Yong Zhao has written a blog article at Washington Post on Common Core.
Zhao’s article was posted at the WaPo blog of Valerie Strauss on January 8, 2013 at 5:00 am
His blog is:
People have posted comments at his blog
=My comment at WaPo
Common Core standards in math are more geared to Euler’s 1765 Algebra text than 19th century understanding of natural numbers and their properties and structure. So Common Core Math is 250 years out of date.
Grassmann, Dedekind and Peano put together the structure of natural numbers and the definition of adding whole numbers and demonstrating their properties. This material is used by math psych researchers like Lance Rips and Jennifer Asmuth or Susan Carey. However, most teachers, standards setters, textbook writers are unfamiliar with this and so can’t read the psych math ed papers.
Having left out the conceptual part of whole numbers, school fall back on the same rote learning that Euler would have recognized. When they get to fractions, the schools make up pseudo nonsense explanations such as that 1/2 + 1/3 = 5/6 can be divined somehow from pizza (It can’t.) Nonetheless, students are made to feel that somehow they are not getting it because they can not accomplish this impossible task.
Having fouled up any possibility of teaching the concepts of numbers, algebra then proceeds to rote problem solving tasks. Students feel it is one random skill after another.
I have developed some versions of the Peano Axioms, the rules of counting by one, suitable for lower grade levels at my blog and in my books. Verbal versions of the Peano Axioms that are easier to grasp are given at my blog New Math Done Right. I also have discussion of some of the math ed psych papers mentioned above.
Common Core is a mixed blessing. It falls far short, but what it replaced is also bad. However, the rigidity of common core now may make it difficult to improve it. For math, it has huge gaps and these will undermine learning.
You can’t teach creativity without mastery of techniques. However, the common core as it plays out in America combined with high stakes testing will tend towards rigidity and to short change more advanced students.
Hermann Grassmann developed his new approach to whole numbers in the 19th century Prussian school system. One imagines that the American Common Core system would not allow that and so is more rigid and bureaucratic even than Prussia. Perhaps even Prussia recognized the need for flexibility and individual initiative in teaching more than No Rule Left Behind does.