Problem solving

This book is addressed to people with research interests in the nature of mathematical thinking at any level, to
people with an interest in "higher-order thinking skills" in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, "rules of thumb" for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.
Train your brain for better decisions, problem solving, and innovation

Think Smarter: Critical Thinking to Improve Problem-Solving and Decision-Making Skills is the comprehensive guide to training your brain to do more for you. Written by a critical thinking trainer and coach, the book presents a pragmatic set of tools to apply critical thinking techniques to everyday business issues. Think Smarter is filled with real world examples that demonstrate how the tools work in action, in addition to dozens of practice exercises applicable across industries and functions, Think Smarter is a versatile resource for individuals, managers, students, and corporate training programs.

Thinking is the foundation of everything you do, but we rely largely on automatic thinking to process information, often resulting in misunderstandings and errors. Shifting over to critical thinking means thinking purposefully using a framework and toolset, enabling thought processes that lead to better decisions, faster problem solving, and creative innovation. Think Smarter provides clear, actionable steps toward improving your critical thinking skills, plus exercises that clarify complex concepts by putting theory into practice. Features include:

A comprehensive critical thinking framework Over twenty-five "tools" to help you think more critically Critical thinking implementation for functions and activities Examples of the real-world use of each tool

Learn what questions to ask, how to uncover the real problem to solve, and mistakes to avoid. Recognize assumptions your can rely on versus those without merit, and train your brain to tick through your mental toolbox to arrive at more innovative solutions. Critical thinking is the top skill on the wish list in the business world, and sharpening your ability can have profound affects throughout all facets of life. Think Smarter: Critical Thinking to Improve Problem-Solving and Decision-Making Skills provides a roadmap to more effective and productive thought.

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