I try to encourage my students to acquire Adaptive expertise. A routine expert might be very accomplished and skilled at exercising a procedural skill, but not well able to deal with one even slightly different. An adaptive expert, partly through conceptual understanding, is able to adapt to new situations. To become adaptive experts, learners must be willing to experiment.
This article, though about math learning for children, provides a good introduction to the notion of adaptive expertise.
Social and Motivational Bases for Mathematical Understanding (Hatano, Giyoo, 1988) DOI: 10.1002/cd.23219884105
[quote] Proposes a model of adaptive expertise that suggests 4 conditions under which students, while using procedures for solving a large number of problems, are motivated to comprehend the procedures and acquire conceptual knowledge: (1) encountering novel types of problems continuously, (2) being encouraged to seek comprehension over efficiency, (3) freedom from urgent need to get external reinforcement, and (4) dialogical interaction. It is noted that when none of these conditions are met, students are unlikely to acquire the conceptual knowledge enabling them to understand the meaning of procedures though they are skilled in the procedures. [/quote]
Prospective Adaptation in the Use of External Representations (Lee Martin Daniel L. Schwartz, 2009) DOI: 10.1080/07370000903221775