A teacher can only do what he or she can do. And incidentally, learning does not occur exclusively in schools. My granddaughter learned to read and write over summer vacation; heck yeah the school helped a lot but she knew ABC backward and forward before she showed up for kindergarten.
There is a strong case for that. Hell, look at it this way - up until 5th or 6th grade, all you are really learning is how to learn, and specifically how to learn in a public-school environment. It's not 'til middle school that you actually start real learning of actual learning stuff.
Using the tools is a part of almost all learning processes. You are right that the lower grades teach skills that are used later but I can argue that if you can't read, you can't interpret Walden for me. Or if you can't do basic math such as factoring, you will never master calculus.
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