The new normal. It turns out that you just can't pass a law or make a regulation these days if it is presented with a readable text of manageable length. Therefore, the new normal is to make the bill or regulation so massive it cannot be understood even by experts. It takes years to read, to modify, and to regulate such instruments. So goes the Affordable Care Act, the Dodd-Frank Act, and outside the Beltway the Common Core Curriculum. In the meantime, lower level functionaries interpret and regulate such ventures. All have in common the aspects of massiveness, incomprehensibility, and interpretable results that take many years to unravel. All have advocates that likewise cannot comprehend what is underway, much less understand long term consequences. This is the new normal of our age. Too big to undermine; too big to critique; too big to deny! Forget simplicity. Forget transparency. Forget clarity. Focus on the talking points - about one page in length.
An inconvenient paradox. Constructivism is a modern, almost post modern, theory of education which promotes students' constructing their own knowledge. We can do away with memorization and rote learning, and replace it by student thinking and learning - is the strong case for constructivism. The curious paradox here is that constructivists marketing this pedagogy in colleges use the traditional lecture format to do so - and without exception. It seems constructivist advocates prefer the teacher centered method of knowledge transfer they lecture to deprecate.
Constructivism is the hot pedagogy of the day. All educators must so advocate it to the exclusion of common sense, history, and results. All too often, we see "research" papers of college faculty invading K-6 classrooms with their new programs, giving heart and soul to their duties, and achieving remarkable conclusions. Yet, the teachers cannot dedicate the kind of time it takes to pull off these miracles of educational excellence - nor can they duplicate the treatment.
All this said, it seems that educators cannot constructively construct a method for pre-service teachers to construct their own understanding of constructivism.
Fuzzy Math. Is 3 x 4 = 11? Certainly not. However, in the newest and currently nearly a national curriculum, the answer is OK, provided the student can give a reasonable explanation, with picture, of why it may be so. The Common Core Curriculum is totally focused on higher order thinking skills even though conclusions may be incorrect. See http://dailycaller.com/2013/08/18/obama-math-under-new-common-core-3-x-4-11-video/
There is much to be said about the student trying to reason out an incorrect answer, but the lesson learned seems that giving a plausible but incorrect answer trumps the correct but possibly memorized answer. There is plenty of time and opportunity to teach students to think and to reason, but it should begin with students having basics for their learning. You've got to begin with something. You must have a knowledge base upon which to think. Moreover, how many teachers have the time or ability to listen to errant explanations?
Problem solving. Many teachers and the entire educational enterprise stress problem solving. Yet, most of them only teach problems solving on problems for which they know well the answers. Few, if any, are active problem solvers on their own. Few know the perils of problem solving when you don't know the answer before hand. Few appreciate the convoluted path the mind may take in solving a problem. Therefore few can really teach a vital skill they do not themselves practice.
Here is an elementary example. The Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,..., with the next being the sum of the previous two. Give an argument that every fourth Fibonacci number is divisible by 3. You can reason this out if you know basics of division, transparently and conveniently. But if you remain at the doorstep of simple computations, you will be lost.
In politics stupidity is not a handicap. --- Napoleon Bonaparte
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