This disagreement demonstrates why professional teachers are so valuable. Sometimes the material is important enough that you want to make it as easy to unders

This disagreement demonstrates why professional teachers are so valuable. Sometimes the material is important enough that you want to make it as easy to understand as possible. Sometimes the material is a chance to teach your students how to problem solve. Or how to teach themselves new material. Or to help them become mathematically literate (i.e., able to read a book or paper on their own without your help). A good course/curriculum does both. Some definitions are carefully explained at an intuitive level so that students can struggle with things beyond the defintion. Sometimes the definition is an opportunity to teach students how to go from a formal definition of an intuitive understanding. Or come up with extensions to the definition on their own. Or explore the implications of a definition on their own. In short, are you teaching the definition of a Markov Chain as key content knowledge, or is this being presented as an exercise in mathematical creativity and mathematical problem solving? There is no "right" answer without more context; a good course will do the former with some topics and the latter with others. So this is not a topic-level question. It's a course-level or curriculum-level question. Interestingly, misunderstanding the fundamental tension between "explain well" and "teach people how t learn for themselves" is the source of many public debates on education. E.g., common core Mathematics. Are we teaching students how to add numbers or how to problem solve? Well, ideally both... but the debates always become an either/or.