If you wish to make an apple pie from scratch, you must first invent the universe.
- Carl Sagan
The above Carl Sagan quote is why most smart people are bad teachers.
Smart, impassioned people know the whole story behind what they're teaching. Smart people like to think about the whole story; they run it through their heads over and over in the shower, while they're cooking, and on the subway. Smart people like to tell other people the whole story, and end up re-inventing the universe when all they set out to do was teach a lesson on a single topic.
(Of course, not all smart people are bad teachers. Being smart and being a good teacher are two separate skills. While being smart certainly can help a teacher's skills, one can not get by as a teacher on being smart alone.)
Telling the whole story is frustrating to students; it's too much to take in all at once. The smart person tends to forget that they learned the whole story over years of intense learning. It's hard for the smart person to let go of pieces of the story -- to consciously omit them -- even if they're not of immediate importance.
If you try to tell the whole story you'll end up writing a whole damned textbook and lose your audience in the process. You'll alienate the people that matter the most: the students. Students are people trying to learn this stuff for the first time and it's easy for a teacher to lose sight of that.
Effective Teaching is a Long ConKnowing what not to teach is just as important as knowing what to teach. If you need to introduce a concept to complete a lesson, then do so -- but don't get pulled into the beauty of the deeper meaning that you understand, because your students don't understand that stuff yet.
Instead, I strive to have my students accidentally learn stuff. Your lessons or lectures or articles should omit the bits that aren't of immediate importance, but leave a little trail of breadcrumbs in the process. Drop little clues about those tangential topics you want your students to come to understand. Eventually your students will piece it all together.
"... this isn't the only way to do this; this is called Euler's method but there are some more sophisticated methods..."
"... electrons orbit the nucleus -- well, almost... Heisenberg's uncertainty principle tells us we can't know exactly what they're doing ..."
"... this is called a linked list -- there's also a doubly-linked list, but we don't need that today ..."
It's hard to accept that many of your students will simply ignore the breadcrumbs you drop, but it's still the right thing to do. Not going into too much detail keeps your lessons accessible. In future lessons you'll leave more breadcrumbs and eventually your students will discover a little puzzle you've left for them.
Why is this my favorite way to teach? The most engaged students will go and research that stuff on their own, and the least engaged students won't get bogged down by extraneous information. Worst-case scenario, a student ends up leaving with exactly what you taught them. Best-case, a student leaves the class with more than you gave them. And often enough, your students will subconsciously piece together the subplot you've laid out -- without even doing the extracurricular research themselves.
The breadcrumb method works because we love solving problems and decoding patterns (see Raph Koster's "A Theory of Fun for Game Design" for some excellent discussion) -- so when the student pieces it together they end up delighted by what they've learned. That's more effective than spoon-feeding them the information, and creates a generation of excited learners in the process.
It's a long con. After months of lessons, you've tricked your students into learning more than they've bargained for. Most students won't even know you conned them. The smart-alecs will even challenge you at times: "you left out ___ !" or "you forgot about friction!" But that's ok -- you're not supposed to impress them. You're supposed to guide and teach the people who need you to keep their best interests in mind, and you need to do that by whatever means necessary.
It sounds strange, but the morally responsible thing to do is carefully and meticulously plan to con your students. With knowledge. Please don't actually con them.