Continuing our series on teaching tech, I’d like to identify another key ingredient of good teaching. (My definition of good teaching is teaching so that the students successfully learn the material that is being taught.) And this ingredient is: It is critical to teach concepts in the proper order. Start with the basics, and build upon them with each subsequent lesson (or section of a lesson). Now, here’s my primary criterion for determining whether lessons are in the proper order: Each lesson can only depend upon previous lessons. That is, a lesson should not yet be taught if understanding it also requires a student to understand another concept that has not been taught yet. Obviously, a new lesson introduces a new concept. But this new concept must have no dependencies upon any concepts that were heretofore not introduced.
The alternative, which is teaching without minding the conceptual dependencies, requires a student to attempt to understand a concept on a superficial level, and wait until its dependencies are taught at which point the student can finally understand the concept more deeply. And that requires the student actually realizing that he or she needs to go back now to this concept and relearn it. It also leaves the student in a confused state until that point. It’s a mind bending and unnatural experience.
While this seems like a no-brainer, it’s actually very tricky to pull off. And that’s because one of our other “Essential Ingredients of Teaching Tech” demands that you can only teach one thing at a time. If you could teach three concepts at once, then things aren’t a big deal. Just teach a concept together with its dependencies all at the same time. But that would be violating the Teach-One-Thing-At-A-Time rule.
Now if understanding C depends upon understanding B, and understanding B depends upon understanding A, then it’s simple. First teach concept A, then B, and then C. But often, your lesson may be a concept that itself has numerous dependencies. Perhaps C depends upon B and A, but it may also depend upon D, G, and Z. And D actually depends on E and T, while T depends upon yet other concepts. And the real world consists primarily of complex examples like this one. And you may even find instances where two concepts depend on each other (a circular dependency), and then you’re really messed over, right?
Like I said, planning a good curriculum is tricky business, but it is doable. The teacher needs to sit down, carefully map out how the various concepts depend on each other, and then carefully arrange the lesson order accordingly. This can take time. This can be painful. But otherwise you’re shifting the pain onto your students. And a good teacher doesn’t do that.
As far as circular dependencies go, I find that the vast majority of the time, the circularity is just an illusion. The trick here is to realize that the concepts really consist of smaller concepts. In most cases, breaking up concepts into smaller ones resolves these infinite loops.