As far as I can tell, the extremely shrill, extremely ideological opposition to Common Core is the educational equivalent of NIMBY-ism: reactionary opposition to change of any kind,
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The more I see parents bringing up stuff like this as to how "stupid" the Common Core math curriculum is, the more I realize that the fundamental problem is that the parents aren't educated well enough to understand why this is a good way to teach math. Which is a great argument for a new way of doing things: the old way of doing things apparently utterly failed with these parents, who don't even understand that they don't understand.
I understand the use of math visualization as one of a number of tools to teach math, and I have seen it used very sucessfully, but the small bit of the "common core" implementation of teaching math is not done well at all. I have also seen the "traditional" method done poorly, so at some level I have to blame the education of our teachers. (i.e. we don't know how to teach teachers to teach).
My example of poorly done traditional method actually leads to my example of well done math visualization. My son had been able to perform basic addition since kindergarten (I had done many math-game type activites, so I knew he was capable.) However, in second grade, his teacher required each student to finish a page of 30 addition problems within a minute, before they could then progress to the next page of 30 addition problems. Easy enough right? this gives you one second to parse the problem, and one second to write. About half way through the year we were informed by the teacher that my son was still on the first page of problems, and was now refusing to even attempt to do them, choosing to put zeros in, or nothing, for every answer. What we didn't realize at the time was that my son was slightly disgraphic (hand-eye writing coordination issue). After another quarter of the year, and many conferences later, my wife thought to ask my son to write the numbers 1 to 30 on a page. Guess what, it took him just slightly longer than 60 seconds to do it. The end of this half of the story is that my son was completely put off of learning math by this teacher.
That summer I saw an ad for Mathnasium, a math tutoring franchise which claimed to "make math fun". We thought it worth a try, and indeed they were able to help with the math self-image/attitude that my son had acquired from the second grade teacher. A big part of Mathnasium's approach involves developing math visualization techniques. The thing is that they don't stop there, they continue on to the more traditional computational methods, which scale much better as the math becomes more complex. ( I highly recommend this franchise if it is available near you.)
Fast forward a couple of years.... math is one of my son's best subjects. The school switches to a new text-book/curriculum across the district. We attend presentations by the publisher. The teaching method presented is to be to introduce multiple ways to do the calculations, such that the student can use whichever method works best for them. Sounds good right? The problem is that when the teachers present it, they insist that all the students learn all of the different methods presented, and they specify that each set of problems is to be performed with a particular method. This doesn't work well, of course, because few students become good at all of the methods. I admit that several of the multiplication and long division methods are interesting shortcuts, but they don't seem lead to a good understanding of how the processes work at a more general level. (ie. they don't scale well). My son manages well enough, anyway.
Another few years, and my younger daughter is now going through the schools, except now it is common core. Instead of multiple methods, there is one method which MUST be followed, and that is the visualization "boxes" that others here have described well. It doesn't matter if you get the answer right in the end, if it looks like you were trying to draw the boxes correctly. On the contrary, if you know how to do math, and get the answer correct, but haven't figured out how the textbook wanted the boxes to be partitioned, you get the problem marked wrong. My daughter is also fairly good at math, and finds this very frustrating. My conclusion is that the talent of the teacher is as much or more than the particular method being used. ( assuming that a better teacher would teach around the text in this case.)
As a result, if it weren't for hearing the same situations described by many other "common core(d)" parents, I would blame the specific teachers. However, with so many similar stories, including from different areas of the country, I can only assume that this is how the teachers are being instructed to present (and grade) the topic. Mathnasium shows that it can be done well, but obviously this isn't what is happening in the standard classroom.
p.s. Before anyone accuses me of disliking teachers, both of my parents were teachers. I just have more respect for some, than I do for others.