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Author: James T. Kinard
Publisher: Cambridge University Press
ISBN: 1139472399
Category : Psychology
Languages : en
Pages : 210
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Book Description
This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.
Author: James T. Kinard
Publisher: Cambridge University Press
ISBN: 1139472399
Category : Psychology
Languages : en
Pages : 210
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Book Description
This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.
Author: Keith J. Devlin
Publisher:
ISBN: 9780615653631
Category : Mathematics
Languages : en
Pages : 0
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Book Description
"Mathematical thinking is not the same as 'doing math'--unless you are a professional mathematician. For most people, 'doing math' means the application of procedures and symbolic manipulations. Mathematical thinking, in contrast, is what the name reflects, a way of thinking about things in the world that humans have developed over three thousand years. It does not have to be about mathematics at all, which means that many people can benefit from learning this powerful way of thinking, not just mathematicians and scientists."--Back cover.
Author: Jordan Ellenberg
Publisher: Penguin Press
ISBN: 1594205221
Category : Mathematics
Languages : en
Pages : 480
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Book Description
A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.
Author: Jonathan D. Katz
Publisher: Rowman & Littlefield
ISBN: 147581058X
Category : Education
Languages : en
Pages : 145
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Book Description
In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.
Author: Jennifer M. Bay-Williams
Publisher: Corwin
ISBN: 1071818430
Category : Education
Languages : en
Pages : 265
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Book Description
Because fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.
Author: Scott V. Burger
Publisher: "O'Reilly Media, Inc."
ISBN: 149197639X
Category : Computers
Languages : en
Pages : 227
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Book Description
Machine learning is an intimidating subject until you know the fundamentals. If you understand basic coding concepts, this introductory guide will help you gain a solid foundation in machine learning principles. Using the R programming language, you’ll first start to learn with regression modelling and then move into more advanced topics such as neural networks and tree-based methods. Finally, you’ll delve into the frontier of machine learning, using the caret package in R. Once you develop a familiarity with topics such as the difference between regression and classification models, you’ll be able to solve an array of machine learning problems. Author Scott V. Burger provides several examples to help you build a working knowledge of machine learning. Explore machine learning models, algorithms, and data training Understand machine learning algorithms for supervised and unsupervised cases Examine statistical concepts for designing data for use in models Dive into linear regression models used in business and science Use single-layer and multilayer neural networks for calculating outcomes Look at how tree-based models work, including popular decision trees Get a comprehensive view of the machine learning ecosystem in R Explore the powerhouse of tools available in R’s caret package
Author: Peter J. Eccles
Publisher: Cambridge University Press
ISBN: 1139632566
Category : Mathematics
Languages : en
Pages : 364
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Book Description
This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
Author: Nicki Newton
Publisher: Routledge
ISBN: 1351164260
Category : Education
Languages : en
Pages : 241
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Book Description
Bring math to life with routines that are academically rigorous, standards-based, and engaging! Go beyond circling ABCD on your bell ringers and do nows and get your students reasoning, modeling, and communicating about math every day! In this new book from bestselling author and consultant Dr. Nicki Newton, you’ll learn how to develop effective daily routines to improve students’ thinking, reasoning, and questioning about math. The book provides a wide variety of rigorous, high-interest routines and explains how to rotate and implement them into your curriculum. Inside, you’ll find: Questioning techniques that encourage students to think beyond the "right vs. wrong" continuum Tips for building a math-learning environment that is friendly and supportive of all students Math vocabulary exercises that are meaningful and fun An assortment of innovative daily activities, including "Fraction of the Day," "Truth or Fib," "Find and Fix the Error," "Guess My Number," "What Doesn’t Belong?" and many, many more. Each chapter offers examples, charts, and tools that you can use immediately. With these resources and the practical advice throughout the book, you’ll increase students’ ability to understand math on a deeper level while keeping them engaged in their own learning processes.
Author: Kassia Omohundro Wedekind
Publisher: Stenhouse Publishers
ISBN: 1571108262
Category : Education
Languages : en
Pages : 216
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Book Description
Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous "math exchanges." The key characteristics of these mathematical conversations are that they are: 1) short, focused sessions that bring all mathematical minds together, 2) responsive to the needs of the specific group of mathematicians, and 3) designed for meaningful, guided reflection. As in reading and writing workshop, students in math workshop become self-directed and independent while participating in a classroom community of learners. Through the math exchanges, students focus on number sense and the big ideas of mathematics. Teachers guide the conversations with small groups of students, mediating talk and thinking as students share problem-solving strategies, discuss how math works, and move toward more effective and efficient approaches and greater mathematical understanding. Although grounded in theory and research, Math Exchanges: Guiding Young Mathematicians in Small Group Meetings is written for practicing teachers and answers such questions as the following: How can I use a math workshop approach and follow a certain textbook or set of standards? How should I form small groups? How often should I meet with small groups? What should I focus on in small groups? How can I tell if my groups are making progress? What do small-group math exchanges look like, sound like, and feel like?
Author: Friedrich Waismann
Publisher: Courier Corporation
ISBN: 0486167429
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Examinations of arithmetic, geometry, and theory of integers; rational and natural numbers; complete induction; limit and point of accumulation; remarkable curves; complex and hypercomplex numbers; more. Includes 27 figures. 1959 edition.
