I think understanding is enhanced by starting with examples and I'll do just that.
Yesterday, I finally appreciated recursion. For those of you who are not into programming and logical problem solving, recursion is defined as applying a series of steps used in solving a problem (algorithm - applying an algorithm to itself) to itself. Huh? Exactly! I have kept this superficial understanding for many years with the only practical example replicated in every programming text being that of writing a factorial function. But it was only yesterday that I was able to come up with a need for recursion. Why did it take so long for me to realise this? Perhaps it was because I had not done a lot of programming. But that line of reasoning can easily be challenged by saying that the reason I had not done lots of programming was that I was never made to appreciate programming. I strongly believe that it is possible to make one gradually, independently and permanently (very important!) grasp certain key concepts by solving a major education problem.
Primarily, any education system should be designed around the user - the student. It makes very little sense to structure a curriculum about the discipline as opposed to the nature of application. This undoubtedly gives rise to more problems than it seeks to solve. First of all, as of any activity without an objective, it does not provide adequate appreciation and 'experience' in the areas of intended application. Then, since each discipline gets more and more knowledge added each and every day, it suggests that it should proportionally increase in breadth with little consideration for the timeline within which an 'education' should be completed.
However, all this is trivial in relation to the actual delivery of the education. True, there might be continuously appearing shortcomings but with the appropriate approach it is possible to highlight and judiciously concentrate on those items that will meet a pre-stated objective.
By this I am attempting to answer the fundamental question of why it seems that, at the time that one receives education, it does not seem significant. And to this I have a very simply answer: the education is not presented with an immediate relevance to the student.
As one progresses in education, one gradually encounters problems of increasing relevance to the real world, but failing to take into account this gradual progression from abstract to concrete can render the learning process void of meaning. Generally, students independently fail to appreciate how the abstract points to the concrete (however, those that do will demonstrate significantly higher focus and direction) but it rests squarely on the educator to perform this. Students will exhibit more patience once they realise the intention of the present education.
Let me rephrase this concept: an education system is a process through which the educatee's mind is gradually trained to model problems and solutions using documented concepts. These concepts are generally introductory but later on the educatee is required to map out her own requisition for concepts. In the course of the education, many of the introductory concepts may not bear any significance to the real world as they form a pool of 'latent' knowledge required to appreciate other concepts of greater significance. One could therefore say that the concepts of greater significance are hidden behind the introductory concepts. However, the problem is not in understanding the introductory concepts; the fundamental problem is in presenting the introductory concept in such a way that is relays significance by making use of all concepts appreciated at the time as well as problems relevant at the time.
Therein lies a fundamental problem of education systems.
However, this cannot be applied in learning languages since languages are not based on concepts; rather, concepts are modeled by language. This presents a potential pitfall to be encountered by anyone who attempts to learn a language by concepts.