A problem is any situation where you have an opportunity to make a difference, to make things better; and problem solving is converting an actual current situation (the NOW-state) into a desired future situation (the GOAL-state). Whenever you are thinking creatively and critically about ways to increase the quality of life (or avoid a decrease in quality) you are actively involved in problem solving.
For example, a motivated student — perhaps inspired by an effective teacher — can adopt a problem-solving approach to personal education by imagining the benefits of improved personal knowledge-and-skill in the future.
Dany Adams (Smith College) helps students learn how to think more effectively by combining critical thinking skill with scientific method: "Because the scientific method is a formalization of critical thinking, it can be used as a simple model that... puts critical thinking at the center of a straightforward, easily implemented, teaching strategy. ... Explicitly discussing the logic and the thought processes that inform experimental methods works better than hoping students will ‘get it’ if they hear enough experiments described."
Problem-Based Learning is a way to improve motivation, thinking, and learning: you can read a brief overview of Problem-Based Learning and (in ERIC Digests) using Problem-Based Learning for science & math plus a longer introduction - ten requirements - challenges for students & teachers (we never said it would be easy!) — two websites to explore (Samford University - PBL background - process - and [click the links] evaluation & more) (Illinois Math & Science Academy - about us [with links to mission,...] and PBL Network [sitemap includes external links]) — the book-intro for Problems as Possibilities - a search in ACSD for problem-based learning - and a comprehensive links-page for Problem-Based Learning. Iowa State University's ThinkSpace is "an instructional and collaborative website designed to provide real-world problems and environments to students."
Basically, this section is Part 2 of Thinking Skills in Education because problem-solving methods (like Design Method and Scientific Method) are just strategies for effectively combining familiar thinking skills in order to achieve a goal, to solve a problem. Thinking Skills and Problem-Solving Methods are closely related, as shown in an Overview of Thinking Skills that compares four perspectives: Design Method (Rusbult), Dimensions of Thinking (Marzano, et al), Infusion of Thinking Skills (Swartz), Four Frames of Knowledge (Perkins); more generally, Problem Solving & Thinking Skills in Education is a sitemap for pages by Craig Rusbult.
ERIC Digests give tips for parents helping their children with problem-solving homework and summarize research about problem solving in science courses.
You can read about "word problems" (like those typically found in textbooks and on exams) and general problem-solving strategies that are also useful outside school. For problem solving in everyday life (including business,...) a series of pages by Robert Harris provides a thorough overview of practical problem solving if you scroll down to the section about "Tools for the Age of Knowledge" and you'll find An Introduction to Creative Thinking, Creative Thinking Techniques, Criteria for Evaluating a Creative Solution, Introduction to Problem Solving, Human-Factor Phenomena in Problem Solving, Problem Solving Techniques, Introduction to Decision Making, and (in other parts of his links-page) much more.
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