In response to another part of Mark's blog post at http://www.amazon.com/gp/blog/post/PLNK13L1MC1Q3613J
I haven't seen the arguments for and against teaching design patterns early. My guess is that the argument for would be that a design pattern might be something easier to have a conversation about than code or pseudo code - and that the conversation is good for learning the structure of complex systems
But the complaint about your blog is really that, to quote alan, that the "three examples are very different and don't really deserve to go together"
I just reread Seymour Papert's "The Gears of My Childhood" and I think you do oversimplify what he was saying to a level which degrades his real communication
He is saying that his early childhood playing with gears, especially the differential gear, played a big part in his creation of a mental model that was invaluable for his later understanding of some aspects of maths, including:
- that a system could be lawful and comprehensible without being rigidly deterministic
- multiplication tables
- equations with two variables
It also served as a model to help him understand Piaget's assimilation. At this point he pauses to mention / criticise Piaget for not saying more about the emotional ("affective") aspect of assimilation, only focusing on the cognitive side.
A bit later Papert says:
"I fell in love with the gears. This is something that cannot be reduced to purely 'cognitive' terms. Something very personal happened ..."
Papert's argument is that intense immersion in certain "objects to think with" (eg. gears in his individual case, logo and LEGO) can lead to the development of internal useful mental models that can be applied to new learning at a later date
I think what Papert is saying is consistent or at least not inconsistent with what you say in paragraph four of your original:
"... As we think about and generalize across our concrete associations, we create new associations that abstract the concrete knowledge we have. These newly inferred associations generalize the concrete details, in the sense that they make clear what's an important detail and what isn't, based on what are the common parts of the concrete associations we're connecting. As we learn new concrete associations, we might recognize the abstractions as being immediately applicable, because they match the common and unnecessary details of other experiences we know. We might also infer new abstractions that take into account both older concrete associations, older abstractions, and new associations."
btw I'm not saying that Papert is necessarily correct. From my reading of more recent research about the mind (eg. Andy Clark, Daniel Dennett) the whole idea of internal mental models (and Minsky's frames) seems to be now regarded as suspect. I don't really know. Nevertheless, my gut feeling is still that Papert's position here does provide a useful guide to good practice. Since there is no unified learning theory we have to cherry pick the best bits.
cheers,
--
Bill Kerr
http://billkerr2.blogspot.com/