
Students often are so confused that they cannot formulate a question. This is not bad, but is a good starting point in their learning. Getting such a student to talk through a problem, to the best of their abilities, typically causes them to stumble through their words. This is great.
Precision in language is precision in thought is a broadly useful aphorism in diagnosis of misunderstanding. It works from chemistry (our specialty) to computer science to history and well beyond. The "is" in the statement is the hinge between language and understanding. Verbal expression is an outward manifestation of internal comprehension. How does it work? That is, what is the method, and what is the mechanism?
The technique is simple: if you are confused, do not know which way to go, or want to test your knowledge—in a process, a problem or a paragraph—talk it out. Whether it is yourself, a student, a colleague—say what you (they) are trying to think out loud. If your thought process is clear and precise, it will come out clearly and precisely. More likely (because we have already said that there is confusion), at some point, the words won't come, or if they do, they get stumbled, mumbled or crumbled. I repeat—this is great. You have found out 1) your thoughts are not crystallized, and 2) now you know the location of the interface between crystalline and fluid thought—between ordered stacking of ideas and those ideas in flux. "Flux" is a good word for this because flux is a substance that allows another substance, say a solder or high temperature metal oxide, to more easily liquefy and work its way into a space where it can make connections.
Computer scientists use this method in programming. In the center of a large program, the connections between parts— counting loops, subroutines, objects and the more complicated—may get confused. Just adding to the program may not help without knowing what the system is doing. Confusion creeps in, and errors can slip in upon execution of the program. So, "Tell the Duck". The programmer will have a rubber duck on the desk to confide in. Our friend Quackers never complains and only occasionally will squeak. But Quackers listens as you try to explain what the program should be doing. When you get to a point where you lack precision in thought, you stumble, and Quackers knows that you have a problem and where the, so to speak, stumbling block is. Quackers is never judgmental, but is never fooled.
This works wherever you are and whatever problem you may have. Communication with yourself is the key. Consider yourself, as a student in a history class writing an essay or in the work-a-day world writing a memo. A paragraph does not work, and you do not know why. Tell Quackers. When you stumble, you know where your blockage is: you need to fix something. Remove that block, and if you no longer stumble, likely it is fixed. It is scary and satisfying how well this works.
As an instructor, in having a student verbally explain (in class, online or in the office), you can go a bit farther than Quackers. You, having identified the understanding/confusion interface (the knowledge space). You can bring your experience to help the student go from the flux of confusion to the crystallization of understanding.
We know that creation of understanding is an ongoing process, just as the ordering and stacking at an interface creates a new interface. We expand the knowledge space; we joyfully expand minds. Joy goes beyond happiness; it brings contentment despite, because and through difficulties—trials. This method—and for that matter, joy—does not dispense with trials, but it identifies the source through verbal reflection. And this joy is just part of the beauty of learning.