Analytical understandingAnalytical understanding, as opposed to descriptive understanding, involves grasping evidence and methods behind a concept. It requires fluency in basic principles and explains why specialists can "flounder" outside their specialty. Fluency requires extensive training and/or reading of primary literature. In a given field some specialists lack these skills, while some nonspecialists acquire them via interest and perseverance. A good example of the latter is Martin Gardner who was trained as a philosopher, but who wrote math columns for Scientific American. His columns inspired readers to become mathematicians.
Analytical understanding requires fluency in reading primary literature and in conversing with experts. It leads to insights ("aha" experiences). Analytical understanding requires accepting expert criticism on points of disagreement and retreating from views that specialists find unconvincing. If your views are truly enlightening, you'll find ways to convince experts.
The basic skills of analytical thinking are the formal reasoning skills of Piaget. Developing these skills and using them appropriately are major goal of lower level science courses. The Test of Logical Thinking (TOLT) is a rough measure of these skills. Most college students use them sparingly or not at all. Individual subject areas have their own specialized knowledge and reasoning skills. The Chemical Concepts Inventory assesses basic analytical skills of chemistry. Many subject areas, including biological sciences, have no such tests. It's not easy to quantitatively assess subject specific analytical skills.
Educational constructivism assumes that learners create concepts rather than memorize them. Concept construction is important for higher level concepts and where learners begin with misconceptions. In physics, for example, Newtonian mechanics involves several independent principles. Students normally begin with intuitive (Aristotelian) notions of mechanics. Students must unlearn old views and construct new views. They use texts, laboratory demonstrations and discussion. Professionals use professional literature, laboratory experiments and peer discussion; the process is ingrained, intuitive, and barely perceived. For beginners the process is likely opaque.
Successful constructivist learning requires intellectual flexibility, perseverance and fluency in employing tools. Naive peers may reinforce rather than correct misconceptions. Academically elite universities provide exceptional peers. Isolated groups can create and maintain idiosyncratic constructs.
Discussions of constructivism: link 1, link 2, at wikipedia