The Art of Problem Solving texts have been used by tens of thousands of outstanding students, including many winners of major national contests such as MATHCOUNTS and the American Mathematics Competitions.

Problem solving consists of using generic or * ad hoc* methods, in an orderly manner, for finding solutions to problems. Some of the problem-solving techniques developed and used in artificial intelligence , computer science , engineering , mathematics , or medicine are related to mental problem-solving techniques studied in psychology.

Considered the most complex of all intellectual functions, problem solving has been defined as a higher-order cognitive process that requires the modulation and control of more routine or fundamental skills. [4] Problem solving has two major domains: mathematical problem solving and personal problem solving where, in the second, some difficulty or barrier is encountered. [5]

How do you go about teaching problem solving skills? How do you teach pupils the thinking skills necessary to solve mathematical problems in contexts that are unfamiliar to them?

These are difficult questions. I’ll declare upfront that I don’t have the answers to them fully. Nonetheless I have been researching and formulating possible approaches. This post shares with you where I am at with my current thinking and I hope will spark an interesting debate in the comments section where our readers can extend the ideas further.

The participants also reported following experiences of enhanced functioning: low inhibition and anxiety, capacity to restructure problem in larger context, enhanced fluency and flexibility of ideation, heightened capacity for visual imagery and fantasy, increased ability to concentrate, heightened empathy with external processes and objects, heightened empathy with people, subconscious data more accessible, association of dissimilar ideas, heightened motivation to obtain closure, visualizing the completed solution.

In the overview of the experiment, Harman and Fadiman mention that experiments on specific performance enhancement through directed use of psychedelics have gone on in various countries of the world, on both sides of the Iron Curtain. [7]

The USA Mathematical Talent Search (USAMTS) is a free mathematics competition open to all United States middle and high school students.

Student solutions to the USAMTS problems are graded by mathematicians and comments are returned to the students. Our goal is to help all students develop their problem solving skills, improve their technical writing abilities, and mature mathematically while having fun. We wish to foster not only insight, ingenuity and creativity, but also the virtue of perseverance, which is equally essential in scientific endeavors.