“Abstraction is only a sort of trickery and deflection of the mind if it doesn’t constitute the crowning stage of a series of previously concrete actions. The real cause of failure in formal education is therefore essentially the fact that one begins with language instead of beginning with real and material action.” -Jean Piaget, 1976
I think this quote is saying that we need to have hands on learning experiences before we can begin to comprehend the abstract concepts behind them. I think that most of us are presented with abstract concepts when it comes to mathematics rather than activities first. In Algebra or Statistics for example you are first presented with a theorem or a formula rather than a situation in which you may need the formula. Maybe what we should be striving to do instead is present students with a hands-on activity like working with manipulates or creating a project and then explain the theory behind it later. I think I would have personally preferred this approach in many of my math classes.
Samantha Orosco 