Download or read book Developing Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9 12 written by Amy B. Ellis and published by National. This book was released on 2012 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on essential knowledge for teachers about proof and the process of proving. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students...and teachers.
Download or read book Developing Essential Understanding of Geometry for Teaching Mathematics in Grades 9 12 written by Nathalie Sinclair and published by National Council of Teachers of English. This book was released on 2012 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why does it matter whether we state definitions carefully when we all know what particular geometric figures look like? What does it mean to say that a reflection is a transformation—a function? How does the study of transformations and matrices in high school connect with later work with vector spaces in linear algebra? How much do you know… and how much do you need to know? Helping your students develop a robust understanding of geometry requires that you understand this mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about geometry. It is organised around four big ideas, supported by multiple smaller, interconnected ideas—essential understandings. Taking you beyond a simple introduction to geometry, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students—and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls, and dispel misconceptions. You will also learn to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently. Move beyond the mathematics you expect your students to learn. Students who fail to get a solid grounding in pivotal concepts struggle in subsequent work in mathematics and related disciplines. By bringing a deeper understanding to your teaching, you can help students who don’t get it the first time by presenting the mathematics in multiple ways. The Essential Understanding Series addresses topics in school mathematics that are critical to the mathematical development of students but are often difficult to teach. Each book in the series gives an overview of the topic, highlights the differences between what teachers and students need to know, examines the big ideas and related essential understandings, reconsiders the ideas presented in light of connections with other mathematical ideas, and includes questions for readers’ reflection.
Download or read book Developing Essential Understanding of Statistics for Teaching Mathematics in Grades 9 12 written by Roxy Peck and published by National. This book was released on 2013 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: How does a statistical model differ from a mathematical model? What are the differences among the sample distribution, the sampling distribution, and the population distribution? In an experiment, what effect does the sampling method have on the results? What are the implications of the use of processes of random selection and random assignment? Can a small sample yield accurate estimates of population parameters? This book examines five big ideas and twenty-four related essential understandings for teaching statistics in grades 9–12. The authors distinguish mathematical and statistical models, explore distributions as descriptions of variability in data, focus on the fundamentals of testing hypotheses to draw conclusions from data, highlight the importance of the data collection method, and recognise the need to examine bias, precision, and sampling method in evaluating statistical estimators. Recognising that analysing data is an important part of understanding the world, the authors discuss the growth of students’ ideas about statistics and examine challenges to teaching, learning, and assessment. They intersperse their discussion with questions for teachers’ reflection.
Download or read book Teaching Mathematics in Grades 6 12 written by Randall E. Groth and published by SAGE Publications. This book was released on 2012-08-10 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching Mathematics in Grades 6 - 12 by Randall E. Groth explores how research in mathematics education can inform teaching practice in grades 6-12. The author shows preservice mathematics teachers the value of being a "researcher—constantly experimenting with methods for developing students' mathematical thinking—and connecting this research to practices that enhance students' understanding of the material. Ultimately, preservice teachers will gain a deeper understanding of the types of mathematical knowledge students bring to school, and how students' thinking may develop in response to different teaching strategies.
Download or read book Answers to Your Biggest Questions About Teaching Secondary Math written by Frederick L. Dillon and published by Corwin Press. This book was released on 2022-03-22 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let’s face it, teaching secondary math can be hard. So much about how we teach math today may look and feel different from how we learned it. Teaching math in a student-centered way changes the role of the teacher from one who traditionally "delivers knowledge" to one who fosters thinking. Most importantly, we must ensure our practice gives each and every student the opportunity to learn, grow, and achieve at high levels, while providing opportunities to develop their agency and authority in the classroom which results in a positive math identity. Whether you are a brand new teacher or a veteran, if you find teaching math to be quite the challenge, this is the guide you want by your side. Designed for just-in-time learning and support, this practical resource gives you brief, actionable answers to your most pressing questions about teaching secondary math. Written by four experienced math educators representing diverse experiences, these authors offer the practical advice they wish they received years ago, from lessons they′ve learned over decades of practice, research, coaching, and through collaborating with teams, teachers and colleagues—especially new teachers—every day. Questions and answers are organized into five areas of effort that will help you most thrive in your secondary math classroom: How do I build a positive math community? How do I structure, organize, and manage my math class? How do I engage my students in math? How do I help my students talk about math? How do I know what my students know and move them forward? Woven throughout, you′ll find helpful sidebar notes on fostering identity and agency; access and equity; teaching in different settings; and invaluable resources for deeper learning. The final question—Where do I go from here?— offers guidance for growing your practice over time. Strive to become the best math educator you can be; your students are counting on it! What will be your first step on the journey?
Download or read book Understanding the Generality of Mathematical Statements written by Milena Damrau and published by Springer Nature. This book was released on with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Developing Essential Understanding of Ratios Proportions and Proportional Reasoning for Teaching Mathematics in Grades 6 8 written by Joanne Elizabeth Lobato and published by National Council of Teachers of English. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A series for teaching mathematics."--P. [1] of cover.
Download or read book Mathematics Teachers Engaging with Representations of Practice written by Orly Buchbinder and published by Springer. This book was released on 2018-01-09 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents innovative approaches and state-of-the-art empirical studies on mathematics teacher learning. It highlights the advantages and challenges of such tools as classroom videos, concept cartoons, simulations, and scenarios. The book details how representations of practice encourage and afford professional development, and describes how these tools help to investigate aspects of teacher expertise, beliefs, and conceptions. In addition, the book identifies the methodological challenges that can emerge and the obstacles educators might encounter when using representations of practice. The book examines the nature of these challenges and provides suggestions for solving them. It offers a variety of different approaches that can help educators to develop professional learning activities for prospective and in-service teachers.
Download or read book We Reason We Prove for ALL Mathematics written by Fran Arbaugh and published by Corwin Press. This book was released on 2018-08-08 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sharpen concrete teaching strategies that empower students to reason-and-prove How do teachers and students benefit from engaging in reasoning-and-proving? What strategies can teachers use to support students’ capacity to reason-and-prove? What does reasoning-and-proving instruction look like? We Reason & We Prove for ALL Mathematics helps mathematics teachers in grades 6-12 engage in the critical practice of reasoning-and-proving and support the development of reasoning-and-proving in their students. The phrase "reasoning-and-proving" describes the processes of identifying patterns, making conjectures, and providing arguments that may or may not qualify as proofs – processes that reflect the work of mathematicians. Going beyond the idea of "formal proof" traditionally relegated only to geometry, this book transcends all mathematical content areas with a variety of activities for teachers to learn more about reasoning-and-proving and about how to support students’ capacities to engage in this mathematical thinking through: Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work that features a range of solution strategies, representations, and misconceptions Modifying tasks from curriculum materials so that they better support students to reason-and-prove Evaluating learning environments and making connections between key ideas about reasoning-and-proving and teaching strategies We Reason & We Prove for ALL Mathematics is designed as a learning tool for practicing and pre-service mathematics teachers and can be used individually or in a group. No other book tackles reasoning-and-proving with such breadth, depth, and practical applicability. Classroom examples, case studies, and sample problems help to sharpen concrete teaching strategies that empower students to reason-and-prove!
Download or read book Developing Essential Understanding of Functions for Teaching Mathematics in Grades 9 12 written by Thomas J. Cooney and published by . This book was released on 2010 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: Are sequences functions? Why can’t the popular “vertical line test” be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? How much do you know… and how much do you need to know? Helping your high school students develop a robust understanding of functions requires that you understand mathematics deeply. But what does that mean? This book focuses on essential knowledge for teachers about functions. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to functions, this book will broaden and deepen your mathematical understanding of one of the most challenging topics for students and teachers. It will help you engage your students, anticipate their perplexities, avoid pitfalls and dispel misconceptions. You will also learn to develop appropriate tasks, techniques and tools for assessing students’ understanding of the topic. Focus on the ideas that you need to understand thoroughly to teach confidently.
Download or read book Mathematical Proficiency for All Students Toward a Strategic Research and Development Program in Mathematics Education written by Deborah Loewenberg and published by Rand Corporation. This book was released on 2003-04-15 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Research in Collegiate Mathematics Education III written by James J. Kaput and published by American Mathematical Soc.. This book was released on 1998 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 3 of Research in Collegiate Mathematics Education (RCME) presents state-of-the-art research on understanding, teaching and learning mathematics at the post-secondary level. This volume contains information on methodology and research concentrating on these areas of student learning: Problem Solving; Understanding Concepts; and Understanding Proofs.
Download or read book Proof and Proving in Mathematics Education written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2012-06-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.
Download or read book Proof in Mathematics Education written by David A. Reid and published by BRILL. This book was released on 2010-01-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education.
Download or read book Principles and Standards for School Mathematics written by and published by . This book was released on 2000 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This easy-to-read summary is an excellent tool for introducing others to the messages contained in Principles and Standards.
Download or read book International Perspectives on the Teaching and Learning of Geometry in Secondary Schools written by Patricio Herbst and published by Springer. This book was released on 2018-04-27 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making.
Download or read book Mathematical Argumentation in Middle School The What Why and How written by Jennifer Knudsen and published by Corwin Press. This book was released on 2017-09-21 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research-based book brings tough Standards for Mathematical Practice 3 standards for mathematical argumentation and critical reasoning alive - all within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding.
