This book encourages readers to shift their thinking about problem posing from the "other" to themselves (i.e. that they can develop problems themselves) and offers a broader conception of what can be done with problems.

As a result of the editors' collaborative teaching at Harvard in the late 1960s, they produced a ground-breaking work -- The Art Of Problem Posing -- which related problem posing strategies to the already popular activity of problem solving. It took the concept of problem posing and created strategies for engaging in that activity as a central theme in mathematics education. Based in part upon that work and also upon a number of articles by its authors, other members of the mathematics education community began to apply and expand upon their ideas. This collection of thirty readings is a testimony to the power of the ideas that originally appeared. In addition to reproducing relevant materials, the editors of this book of readings have included a considerable amount of interpretive text which places the articles in the context of problem solving. While the preponderance of essays focus upon mathematics and mathematics education, some of them point to the relevance of problem posing to other fields such as biology or psychology. In the interpretive text that accompanies each chapter, they indicate how ideas expressed for one audience may be revisited or transformed in order to ready them for a variety of audiences.

The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students’ learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years. ​​

" ... offer[s] a challenging exploration of problem solving mathematics and preparation for programs such as MATHCOUNTS and the American Mathematics Competition."--Back cover

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.

Photographer, author, and educator Roberto Valenzuela has a proven track record for teaching and explaining difficult concepts to photographers of all skill levels. His remarkable ability to break down complicated ideas into understandable, approachable elements that photographers can truly grasp–and then use their newfound knowledge to improve their photography–made his first book, Picture Perfect Practice, a breakout success. In Picture Perfect Posing, Roberto takes on the art of posing. For many photographers, after learning to compose an image and even light it properly, a portrait can still easily be a failure if the pose is not natural, elegant, and serving the needs of both the subject and the photographer. Instead of just showing page after page of poses–like most posing books on the market–Roberto actually breaks down the concept of posing by examining the anatomy, starting with the core foundation: the spinal chord and neck. Building from there, Roberto discusses every component of what makes poses work, as well as fail. How should the model hold her hands? Bend her elbows? Position her fingers? Should the model look toward or away from the camera, and why? It all depends on what the photographer wants for the shot, and Roberto discusses the entire process, from the intent of the photographer through the execution of the pose. For those who have been discouraged by an inability to pose their subjects, or who have simply not known where to start in order to "figure it out," Picture Perfect Posing is the essential resource they need to learn how posing truly works, and how they can learn to direct the exact pose they need for the shot they want.

Can a Christian escape from a lion? How quickly can a rumour spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions where the mathematician's art can be brought to bear. But play often has a purpose. In mathematics, it can sharpen skills, provide amusement, or simply surprise, and books of problems have been the stock-in-trade of mathematicians for centuries. This collection is designed to be sipped from, rather than consumed in one sitting. The questions range in difficulty: the most challenging offer a glimpse of deep results that engage mathematicians today; even the easiest prompt readers to think about mathematics. All come with solutions, many with hints, and most with illustrations. Whether you are an expert, or a beginner or an amateur mathematician, this book will delight for a lifetime.

From facial expression and body angles to camera optics and ideal lighting, this invaluable photography reference discusses all the facets of posing. Featuring 10 acclaimed photographers and their exceptional images, this detailed guidebook illustrates how each artist approaches the practice of posing and offers his/her advice on how to achieve more successful and visually appealing portraits. Business-related concerns are also addressed, ensuring that the professional photographer remains relevant and marketable in terms of composition and style.

Anyone can master the fundamentals of game design - no technological expertise is necessary. The Art of Game Design: A Book of Lenses shows that the same basic principles of psychology that work for board games, card games and athletic games also are the keys to making top-quality videogames. Good game design happens when you view your game from many different perspectives, or lenses. While touring through the unusual territory that is game design, this book gives the reader one hundred of these lenses - one hundred sets of insightful questions to ask yourself that will help make your game better. These lenses are gathered from fields as diverse as psychology, architecture, music, visual design, film, software engineering, theme park design, mathematics, writing, puzzle design, and anthropology. Anyone who reads this book will be inspired to become a better game designer - and will understand how to do it.

Photographers are guided through every aspect of posing—beginning with the consultation and continuing with specific tips for posing children, high school seniors, wedding parties, families, events, teams, groups, and pets—in this comprehensive manual. Maintaining that good posing is 80 percent mental and only 20 percent technical, this guide stresses the importance of communication between photographer and subject to creating a portrait that not only captures the subject’s personality but also makes the subject comfortable, fostering repeat business.