This article gives supposedly good advice on what Common Core standards are all about, including this gem:
“Today’s students are learning math differently than their parents, but they are also showing a more sophisticated understanding of math problems and how the answers are derived, rather just than memorizing facts.”
In fact, the emphasis on alternative methods for basic computations in lieu of teaching standard algorithms first often results in confusion and frustration. It used to be that standard algorithms were taught first, and then the alternatives were presented as a “side dish” that provided short cuts as well as additional understanding of how the algorithm worked. Jason Zimba on of the lead writers of the CC math standards has stated that the CC standards do NOT prohibit teaching the standard algorithms earlier than the grade level in which they appear and recommends teaching the standard multi-digit algorithm for addition and subtraction, starting as early as first grade. Nevertheless, the prevalent interpretation of CC standards is to delay teaching the standard algorithms until 4th, 5th and 6th grades, resulting in years of inefficient methods, picture drawing and lack of understanding, despite claims that students show “sophisticated understanding” of math problems.
The article also states:
“Students who are good at listening and following instructions may not be as successful in a Common Core classroom. More emphasis is placed on critical thinking and taking time to explain their thought process, according to The Santa Barbara Independent.”
While the CC web site claims up and down that it does not dictate pedagogy, on the other hand the CC website states: “Students who lack understanding of a topic may rely on procedures too heavily. But what does mathematical understanding look like?” And how can teachers assess it? One way is to ask the student to justify, in a way that is appropriate to the student’s mathematical maturity, why a particular mathematical statement is true, or where a mathematical rule comes from.”
The underlying assumption here is that if a student understands something, he or she can explain it—and that deficient explanation signals deficient understanding. The result has been for students in lower grades to “explain their reasoning” in solving problems so simple that they defy explanation. This passes for “understanding” and “critical thinking” but is really an exercise in frustration for most students, with more important matters like procedures and skills left by the wayside.