Based on a long experience in problem posing and solving, the author gathers into this book a selection of problems addressing middle school, distributed in 8 chapters: numbers and operations on numbers, plane geometry, space geometry, algebraic computation, logic and sets, patterns and functions, measurement, and data processing. Many of these problems are related to the International Kangaroo Competition.
The book focuses on problems that are challenging, routine-free, and inquiry-based, able to involve the solver in rich, authentic mathematical activities. At the same time, within each topic and sub-topic, the solver advances gradually from very simple one-step problems into complex tasks. The purpose is to raise students' interest and willingness to use mathematical modes of thought and presentation (e.g. formulas, models, constructs, graphs, charts) to solve a range of problems in everyday situations. The book content (the page design included) tries to stimulate a positive attitude toward mathematics and towards problem-solving in general, based on respect for truth and a willingness to look for reasons and to assess their validity.
Along the way, insight problems are meant to raise curiosity and motivation, balancing the relationship between mathematics education for the gifted and equity of education for all students. Insight refers to the ability to have a clear, deep, and sometimes sudden, intuitive, understanding of a complicated problem or situation. In this case, the solution may appear as the result of processes that occur when solvers get trapped in an impasse and need to overcome the difficulty by seeing the problem in another way, "outside the box", or by changing the initial representational goal.
For a long time, insight problems have been addressed to the gifted ones only. However, today and tomorrow's workplaces request creativity (as more and more advanced mechanisms and robots take over repetitive work). Therefore, thinking "outside the box" and having the capacity of seeing patterns and making transfers become important features of a successful person, in both the job market and personal life. These capacities can be successfully trained if the method is appropriate, and this book provides such training.
