Lots of interesting reflections here...
I think it's a mistake to create or amplify the already existing dichotomy that would divide kids (and later adults) into those who can to think and those who can make things. IMHO, all kids (and adults) need opportunities to do BOTH, and the two activities are not really as separate as all that.
Given budget cuts, and the trimming of anything that can be portrayed as "extra" (arts, music, shop), one is hard pressed to see clear pathways to any of the skilled trades or artisan crafts....whether it is woodworking, quilting, or pottery, etc. All of these CAN be hobbies, and CAN be much more... to some degree they are rendered hobbies (along with sewing/needlework, cobbling, metal work, glassblowing, much small scale food growing/preparation,etc. ) by the fact that most of the results of these trades are mimicked by mass-produced products, made quickly and cheaply and available in Wal-marts everywhere. Making any of these trades a livelihood only for those who can do (and market) high-end custom work.
Add to that the cultural context of an increasingly passive populus...we are taught to watch things instead of do them, listen to music instead of make it, buy things instead of creating them...taught to seek the instant gratification instead of enjoying the process/journey...
Given all these cultural factors, and the economic ones others have mentioned, I'm not sure we can expect schools to be able to continue and promote what the broader society has explicitly devalued.
Somehow people don't seem to have a problem understanding the merit of keeping sports programs around (sometimes at great expense) because the broader society VALUES the activity (at least in terms of what is displayed). People can argue the benefits of learning teamwork and how to be a "good sport", and encouraging early fitness habits. But having sports stars constantly in the media and the Olympics to strive for is also part of it...
Maybe we need better media coverage...
Like Iron Chef, and Martha Stewart, Trading Spaces and Extreme Makeover Home Edition are starting to create "stars" in cooking, hospitality, home decor, and housebuilding
...maybe we need an American Idol show for luthiers, Instrument Makers of the Rich and Famous?
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