There are cognitive lessons that require a certain level of maturity to understand. They can be taught by rote prior to the child's readiness but will not truly be understood until the child matures into the lesson. Algebra is taught at a certain age in school mainly because it can't be taught any sooner with much success, and is one example of this kind of learning. It is not merely that the child hasn't learned enough about mathematics to gain from this new twist, it's also that their brains are not developed enough, not ready to think in these new ways. There are studies on this. I looked these up after writing my observations on this matter.
http://www.brainstages.net/Stages1.htm (I'm ending a mental growth spurt.)
http://www.education.com/reference/article/development-cognitive-structure-mathematics/?page=2 (Nichan, read what's "normal" for a child of 18 months!)
Based upon my own experiences and the lives of other people, I have discovered that lessons requiring a certain maturity level continue all through life. There are things I did not understand until a certain level of maturation, and this seems to be true almost every time I learn something new. Furthermore, it explains why past cultures have revered older people. It isn't just that they have more experience; they have actually learned unique-to-their-age lessons from that experience - lessons we can't even perceive till we get there ourselves. These may be cultural adjustments, or adaptive behaviors learned at advanced ages, or it might be due to the 4-year brain maturity model. I'm not a scientist. The fact that this became evident to me without having studied anything about it should indicate that it's an observation with some merit.
Not every "old person" learns all the lessons. Many are stunted due to alcoholism or other barriers to growth but, for the most part, the older a person gets and the more experiences they have, the more they understand about life, particularly if they're paying attention to the lessons. If this sounds like a "duh" statement to you, then you're probably not getting what I mean. I'm saying that there are things we, even as adults, are not cognitively ready to learn or understand until our brains develop fully for understanding the new twist.
Explaining a lesson to someone younger - if the younger person listens - can assist them in the way that rote knowledge can assist you in school. They can avoid pitfalls if they do what they were told. But, even if the advice makes sense to the younger person, they aren't likely to fully understand why they were given that advice until they reach the maturity needed, themselves. This is more than just remembering advice our mothers gave us and finally understanding it due to a life change; it's a biological advancement within the brain.
We can easily see this, as parents, when we try to get a toddler to avoid fire or a young teen to avoid expanding their horizons too quickly for their maturity level. The disconnect between our advice and their understanding is much easier to see at these ages. But, there are similar cognitive disconnects at all ages, something not easily explained to "fully grown" adults in their 20s, 30s, and older. Many of us find the thought offensive that older people might really have some mental advantage to our current selves. Younger brains might work faster, but older brains may actually be more fully developed.
We have not been raised to truly listen to our elders and many of us pooh-pooh their wisdom. Their generation is different from our own. Times are changing too quickly for them to keep up with modern issues. There are a million excuses. I'm guilty of this behavior, myself. And, as I said, not every elderly person paid attention to their lessons. Many had barriers to learning. But, we need to listen. If someone older makes any sense at all, at least pay attention to their advice, whether you follow it or not. They're probably trying to teach you algebra when you're in kindergarten.