This self directed style of learning is called Unschooling. And I highly recommend it.
We are raising our children this way which is much better than the 'modern' method of schooling:
Get up too early after you've had far too little sleep for a young developing brain.
Go to school and learn this random subject for 45 minutes, bzzzz...
Now learn this different random subject for 45 minutes, bzzzz...
Now learn this different random subject for 45 minutes, bzzzz...
Now take a 10 minute recess, bzzzz...
Now learn this different random subject for 45 minutes, bzzzz...
Now eat some horrible food produced by the lowest bidder, bzzzz...
Now learn this different random subject for 45 minutes, bzzzz...
Now learn this different random subject for 45 minutes, bzzzz...
Now go home and do a bunch of homework with the hopes that this will cement the fragmented 'schooling' you've been doing all day, then go to sleep and start all over tomorrow.
Humans learn organically, by following our passions and interests. Traditional school suppresses this in an effort to create more cogs for our consumption based economy.
I suggest reading, Dumbing us Down by John Taylor Gatto, Unschooling Rules: 55 Ways to Unlearn What We Know About Schools and Rediscover Education by Clark Aldrich, and if you want to take it to the parenting level read Radical Unschooling by Dayna Martin.