Types of Knowledge Within a Personal Learning Network

Originally posted as a response to Downes's Mental Models I Find Repeatedly Useful.

"...a carpenter has an understanding that goes beyond the tools...This, not the tools, makes a carpenter."

A carpenter comes to my house and makes claims of her craft, articulating a comprehensive understanding of principles related to her profession.  But after beginning the job,  it is apparent that she lacks the tools necessary to bring about this understanding in the form of evidence.  

The tools are never more important than one's understanding (knowledge, etc.), but they are necessary in reifying an understanding.   That is, knowledge, understanding, etc. are not more important than the materials, objects, technologies, etc. used to demonstrate such knowledge, etc...what is more important is understanding the (synchronic/diachronic) associations between the ideational, material, and social relationships that exist around a particular domain, event, or circumstance.  

How relevant is a knowledgable carpenter who is unable to perform (because of a lack of tools) than one who has no knowledge at all.  Ideas (including declarative knowledge), materials, and social relationships (aka a personal learning network) together bring about tacit knowledge.  To understand any one of them is to understand how the other two form a single (synchronic/diachronic) aggregate. 

It is hard to see how an understanding can ever go beyond the tool.  Artificially, I can see how some might view formal education through the use of quizzes and standardized tests as measuring declarative knowledge in the absence of tacit knowledge (practical skills), where perhaps one could admit that understandings go beyond the tool, but I would not put much weight behind this argument. 

Finally, I can see when one might find clever ways to use simpler or more antiquated technologies to become more effective, efficient, and engaged, but one's understanding is not going beyond the tool.  Instead, this is just an example of understanding ideational, material, and social relationships within a particular context.  Conversely, a teacher who has a traditional ideology related to teaching and learning (which creates inefficiencies, etc.) but uses different kinds of technology in his practice is just demonstrating a lack of understanding between the ideational, material, and social relationships that help define the situation.  It is not a misunderstanding of the technology, course content, or interactional pattern(s) as separate entities, but rather how these three come together and how they influence one another.

Curious how others feel.  When do declarative knowledge, understandings, etc. go beyond the tool?