I hope you've taken some behavior analysis classes. I know behaviorism is not very popular in psychology right now but you'd be surprised at just how much research supports the effectiveness of behaviorist methods. It's actually a very misunderstood field, even by psychologists. Contrary to popular belief, behaviorist principles are not relegated to simple behaviors. They can be used to not only explain but also shape some very complex behaviors.
As for Piaget, I do agree that children do go through some biologically determined developmental stages but I think that people too often overestimate just how much of an effect biology has.
No, I didn't take any behaviorism classes. I was in secondary education, and was told those there was only one class at the time, and they prefer that people going into the Master's degree program, or current teachers in the elementary level program take those classes first.
I ended up in an elementary school anyway. But I do have a prospect to land a high school job hopefully next year.
I think that biology does have a fairly large impact on development, though. I wouldn't know how to measure whether you are "overestimating" the impact it may have. But certainly, I am of the strong opinion that age does matter quite a bit. Of course, individuals may vary greatly. But as an example:
Young children are obviously far more emotional than older kids and adults. This, perhaps due to the frontal lobe not fully functional yet, and the neurotransmitters going like crazy in young children. They have yet to develop fully in the area that controls emotion, and planning.
When it comes to education, certainly teaching children plays an enormous role in making the connections. Biology alone cannot get a person to understand even rudimentary arithmetic skills. However, I think that biology does play quite a large role in making it easier to acquire those skills as they get to be around the age of 6 or 7.* Around the age of 12,* for example, is when the frontal lobe naturally grows more connections and develops more fully, increasing the ability to plan out events, and to become more self-conscious about the effects their actions have on those around them.
*Individuals vary to a great degree as I have said. Some, such as those with social disorders, never fully develop the capability to stop themselves from doing something stupid that will result in negative consequences for themselves, like calling a boss a jerk for instance.
So I think it is entirely appropriate to use Piaget as a guideline of what you might expect in any child as they grow older. But certainly, one should be cautious, and take it with a grain of salt.
There have been many and great experiments done with Object Permanence, such as Bower, Baillargeon, Gratch, and etc. I have currently run out of time, so I can't get into this one atm.