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Download Making Sense of Algebra : Developing Students' Mathematical Habits of Mind TXT, DJV, DOC

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"This book has much to offer teachers of middle and high school algebra who wish to implement the Common Core Standards for all of their students." -Hyman Bass, Samuel Eilenberg Distinguished University Professor of Mathematics & Mathematics Education, University of Michigan "One of the joys of Making Sense of Algebra is how clearly and practically the 'how' question is answered." -Steven Leinwand, American Institutes for Research, author of Accessible Mathematics "Paul Goldenberg and his colleagues have done a fantastic job of connecting mathematical ideas to teaching those ideas." -David Wees, New Visions for Public Schools, New York City "Rare is the resource that offers first-person accounts of teacher experience and insight, accompanied by broad and deep knowledge of the research literature. This book fits the bill, and does so with clarity, warmth, and humor." -Mark Driscoll, Education Development Center, author of Fostering Algebraic Thinking Every teacher wants to help students make sense of mathematics; but what if you could guide your students to expect mathematics to make sense? What if you could help them develop a deep understanding of the reasons behind its facts and methods? In Making Sense of Algebra, the common misconception that algebra is simply a collection of rules to know and follow is debunked by delving into how we think about mathematics. This "habits of mind" approach is concerned not just with the results of mathematical thinking, but with how mathematically proficient students do that thinking. Making Sense of Algebra addresses developing this type of thinking in your students through: using well-chosen puzzles and investigations to promote perseverance and a willingness to explore seeking structure and looking for patterns that mathematicians anticipate finding-and using this to draw conclusions cultivating an approach to authentic problems that are rarely as tidy as what is found in textbooks allowing students to generate, validate, and critique their own and others' ideas without relying on an outside authority. Through teaching tips, classroom vignettes, and detailed examples, Making Sense of Algebra shows how to focus your instruction on building these key habits of mind, while inviting students to experience the clarity and meaning of mathematics-perhaps for the first time. Discover more math resources at Heinemann.com/Math, Developing Students'Mathematical Habits of Mind E. Paul Goldenberg, EDC, Inc., June Mark, EDC, Inc., Jane M. Kang, EDC, Inc., Mary Fries, EDC, Inc., Cynthia J. Carter, The Rashi School,Tracy Cordner, EDC, Inc. Foreword by Steven Leinwand Every teacher wants to help students make sense of mathematics; but what if you could guide your students to expect mathematics to make sense? What if you could help them develop a deep understanding of the reasons behind its facts and methods? In Making Sense of Algebra, the common misconception that algebra is simply a collection of rules to know and follow is debunked by delving into how we think about mathematics. This "habits of mind" approach is concerned not just with the results of mathematical thinking, but with how mathematically proficient students do that thinking. Making Sense of Algebra addresses developing this type of thinking in your students through: using well-chosen puzzles and investigations to promote perseverance and a willingness to explore seeking structure and looking for patterns that mathematicians anticipate finding-and using this to draw conclusions cultivating an approach to authentic problems that are rarely as tidy as what is found in textbooks allowing students to generate, validate, and critique their own and others' ideas without relying on an outside authority. Through teaching tips, classroom vignettes, and detailed examples, Making Sense of Algebra shows how to focus your instruction on building these key habits of mind, while inviting students to experience the clarity and meaning of mathematics-perhaps for the first time., Every teacher wants to help students make sense of mathematics; but what if you could guide your students to expect mathematics to make sense? What if you could help them develop a deep understanding of the reasons behind its facts and methods? In Making Sense of Algebra, the common misconception that algebra is simply a collection of rules to know and follow is debunked by delving into how we think about mathematics. This "habits of mind" approach is concerned not just with the results of mathematical thinking, but with how mathematically proficient students do that thinking. Making Sense of Algebra addresses developing this type of thinking in your students through: using well-chosen puzzles and investigations to promote perseverance and a willingness to explore seeking structure and looking for patterns that mathematicians anticipate finding-and using this to draw conclusions cultivating an approach to authentic problems that are rarely as tidy as what is found in textbooks allowing students to generate, validate, and critique their own and others' ideas without relying on an outside authority. Through teaching tips, classroom vignettes, and detailed examples, Making Sense of Algebra shows how to focus your instruction on building these key habits of mind, while inviting students to experience the clarity and meaning of mathematics-perhaps for the first time.

George McClements - Making Sense of Algebra : Developing Students' Mathematical Habits of Mind read book FB2

Students have grown up with computer-based tools including numerical calculations and computer graphics; the worked-out examples as well as the end-of-chapter exercises often use computers for numerical and symbolic computations and for graphical display of the results.Information Theory is studied from the following points of view: (1) the theory of entropy as amount of information; (2) the mathematical structure of information sources (probability measures); and (3) the theory of information channels.Students already schooled in matrices and linear mappings as well as theorem-proving will quickly proceed to selected chapters from part two.In addition, you may need a CourseID, provided by your instructor, to register for and use Pearson's MyLab & Mastering products.Succeed.Beecher, Penna, and Bittinger's "College Algebra "is known for enabling students to "see the math" through its focus on visualization and early introduction to functions.These chapters demonstrate how observed variables share variance in defining a latent variables and introduce how measurement error can be removed from observed variables.Emphasize problem-solving and reasoning.4.Full solutions. More than 450 illustrations., One of the largest puzzle collections 430 brainteasers based on algebra, arithmetic, permutations, probability, plane figure dissection, properties of numbers, etc.From the simplest concepts of numbers and arithmetic, geometry and algebra, trigonometry and calculus, right through to infinity and chaos theory, Mathematics introduces and explains the most important concepts in accessible, non-technical language.With the Fifth Edition, the authors continue to innovate by creating and positioning review material to provide a more effective tool for teachers and students.