When people are interested in a problem, it seems to me they are more likely to solve it (or at least gain insight into it) on their own, or to be able to follow an offered solution, than when they are not interested in it. When they are interested in a topic, they are more likely to attend to the details offered and to appreciate the significance of those details, than when they are not interested in the topic. There is something about attending to an issue with full energy and focus that makes discovering things about it more likely or more possible than attending to it without any real interest in it. So it seems to me that part of the job of teaching requires nurturing or inspiring genuine interest in a problem or a topic -- or in thinking in general -- by those students who are do not already have the interest. And it certainly requires not killing genuine interest in a subject, or in thinking in general, for those students who already have the interest. By "genuine" interest I mean something like intrinsic interest, not interest in learning just for a grade.
That being said, for even students with fairly high interest, there are better and worse ways to teach in regard to organizing and presenting material, either for lecturing or for asking Socratic questions.
1) If a large amount of information or a substantial series of questions do not have some significant logical or recognizable pattern, students are not likely to see its significance or to retain interest in the material.
2) Even if there is a significant (logical) pattern to information or questions, students may still need help seeing that it exists, and what it is. It is extremely important not only to make sure that students understand material but that they also understand its significance and logic in many cases. Learning material and seeing its significance are two separate things. I write about that more fully in "Writing College Papers (and Exam Answers)" and point out examples in many of the essays in this collection, for the principle applies in teaching as well as in writing nonfiction papers. Many, though not all, topics in school have significance which students never learn while they are just memorizing, or perhaps even understanding, the material.
3) If information or questions have too large a gap between the steps of their logic, students may get frustrated, or conversely may get bored if the gaps between the logical steps are too small. The tendency is to be bored by too much that is obvious, and frustrated by things that do not seem to be related in a way that can be detected.
4) In some cases it is important to let students know that the way material is being presented has nothing to do with how it was discovered. Material in physics or chemistry classes, for example, often is presented through derivations which were only figured out after some phenomenon was discovered by accident, and then tried to be accounted for. But the presentation makes it look like the phenomenon should be obvious from the math, even though it is not. And this can make students mistakenly believe they have no affinity for physics or chemistry or must not really be understanding it, and it can unnecessarily discourage them from learning as much about it as they might. I even tend to think that students would learn physics and chemistry better if it were presented in an "intellectual history" format whereby phenomena that prompted questions were made known, the questions made known, possible answers discussed, the reasons (and experiments) given for the solutions that were accepted historically, and then ensuing phenomena and discoveries that added confirmation or that cast doubt on the theories and or math accepted. I think that would just make physics and chemistry make far more sense than does presenting it as though one ought to be able to just derive everything or understand everything from hearing it "explained."
Now fortunately, various, different, optimal organizational possibilities tend to work for large proportions of people, so that developing optimal, logically organized presentations of questions or information does not need to be totally individualized, and can be done for classroom teaching. The few students, if any, then, who cannot follow one of these generally optimal patterns at some given time can be approached individually to find out where their particular difficulties in understanding lie. Furthermore, astute teachers will learn from the problems groups of students have in understanding any particular presentation, in order to develop and refine it into a more effective lesson the next time they teach it. If there is a necessary step missing in a set of questions or instructions, or if there is an ambiguity that students tend to take the wrong way, or if there is vagueness or anything else that causes misunderstanding, and the teacher is able to figure out what it is, the competent teacher will incorporate it into the presentation next time in order to avoid the same problem with the next class.
Unfortunately figuring out the proper logical teaching steps, which often means figuring out the proper size of the gaps between the steps, is an art rather than a science. It also requires empirical confirmation that one has got it right, for one can be quite confident in one's crafting of an optimal logical layout only to have it not work with students. Proper preparation makes optimal learning possible, but the proof of the value of the presentation is in the students' learning. Although one might be fairly confident in getting close to the proper gaps just by thinking about the material, especially in light of past experiences with students in general or in light of one's own intellectual history of actually learning the material (as opposed to being "taught" it), one can not be reasonably certain of the proper size of logical gaps other than by trial and error with groups of students. Teaching a given lesson requires being able to step in to fill gaps, or to step back and leave out steps, if students seem to be respectively lost or bored.
What strikes me as interesting, though, is that writers and teachers seem to have widely diverse gaps they think appropriate. Math and physics explanations often seem to leave particularly large gaps that students are unlikely to be able to fill by their own thinking, or textbooks and some teachers put in so many minute steps that students cannot see the important points or see the underlying or overarching logic of the principles involved because they get bogged down in the individual details.
In short, it is not clear to me what specifically is involved in helping students have insight into a concept, principle, problem, or solution. Insight does not seem to me to be a verbal matter, nor a verbally transmitted matter. Words can prompt an insight, but the verbal depiction of one person's insight does not necessarily convey the actual insight to a listener or reader who then learns those words. This can be seen in cases where a student can state a principle or solution but not apply it to the next case, or even see that it does apply. And it can be seen in those amusing sorts of situations where after "the light dawns" in the listener, s/he then says exactly what the speaker had earlier said with an intensity of discovery as though s/he had never heard it before. In a sense, s/he had heard the words before, but not the insight. Yet once gaining the insight, s/he uses the exact same words. The insight is not in the words; the words are just a depiction or portrayal of the insight. (See also "Having Understanding Versus Knowing Correct Explanations.")
What is important is for teachers to be continually
looking for gaps or other problems with their explanations and presentations
-- based on whether they are presenting inadequate material or material
inadequately for student comprehension and appreciation, or whether they
are confusing, misleading, boring, or frustrating students into not understanding,
or appreciating the signficance, of the material.