"We have to learn our own lessons." (1x06, If Tomorrow Never Comes)

There are four major problem solving approaches: Algorithmic, Heuristic, Insight, and Intuition.  The algorithmic approach involves methodical, logical step taking and is the longest process but results in the least amount of mistakes.  Heuristic problem solvers tend to make quick judgements and go off of past experiences.  They are not the best exam takers and tend to make mistakes much more often.  Insight is usually guided by a sudden novel solution that just comes to you.  This also includes learning from the mistakes of both oneself and others.  Intuitive problem solvers figure everything out with sudden feelings or thoughts.  They don't need practice, they just know exactly what to do.

Christina Yang is a cardiothoracic surgical fellow at Seattle Grace hospital.  Yang graduate from Berkeley and Stanford University and, just like all the others at Seattle Grace, has worked exceptionally hard to get to where she is. Yang is an algorithmic problem solver.  She thinks things through before acting, practices before big surgeries and other activities, and plans out steps to get to where she needs to be.  She knows that no matter how long it takes to finish her job, it will be worth it because she knows that she will be doing her absolute best.

Alex Karev is a resident pediatric surgeon who commonly uses heuristic approaches.  He is known for his egocentric attitude and tends to let his bad attitude get the best of him.  He makes many judgements and knee-jerk reactions without thinking things through all the way.

Mark Sloan was an insightful surgeon and had been referred to as the "go-to-guy" for plastic surgery by Karev (while he was being mentored in plastics by Sloan).  He never really thought things through all the way, and the best ideas would just come to him.  Although he wasn't always successful in his attempts and actions, he still had a consistantly high number number of good outcomes.

Miranda Bailey is an attending specialized in general surgery.  She was referred to as The Nazi because of her intimidating personality, but was always the person who everyone went to for answers.  Bailey always knew just what to do in any given situation, even in the case of the two teenagers who super glued themselves together so they'd never have to part.

(If you're wondering, warm soapy water mixed with acetone - that super glue won't stand a chance.)