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On this page you'll find books and references to
increase your problem solving capabilities.

  A Problem Solving Approach to Mathematics for Elementary Teachers

Rick Billstein is a Professor of Mathematics at the University of Montana. He is currently working half time in the Mathematics Department teaching courses for future teachers and half time on the Show-Me Project, a NSF-funded project supporting dissemination and implementation of standards-based middle grades mathematics curricula. He has worked in mathematics teacher education at the University of Montana for 30 years and his current research is in the areas of curriculum development and mathematics teacher education. He has served on the Board of Directors of the Montana Council of Teachers of Mathematics and has served and chaired the National Council of Teachers of Mathematics (NCTM) Instructional Issues Advisory Committee. Dr. Billstein has co-authored 18 books including eight editions of A Problem Solving Approach to Mathematics for Elementary Teachers . He typically does about 25 regional and national presentations per year and has traveled to Thailand to work with the international schools there. He also presented at the Fourth International Conference on Mathematics Education in Chicago and served as an organizer and presenter for the ICME-9 conference in Tokyo

  Problem-solving approach to technical and professional writing

Taking a research-based, integrated problem-solving approach to technical and professional writing, this text provides a model that illustrates real working-world solutions to problems that students are likely to encounter in the workplace.

Each chapter begins with a short scenario case study that deals with theoretical or applied issues of technical and professional communication. The problem is carried through its development and resolution, thereby preparing students to deal appropriately and successfully in the professional world.

  Mathematical Thinking: Problem-Solving and Proofs

This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation.

Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics.

Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and Functions. Language and Proofs. Properties of Functions. Induction. PROPERTIES OF NUMBERS. Counting and Cardinality. Divisibility. Modular Arithmetic. The Rational Numbers. DISCRETE MATHEMATICS. Combinatorial Reasoning. Two Principles of Counting. Graph Theory. Recurrence Relations. CONTINUOUS MATHEMATICS. The Real Numbers. Sequences and Series. Continuity. Differentiation. Integration. The Complex Numbers.

For anyone interested in learning how to understand and write mathematical proofs, or a reference for college professors and high school teachers of mathematics.

  Why Not?

Yale professors Barry Nalebuff and Ian Ayres engage readers in an intriguing oxymoron. They believe invention can be automated. Why Not? outlines a populist high-octane approach to creative problem solving. "We aspire for this book to change the way people think about their own ability to change the world."

The authors' ideas and examples--from adopting British water conserving toilets to having telemarketers pay you to listen--bristle with energy, conviction, and occasional loopiness. Their approach upends cliched problem solving models by asking, "What would Croseus (the ancient rich king) do?" They take Edward de Bono's lateral thinking out for a spin, suggesting pay for view television might include a fee for eliminating commercials.

Nalebuff and Ayres are at their best in exploring "Idea Arbitrage," a tool for applying one solution to a host of other problems and yielding day care at IKEA, corporate vanity stamps, and library coffee houses. Some promising concepts, such as the technique of leveraging mistakes to create new solutions, are not as clear as others. Overall, the authors make an entertaining case for the idea that innovators are made and not born.

  Problem-Solving Therapy

"Both revolutionary and pragmatic. It is written by a teacher of therapy, and it stands as one of the very few "how-to" books that really give the reader an opportunity to learn from example."


"The book has justifiably become 'must' reading for family therapy practitioners and supervisors.''

A classic that teaches you how to think in a contextually sensitive, directive, and goal-focused way. A highly readable and practical volume that focuses on solving problems within the context of the entire social unit--the family, the school, the community.
 

  The Art and Craft of Problem Solving

Are you up for the challenge? "This is the only book I know that can be used as a source of problems (as opposed to exercises), provides strategies and intuition into problem solving, and also provides tools and techniques for solving problems.

The integration of these three areas is extremely distinctive and highly commendable." Jeffery Bergen, DePaul University In many ways, solving a mathematical problem is as challenging and exhilarating as reaching the peak of a majestic mountain. Like the climber, the problem solver sets out on a journey where getting lost and finding one’s way are part of the fun. The solution may be elusive, but creative investigation and an adventurous spirit often bring it within grasp.

The challenge is waiting for you inside this exciting text!

This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective

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