Search Results for "mathematical-discovery-on-understanding-learning-and-teaching-problem-solving-volume-ii-2"

Mathematical discovery

Mathematical discovery

on understanding, learning, and teaching problem solving

  • Author: George Pólya
  • Publisher: N.A
  • ISBN: N.A
  • Category: Mathematics
  • Page: N.A
  • View: 5401
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Mathematics and Plausible Reasoning: Patterns of plausible inference

Mathematics and Plausible Reasoning: Patterns of plausible inference

  • Author: George Pólya
  • Publisher: Princeton University Press
  • ISBN: 9780691025100
  • Category: Mathematics
  • Page: 225
  • View: 3715
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A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. II, on Patterns of Plausible Inference, attempts to develop a logic of plausibility. What makes some evidence stronger and some weaker? How does one seek evidence that will make a suspected truth more probable? These questions involve philosophy and psychology as well as mathematics.

Knowing and Teaching Elementary Mathematics

Knowing and Teaching Elementary Mathematics

Teachers' Understanding of Fundamental Mathematics in China and the United States

  • Author: Liping Ma
  • Publisher: Routledge
  • ISBN: 1135149496
  • Category: Education
  • Page: 232
  • View: 2606
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Studies of teachers in the U.S. often document insufficient subject matter knowledge in mathematics. Yet, these studies give few examples of the knowledge teachers need to support teaching, particularly the kind of teaching demanded by recent reforms in mathematics education. Knowing and Teaching Elementary Mathematics describes the nature and development of the knowledge that elementary teachers need to become accomplished mathematics teachers, and suggests why such knowledge seems more common in China than in the United States, despite the fact that Chinese teachers have less formal education than their U.S. counterparts. The anniversary edition of this bestselling volume includes the original studies that compare U.S and Chinese elementary school teachers’ mathematical understanding and offers a powerful framework for grasping the mathematical content necessary to understand and develop the thinking of school children. Highlighting notable changes in the field and the author’s work, this new edition includes an updated preface, introduction, and key journal articles that frame and contextualize this seminal work.

The Portable T.A.

The Portable T.A.

A Physics Problem Solving Guide

  • Author: Andrew Elby
  • Publisher: Benjamin-Cummings Publishing Company
  • ISBN: 9780132317139
  • Category: Science
  • Page: 940
  • View: 6507
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For introductory calculus-based physics courses. Volume I covers Mechanics. Volume II covers Electricity and Magnetism. Suitable for use with any calculus-based physics text, this stand-alone collection of problems gives students extensive practice applying the central concepts of physics i.e., the ones most likely to show up on tests. It includes exceptionally detailed solutions that explain the relevant concepts and problem-solving skills involved.

Problem-Solving Through Problems

Problem-Solving Through Problems

  • Author: Loren C. Larson
  • Publisher: Springer Science & Business Media
  • ISBN: 1461254981
  • Category: Mathematics
  • Page: 352
  • View: 6548
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This is a practical anthology of some of the best elementary problems in different branches of mathematics. Arranged by subject, the problems highlight the most common problem-solving techniques encountered in undergraduate mathematics. This book teaches the important principles and broad strategies for coping with the experience of solving problems. It has been found very helpful for students preparing for the Putnam exam.

How People Learn

How People Learn

Brain, Mind, Experience, and School: Expanded Edition

  • Author: National Research Council,Division of Behavioral and Social Sciences and Education,Board on Behavioral, Cognitive, and Sensory Sciences,Committee on Developments in the Science of Learning with additional material from the Committee on Learning Research and Educational Practice
  • Publisher: National Academies Press
  • ISBN: 0309131979
  • Category: Education
  • Page: 384
  • View: 691
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First released in the Spring of 1999, How People Learn has been expanded to show how the theories and insights from the original book can translate into actions and practice, now making a real connection between classroom activities and learning behavior. This edition includes far-reaching suggestions for research that could increase the impact that classroom teaching has on actual learning. Like the original edition, this book offers exciting new research about the mind and the brain that provides answers to a number of compelling questions. When do infants begin to learn? How do experts learn and how is this different from non-experts? What can teachers and schools do-with curricula, classroom settings, and teaching methods--to help children learn most effectively? New evidence from many branches of science has significantly added to our understanding of what it means to know, from the neural processes that occur during learning to the influence of culture on what people see and absorb. How People Learn examines these findings and their implications for what we teach, how we teach it, and how we assess what our children learn. The book uses exemplary teaching to illustrate how approaches based on what we now know result in in-depth learning. This new knowledge calls into question concepts and practices firmly entrenched in our current education system. Topics include: How learning actually changes the physical structure of the brain. How existing knowledge affects what people notice and how they learn. What the thought processes of experts tell us about how to teach. The amazing learning potential of infants. The relationship of classroom learning and everyday settings of community and workplace. Learning needs and opportunities for teachers. A realistic look at the role of technology in education.

The Stanford Mathematics Problem Book

The Stanford Mathematics Problem Book

With Hints and Solutions

  • Author: George Polya,Jeremy Kilpatrick
  • Publisher: Courier Corporation
  • ISBN: 048631832X
  • Category: Mathematics
  • Page: 80
  • View: 9045
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Based on Stanford University's well-known competitive exam, this excellent mathematics workbook offers students at both high school and college levels a complete set of problems, hints, and solutions. 1974 edition.

Mathematics and Plausible Reasoning: Induction and analogy in mathematics

Mathematics and Plausible Reasoning: Induction and analogy in mathematics

  • Author: George Pólya
  • Publisher: Princeton University Press
  • ISBN: 9780691025094
  • Category: Mathematics
  • Page: 280
  • View: 4728
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A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. I, on Induction and Analogy in Mathematics, covers a wide variety of mathematical problems, revealing the trains of thought that lead to solutions, pointing out false bypaths, discussing techniques of searching for proofs. Problems and examples challenge curiosity, judgment, and power of invention.

Powerful Problem Solving

Powerful Problem Solving

Activities for Sense Making with the Mathematical Practices

  • Author: Max Ray
  • Publisher: Heinemann Educational Books
  • ISBN: 9780325050904
  • Category: Education
  • Page: 192
  • View: 7709
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How can we break the cycle of frustrated students who "drop out of math" because the procedures just don't make sense to them? Or who memorize the procedures for the test but don't really understand the mathematics? Max Ray and his colleagues at the Math Forum @ Drexel University say "problem solved," by offering their collective wisdom about how students become proficient problem solvers, through the lens of the CCSS for Mathematical Practices. They unpack the process of problem solving in fresh new ways and turn the Practices into activities that teachers can use to foster habits of mind required by the Common Core: communicating ideas and listening to the reflections of others estimating and reasoning to see the "big picture" of a problem organizing information to promote problem solving using modeling and representations to visualize abstract concepts reflecting on, revising, justifying, and extending the work. Powerful Problem Solving shows what's possible when students become active doers rather than passive consumers of mathematics. Max argues that the process of sense-making truly begins when we create questioning, curious classrooms full of students' own thoughts and ideas. By asking "What do you notice? What do you wonder?" we give students opportunities to see problems in big-picture ways, and discover multiple strategies for tackling a problem. Self-confidence, reflective skills, and engagement soar, and students discover that the goal is not to be "over and done," but to realize the many different ways to approach problems. Read a sample chapter. Save 15% when you purchase 15 copies with a Book Study Bundle!

Proofs and Refutations

Proofs and Refutations

The Logic of Mathematical Discovery

  • Author: Imre Lakatos
  • Publisher: Cambridge University Press
  • ISBN: 1316425339
  • Category: Science
  • Page: N.A
  • View: 7010
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Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.

How Students Learn

How Students Learn

Mathematics in the Classroom

  • Author: Committee on How People Learn: A Targeted Report for Teachers,Board on Behavioral, Cognitive, and Sensory Sciences,Division of Behavioral and Social Sciences and Education,National Research Council
  • Publisher: National Academies Press
  • ISBN: 0309548020
  • Category: Education
  • Page: 231
  • View: 633
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How Students Learn: Mathematics in the Classroom builds on the discoveries detailed in the best-selling 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. This book 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.

Problem Solving in Mathematics Education

Problem Solving in Mathematics Education

  • Author: Peter Liljedahl,Manuel Santos-Trigo,Uldarico Malaspina,Regina Bruder
  • Publisher: Springer
  • ISBN: 3319407309
  • Category: Education
  • Page: 39
  • View: 5605
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This survey book reviews four interrelated areas: (i) the relevance of heuristics in problem-solving approaches – why they are important and what research tells us about their use; (ii) the need to characterize and foster creative problem-solving approaches – what type of heuristics helps learners devise and practice creative solutions; (iii) the importance that learners formulate and pursue their own problems; and iv) the role played by the use of both multiple-purpose and ad hoc mathematical action types of technologies in problem-solving contexts – what ways of reasoning learners construct when they rely on the use of digital technologies, and how technology and technology approaches can be reconciled.

Improving Instruction in Algebra

Improving Instruction in Algebra

  • Author: Margaret Schwan Smith,Edward A. Silver,Mary Kay Stein
  • Publisher: N.A
  • ISBN: 9780807745304
  • Category: Education
  • Page: 150
  • View: 8176
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Helping students develop an understanding of mathematical ideas is a persistent challenge for teachers. This work focuses on ways to engage upper elementary, middle school, and high school students in thinking, reasoning, and problem solving to build their mathematics understanding and proficiency.

Philosophical Dimensions in Mathematics Education

Philosophical Dimensions in Mathematics Education

  • Author: Karen Francois,Jean Paul Van Bendegem
  • Publisher: Springer Science & Business Media
  • ISBN: 0387715754
  • Category: Education
  • Page: 242
  • View: 2361
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This book brings together diverse recent developments exploring the philosophy of mathematics in education. The unique combination of ethnomathematics, philosophy, history, education, statistics and mathematics offers a variety of different perspectives from which existing boundaries in mathematics education can be extended. The ten chapters in this book offer a balance between philosophy of and philosophy in mathematics education. Attention is paid to the implementation of a philosophy of mathematics within the mathematics curriculum.

The Art of Problem Solving

The Art of Problem Solving

The Basics Solutions

  • Author: Sandor Lehoczky,Richard Rusczyk
  • Publisher: N.A
  • ISBN: 9781885875006
  • Category: Problem solving
  • Page: 174
  • View: 1442
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Pedagogy for Creative Problem Solving

Pedagogy for Creative Problem Solving

  • Author: Peter Merrotsy
  • Publisher: Taylor & Francis
  • ISBN: 1351771736
  • Category: Education
  • Page: 254
  • View: 5351
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This book provides students and practising teachers with a solid, research-based framework for understanding creative problem solving and its related pedagogy. Practical and accessible, it equips readers with the knowledge and skills to approach their own solutions to the creative problem of teaching for creative problem solving. First providing a firm grounding in the history of problem solving, the nature of a problem, and the history of creativity and its conceptualisation, the book then critically examines current educational practices, such as creativity and problem solving models and common classroom teaching strategies. This is followed by a detailed analysis of key pedagogical ideas important for creative problem solving: creativity and cognition, creative problem solving environments, and self regulated learning. Finally, the ideas debated and developed are drawn together to form a solid foundation for teaching for creative problem solving, and presented in a model called Middle C. Middle C is an evidence-based model of pedagogy for creative problem solving. It comprises 14 elements, each of which is necessary for quality teaching that will provide students with the knowledge, skills, structures and support to express their creative potential. As well as emphasis on the importance of self regulated learning, a new interpretation of Pólya's heuristic is presented.

Becoming a Problem Solving Genius

Becoming a Problem Solving Genius

A Handbook of Maths Strategies

  • Author: N.A
  • Publisher: N.A
  • ISBN: 9781742396156
  • Category: Problem solving
  • Page: 321
  • View: 4266
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How to Solve It

How to Solve It

A New Aspect of Mathematical Method

  • Author: G. Polya
  • Publisher: Princeton University Press
  • ISBN: 1400828678
  • Category: Mathematics
  • Page: 288
  • View: 9215
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A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out—from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft—indeed, brilliant—instructions on stripping away irrelevancies and going straight to the heart of the problem.

Essays on the Foundations of Mathematics and Logic

Essays on the Foundations of Mathematics and Logic

  • Author: Giandomenico Sica
  • Publisher: Polimetrica s.a.s.
  • ISBN: 8876990143
  • Category: Mathematics
  • Page: 351
  • View: 6355
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Learn Math Fast System

Learn Math Fast System

  • Author: Joleen Mergens
  • Publisher: N.A
  • ISBN: 9780984381494
  • Category:
  • Page: N.A
  • View: 1793
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