Problem Solving in Education

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, and being motivated to pursue this goal of self-improvement.
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 (including Design Method) on thinking skills and how to categorize, organize, and teach them. These two pages, about motivation and skills/methods, are part of a set of related pages by Craig Rusbult about Thinking Skills in Education: Problem Solving (using Design Method & Scientific Method) in a Goal-Directed Curriculum.
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 PBL for science & math - a longer introduction to PBL - ten requirements - challenges for students & teachers (we never said it would be easy!) - two websites to explore (Samford University) (Illinois Math & Science Academy - overview tutorial-intro sitemap book-intro for Problems as Possibilities) - and a links-page. How to use PBL in the Classroom (book intro & two chapters) and Using Real-Life Problems to Make Real-World Connections.
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: 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.