning about mathematics within the broader context of educational psychology research and theory and brings them to a wider audience. With chapters on knowing and understanding mathematics, mathematical habits, early mathematical thinking, and learning mathematics, this concise volume is designed for any educational psychology, mathematics education, or general education course that includes student learning in the curriculum. It will be indispensable for student researchers and both pre- and in-service teachers alike. |
| 5 strands of mathematical proficiency: Teaching Secondary and Middle School Mathematics Daniel J. Brahier, 2020-03-09 Teaching Secondary and Middle School Mathematics combines the latest developments in research, technology, and standards with a vibrant writing style to help teachers prepare for the excitement and challenges of teaching secondary and middle school mathematics. The book explores the mathematics teaching profession by examining the processes of planning, teaching, and assessing student progress through practical examples and recommendations. Beginning with an examination of what it means to teach and learn mathematics, the reader is led through the essential components of teaching, concluding with an examination of how teachers continue with professional development throughout their careers. Hundreds of citations are used to support the ideas presented in the text, and specific websites and other resources are presented for future study by the reader. Classroom scenarios are presented to engage the reader in thinking through specific challenges that are common in mathematics classrooms. The sixth edition has been updated and expanded with particular emphasis on the latest technology, resources, and standards. The reader is introduced to the ways that students think and how to best meet their needs through planning that involves attention to differentiation, as well as how to manage a classroom for success. Features include: The entire text has been reorganized so that assessment takes a more central role in planning and teaching. Unit 3 (of 5) now addresses the use of summative and formative assessments to inform classroom teaching practices. ● A new feature, Links and Resources, has been added to each of the 13 chapters. While the book includes a substantial listing of citations and resources after the chapters, five strongly recommended and practical resources are spotlighted at the end of each chapter as an easy reference to some of the most important materials on the topic. ● Approximately 150 new citations have either replaced or been added to the text to reflect the latest in research, materials, and resources that support the teaching of mathematics. ● A Quick Reference Guide has been added to the front of the book to assist the reader in identifying the most useful chapter features by topic. ● A significant revision to Chapter 13 now includes discussions of common teaching assessments used for field experiences and licensure, as well as a discussion of practical suggestions for success in methods and student teaching experiences. ● Chapter 9 on the practical use of classroom technology has been revised to reflect the latest tools available to classroom teachers, including apps that can be run on handheld, personal devices. An updated Instructor’s Manual features a test bank, sample classroom activities, Powerpoint slides, chapter summaries, and learning outcomes for each chapter, and can be accessed by instructors online at www.routledge.com/9780367146511 |
| 5 strands of mathematical proficiency: Culturally Responsive Mathematics Education Brian Greer, Swapna Mukhopadhyay, Arthur B. Powell, Sharon Nelson-Barber, 2009-05-20 At a time of rapid demographic change and amidst the many educational challenges facing the US, this critical new collection presents mathematics education from a culturally responsive perspective. It tackles the most crucial issues of teaching mathematics to an ethnically diverse school population, including the political dimension of mathematics education within the context of governmental efforts to improve achievement in school mathematics. Culturally Responsive Mathematics Education moves beyond a point of view that is internal to mathematics education as a discipline, and instead offers a broad perspective of mathematics as a significant, liberating intellectual force in our society. The editors of this volume bring together contributions from many of the leading teachers, teacher educators, researchers, scholars, and activists who have been working to reorient mathematics education in ways that reflect mathematics education as accomplished, first and foremost, through human interactions. |
| 5 strands of mathematical proficiency: Visible Thinking in the K–8 Mathematics Classroom Ted H. Hull, Don S. Balka, Ruth Harbin Miles, 2011-01-21 This book is a crucial tool for meeting NCTM mathematical content and process standards. Through the useful problems and strategies presented within, teachers will definitely know how well their students will comprehend. If comprehension is an issue in your class, this book is a must have! —Therese Gessler Rodammer, Math Coach Thomas W. Dixon Elementary School, Staunton, VA Seeing is believing with this interactive approach to math instruction Do you ever wish your students could read each other′s thoughts? Now they can—and so can you! Veteran mathematics educators Ted Hull, Don Balka, and Ruth Harbin Miles explain why making students′ thought processes visible is the key to effective mathematics instruction. Their newest book contains numerous grade-specific sample problems and instructional strategies for teaching essential concepts such as number sense, fractions, and estimation. Among the many benefits of visible thinking are: Interactive student-to-student learning Increased class participation Development of metacognitive thinking and problem-solving skills Helpful features include vignettes, relevant word problems, classroom scenarios, sample problems, lesson adaptations, and easy-to-follow examples of each strategy in action. The authors also explain how students can demonstrate their thinking using calculators and online tools. The final chapter outlines steps math leaders can take to implement visible thinking and maximize mathematics comprehension for all students. |
| 5 strands of mathematical proficiency: Teaching by Design in Elementary Mathematics, Grades 4–5 Melinda Leong, Jennifer Stepanek, Linda Griffin, Lisa Lavelle, 2010-12-01 Strengthen your mathematics lessons through collaborative planning Teaching by Design in Elementary Mathematics is a series of comprehensive professional development guides that help teachers investigate how students learn. Grounded in the latest research, this book is one of three volumes focused on grade-appropriate number and operations topics aligned with the Common Core State Standards. The capstone activity of each book guides the group through the co-creation and implementation of a prototype lesson. The teacher teams then evaluate the impact of the lesson on student learning and work together to revise it for maximum effectiveness. Through the process, teachers develop: Deeper content knowledge of important mathematical concepts Improved understanding of how students learn these mathematical ideas A stronger foundation for developing effective lessons and improving instruction Enhanced collaboration skills Each volume includes a large assortment of reproducible handouts as well as built-in facilitation notes. Teachers will also find helpful resources that address the issue of finding time for school-based professional development and teacher collaboration. |
| 5 strands of mathematical proficiency: What If Your ABCs Were Your 123s? Leslie Minton, 2007-06-01 Includes teaching scenarios modeling the crossover of literacy and math strategies, and provides techniques to strengthen students' grasp of foundational concepts and advance their skills in reasoning and problem solving. |
| 5 strands of mathematical proficiency: Curriculum Focal Points for Prekindergarten Through Grade 8 Mathematics National Council of Teachers of Mathematics, 2006 Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics: A Quest for Coherence provides a rationale for focal points for each grade level, prekindergarten - 8. |
| 5 strands of mathematical proficiency: Guided Math: A Framework for Mathematics Instruction Sammons, Laney, 2017-03-01 Use a practical approach to teaching mathematics that integrates proven literacy strategies for effective instruction. This professional resource will help to maximize the impact of instruction through the use of whole-class instruction, small-group instruction, and Math Workshop. Incorporate ideas for using ongoing assessment to guide your instruction and increase student learning, and use hands-on, problem-solving experiences with small groups to encourage mathematical communication and discussion. Guided Math supports the College and Career Readiness and other state standards. |
| 5 strands of mathematical proficiency: Teaching Student-Centered Mathematics Pearson Etext Access Code John a. Van De Walle, Jennifer M. Bay-Williams, LouAnn H. Lovin, Karen S Karp, 2017-01-28 NOTE: Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the Enhanced Pearson eText may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase. This access code card provides access to the Enhanced Pearson eText. Helping students make connections between mathematics and their worlds-and helping them feel empowered to use math in their lives-is the focus of this widely popular guide. Designed for classroom teachers, the book focuses on specific grade bands and includes information on creating an effective classroom environment, aligning teaching to various standards and practices, such as the Common Core State Standards and NCTM's teaching practices, and engaging families. The first portion of the book addresses how to build a student-centered environment in which children can become mathematically proficient, while the second portion focuses on practical ways to teach important concepts in a student-centered fashion. The new edition features a corresponding Enhanced Pearson eText version with links to embedded videos, blackline masters, downloadable teacher resource and activity pages, lesson plans, activities correlated to the CCSS, and tables of common errors and misconceptions. Invigorate learning with the Enhanced Pearson eText This access code card provides access to the new Enhanced Pearson eText, a rich, interactive learning environment designed to improve student mastery of content with the following multimedia features: NEW! Embedded videos. The Enhanced Pearson eText now includes links to videos throughout the text that provide examples of students' misconceptions, expand on key concepts, and demonstrate how to implement strategies and techniques in real classrooms. NEW! Downloadable Teacher Resource and Activity Pages that support teaching activities such as formative assessment and team-building are now available in the Enhanced Pearson eText at the point of use. NEW! Downloadable Blackline Masters in Part 2 Chapters. Readers may download Blackline Masters that support the activities and Expanded Lessons by clicking on hyperlinks embedded in the Enhanced Pearson eText. Appendix E includes a list of the Blackline Masters and a thumbnail version of each. *The Enhanced eText features are only available in the Pearson eText format. They are not available in third-party eTexts or downloads. *The Pearson eText App is available on Google Play and in the App Store. It requires Android OS 3.1-4, a 7 or 10 tablet, or iPad iOS 5.0 or later. |
| 5 strands of mathematical proficiency: Helping Children Learn Mathematics National Research Council, Division of Behavioral and Social Sciences and Education, Center for Education, Mathematics Learning Study Committee, 2002-08-31 Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society. |
万分之五怎么写？0.5% 0.5‰ 5‰ ？到底是那个啊？谢谢
万分之五是千分之0.5，也就是0.05%，但是一般不这样写，不过你也可以这样写，有一种新的表达就是千分之0.5，所以是0.5‰。 千分号就是在百分号的基础上再加一个根据好似的圆圈，如 …
上古卷轴5技能点代码是什么-上古卷轴5技能点代码大全_百度知道
Nov 22, 2024 · 上古卷轴5技能点代码是什么呢?在上古卷轴5游戏里，玩家想要升级技能点需要消耗技能点数，因此技能点是相当重要的，那么究竟有什么代码可以帮助大家快速拥有技能点 …
英语的1~12月的缩写是什么？ - 百度知道
5、May无缩写 五月； 6、Jun. June 六月； 7、Jul. July 七月； 8、Aug. August 八月； 9、Sep. September九月； 10、Oct. October 十月； 11、Nov. November 十一月； 12、Dec. …
如何设置win10自动关机命令 - 百度知道
5、确定关机时间，比如图上是2016年5月23日14点整，点击“下一步”。 6、这一步，默认即可，点击“下一步”。 7、程序或脚本输入“shutdown”，添加参数输入“-s”，点击下一步。 8、确认无 …
大乐透的中奖规则 - 百度知道
Aug 19, 2024 · 或者前区5个号码命中2个，后区2个号码命中2个。奖金：15元。追加无奖励。 9、九等奖。中奖规则：前区5个号码命中3个，后区2个号码命中0个。或者前区5个号码命中1 …
月份的英文缩写及全名 - 百度知道
提供月份的英文全名和缩写对照表，帮助用户快速查询和学习。
英文1号到31号日期缩写 - 百度知道
Jun 10, 2022 · 1日：first（1st）、2日：second（2nd）、3日：third（3rd）、4日：fourth（4th）、5日：fifth（5th）、6日：sixth（6th）、7日：seventh（7th ...
身份证尺寸是多少厘米?身份证在a4纸的尺寸大小是多少？
Sep 15, 2024 · 身份证在a4纸的尺寸大小为5.4*8.57厘米。 下面演示身份证图片插入Word时设置为身份证1：1大小的操作流程： 1、首先打开Word，进入“页面布局”下，点击“纸张大小”，把纸 …
取得保密资质的企业事业单位违反国家保密规定的,应受到吊销保密 …
Apr 24, 2025 · 取得保密资质的企业事业单位违反国家保密规定的,应受到吊销保密资质处罚的情取得保密资质的企业事业单位，有下列情形之一的，会被吊销保密资质：资质证书违规使用：变 …
I,IV ,III,II,IIV是什么数字. - 百度知道
对应阿拉伯数字，也就是现在国际通用的数字为：Ⅰ是1，Ⅱ是2，Ⅲ是3，Ⅳ是4，Ⅴ是5，Ⅵ是6，Ⅶ是7，Ⅷ是8，Ⅸ是9，Ⅹ是10。 可以通过打开软键盘打出罗马数字。 点击“软键盘”，选 …
万分之五怎么写？0.5% 0.5‰ 5‰ ？到底是那个啊？谢谢
万分之五是千分之0.5，也就是0.05%，但是一般不这样写，不过你也可以这样写，有一种新的表达就是千分之0.5，所以是0.5‰。 千分号就是在百分号的基础上再加一个根据好似的圆圈，如 …
上古卷轴5技能点代码是什么-上古卷轴5技能点代码大全_百度知道
Nov 22, 2024 · 上古卷轴5技能点代码是什么呢?在上古卷轴5游戏里，玩家想要升级技能点需要消耗技能点数，因此技能点是相当重要的，那么究竟有什么代码可以帮助大家快速拥有技能点 …
英语的1~12月的缩写是什么？ - 百度知道
5、May无缩写 五月； 6、Jun. June 六月； 7、Jul. July 七月； 8、Aug. August 八月； 9、Sep. September九月； 10、Oct. October 十月； 11、Nov. November 十一月； 12、Dec. …
如何设置win10自动关机命令 - 百度知道
5、确定关机时间，比如图上是2016年5月23日14点整，点击“下一步”。 6、这一步，默认即可，点击“下一步”。 7、程序或脚本输入“shutdown”，添加参数输入“-s”，点击下一步。 8、确认无 …
大乐透的中奖规则 - 百度知道
Aug 19, 2024 · 或者前区5个号码命中2个，后区2个号码命中2个。奖金：15元。追加无奖励。 9、九等奖。中奖规则：前区5个号码命中3个，后区2个号码命中0个。或者前区5个号码命中1 …
月份的英文缩写及全名 - 百度知道
提供月份的英文全名和缩写对照表，帮助用户快速查询和学习。
英文1号到31号日期缩写 - 百度知道
Jun 10, 2022 · 1日：first（1st）、2日：second（2nd）、3日：third（3rd）、4日：fourth（4th）、5日：fifth（5th）、6日：sixth（6th）、7日：seventh（7th ...
身份证尺寸是多少厘米?身份证在a4纸的尺寸大小是多少？
Sep 15, 2024 · 身份证在a4纸的尺寸大小为5.4*8.57厘米。 下面演示身份证图片插入Word时设置为身份证1：1大小的操作流程： 1、首先打开Word，进入“页面布局”下，点击“纸张大小”，把纸 …
取得保密资质的企业事业单位违反国家保密规定的,应受到吊销保 …
Apr 24, 2025 · 取得保密资质的企业事业单位违反国家保密规定的,应受到吊销保密资质处罚的情取得保密资质的企业事业单位，有下列情形之一的，会被吊销保密资质：资质证书违规使用：变 …
I,IV ,III,II,IIV是什么数字. - 百度知道
对应阿拉伯数字，也就是现在国际通用的数字为：Ⅰ是1，Ⅱ是2，Ⅲ是3，Ⅳ是4，Ⅴ是5，Ⅵ是6，Ⅶ是7，Ⅷ是8，Ⅸ是9，Ⅹ是10。 可以通过打开软键盘打出罗马数字。 点击“软键盘”，选 …
