"The famous Swiss psychologist Jean Piaget stated: "to understand is to invent", highlighting the active nature of the learner. The above discussion provides an outline of the theoretical foundation on which Inquiry-Based Learning rests. Furthermore, it provides a summary of the mounting evidence that students who are given the opportunity to learn mathematics through inquiry develop better strategic competence and deeper conceptual understanding of mathematics. "
"the more I questioned the wisdom of this rigid requirement. And eventually my message for students changed from you must show your work to you may show your work. Here's why." The goal of showing work is to understand thinking ... requiring showing work may hinder mathematical thinking by emphasizing computation.
This originally came from Joe. Nice little article on teaching reasoning rather symbol shunting. Uses a study that indicates that most students don't know what an equal sign means (which is certainly my experience) to make its point.