At the elementary, our teachers utilize CGI or cognitively guided instruction to teach students the fundamentals of math. I must confess this process drives me insane because I actually like rote memorization when it comes to math. I don't have to "think" about how much 9 X 8 equals. I just know. It works for me. I memorized all the formulas in geometry and algebra and chemistry. And I knew when to use them. And at the time, I knew how to use them. Of course those brain cells were destroyed by atrophy because I don't teach math, but every once in awhile, I can dredge up the necessary knowledge to calculate how much tile I need for a bathroom floor or how much paint I need for a room. But I couldn't use a graphing calculator to save my life--unless I can throw it at the threat creating a distraction for my escape!
I must admit that I do find the constructivist approach to knowledge and learning to be an attractive alternative to the drill and kill strategy. And learning by doing is great, as long as what you're learning to do has value outside of the classroom environment. I do believe that students create their knowledge base, and part of our role as educators is to help them make sure that base is a wide, solid platform, and not a spindly, rickety table upon which to build the rest of their house of knowledge. We must bridge the gaps for those students who have not had much exposure and for those students who believe they know everything.
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