There are many ways to face this issue.
Here's a bitter approach: "At what stage is it right to turn the happy little kids into sad little adults?" Whoa! This looks like a leading question, and it doesn't seem to lead to useful action.
Let's tone it down a little bit: "What is the right mix of work and play for kids of different ages?" One can already see a the committee forming to start discussing the types of committees that would be necessary to define the age groups. Lots of stuff to discuss. Not much useful action in the horizon.
Narrowing the previous question down: "At what age should we start teaching kids how to read and write?" This question assumes reading and writing is the first "academic" subject to be taught. The assumption may be wrong, but let's go ahead with it for a while. Since in the modern - knowledge driven - world, it is commonly accepted that academic achievement is critical to personal success, there is a natural tendency to start as early as possible. In many countries the age of starting school is 6, and there is a drive to push a certain level of literacy into kindergarten at the age of 5: Recognizing all the letters, and writing one's own name. In Finland, our favorite example, comprehensive education starts at 7 years old. And, in spite of the late start, Finland scores very high in international reading performance tests - second place in PISA 2006. At the extreme, reading lessons in some traditional Jewish communities starts at the age of 3. A more thorough analysis of literacy studies starting-age vs. achievement can be preformed to make clear statements, but the Finnish example at least suggests that the intuitive tendency to start early may be wrong.
"How much time should be dedicated to formal study?" Raw intuition may suggest that more is better, yet looking at the number of instruction hours vs reading achievements finds Finland and Korea with some of the lowest hours-count and with the highest achievements. In this, too, a thorough analysis is due, but this anecdotal evidence suggests that the intuitive tendency to study a lot may be wrong.
An underlying question is "What activities is the kid's mind geared for, at different ages?" Developmental psychologists have their theories. It is evident that at a young age children can learn to understand and speak languages quite effortlessly. In immigrant communities, it is common to see 3-4 year-olds speaking one language at home, and another language at the playground. In some cases, it's even one language with their father, another with their mother, and a third language outside. They can generally do that without confusing among the different languages. So, if we think being multilingual is good, it would be wise to give very young children the opportunity to study different languages at a very young age. This doesn't take much effort: We only need to expose children to a language, in any context that is interesting to them. No need to study grammar, just play with speakers of that language - either adults or other children.
What about arithmetic? At the age of 3, children seem to enjoy counting. When they start getting an allowance, they start being earnestly interested in adding, and worried about subtracting. If they have siblings, there appears the somewhat stressful issues of comparing amounts and of dividing. Opportunities for learning the basics occur naturally, and can be seized by parents and other educators.
But we don't settle for only the basics. Making a living in the modern world, requires in-depth studies. The same is true of we consider our society as post-modern. The same is also expected to be true for the next few decades - the time in which the graduates of today's education system will live - and make a living. In-depth studies are not quite as natural for young children. They may not be very natural for anybody, but over the years of going through one class after another, we condition ourselves into being able to learn a lot about a little. And many of us are happy with it. We often find our identity in our particular expertise.
About that conditioning: Looking for a bright future for our kids, we keep looking ahead. In kindergarten there is a lot of emphasis on preparing the children for primary school. In primary school, part of the work is directed at preparing the pupils to secondary or intermediate school - the structure varies among countries. And so on: High-School prepares the students for college, and on to the university. Since we keep looking ahead for the next phase, we are in danger of losing sight of where the children are right now: What is the best skill for them to acquire right now, at their present level of development? Maybe it doesn't have anything to do with the university? In the context of education we consistently neglect the present in favor of a vision of the future. This is probably true for many other aspects of our lives, but that's a matter for self-help books, and not for a blog about k12 education.
We manufacture for our children an environment of study throughout the school year. We manufacture after-school enrichment studies . We manufacture summer-school and camp for them to do something useful with their time. We got convinced that anything worth doing, is managed by someone whose profession is to do it. Unless a product, service provider or an activity is formally certified, we don't quite believe it is real. This is not a surprise: The world has become very complex, so we genuinely don't understand much of what is around us. We really don't have control over much that determines how we live. And in the consumer society there are great forces who have a powerful interest in maintaining our sense that we need someone else to make things for us and do things for us. In general, we create an environment for studying, instead of learning.
Together with the many negative traits of humanity, there are a few nice ones. One of them is our capacity to learn naturally. This capacity is very clearly relevant for the basics: Spoken language, literacy, numeracy and quite a few other skills not mentioned here. We humans do have the additional capacity to condition ourselves to do just about anything, including studying in-depth. And we like knowing things in-depth, so we need our education system to promote that ability. We probably can't rely on natural learning alone.
As a result of this discussion, a personal take-home idea for me is this: As much as possible, we should make use of the natural tendency to learn new things, just by exposing children to opportunities and simple motivations to learn the basics: Spoken language, reading & writing, arithmetic, etc. this can be done in play - no need for classes and lessons for learning. Studying should be introduced later, in order to acquire in-depth knowledge of whatever is deemed useful. It is useful to think in concrete terms, just as an example - the ages here are arbitrary and need to be considered carefully. How about: Promote natural learning through play for children up to the age of 9. Then start phasing in some studying (as opposed to learning.) By the age of 18, as much as 50% of a student's time would be studying, the rest will be still natural learning - why give it up?
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