I understand both that this is valuable AND how many (most?) education environments are (supposed) to work, but 2 interesting things can happen with the best & brightest:
1. they skip what are to them the obvious steps (we all do as we achieve mastery) and then get penalized for not showing their work.
2. they inherently know and understand the task abut not the mechanized minutia. Think of learning a new language. A diligent student can work through the problem and complete an a->b translation, then go the other way, and repeat. Someone with mastery doesn't do this; they think within one language and then only pass the contextual meaning back and forth when explicitly required.
"showing your work" is really the same thing as "explain how you think" and may be great for basics in learning, but also faces levels of abstraction as you ascend towards mastery.
1. they skip what are to them the obvious steps (we all do as we achieve mastery) and then get penalized for not showing their work.
2. they inherently know and understand the task abut not the mechanized minutia. Think of learning a new language. A diligent student can work through the problem and complete an a->b translation, then go the other way, and repeat. Someone with mastery doesn't do this; they think within one language and then only pass the contextual meaning back and forth when explicitly required.
"showing your work" is really the same thing as "explain how you think" and may be great for basics in learning, but also faces levels of abstraction as you ascend towards mastery.