I recently came across some posts by my brother in the comments section over on NRO. The subject was the Common Core. He and I seem to agree about one thing: there is nothing, or little, actually in the math standards that are objectionable. The point-by-point details in the Common Core, of what students should learn each year, aren't that bad. Many people—even the CC’s strongest critics—admit that the CC math standards are better than what most of the states had before. I follow the arguments surrounding the Common Core's math standards fairly intensively and rarely have I seen actual nit-picking of individual standards. (Apart from the fact that they are often written in bureaucratic gobbledygook.)

The criticism I have seen hits many different notes:

- The pacing is slow. James Milgram, one of the CC's major critics, has said that the CC puts US kids one year behind our peer countries' math curricula by 5th grade, and two years behind by the end of 7th grade. In other words, what we teach in 7th, other countries cover in 5th. And it gets worse every year.
[ James Milgram ] For example, by the end of fifth grade the material being covered in arithmetic and algebra in the Core Standards is more than a year behind the early grade expectations in most high achieving countries. By the end of seventh grade Core Standards are roughly two years behind.

In addition, a lead writer of the Core, Jason Zimba, has said in a public forum and on camera that the math standards are "not only not for STEM, they are also not for selective colleges." In other words, students who follow the CC pacing in math will not be prepared to get into a selective college and will not be prepared to study a STEM field if they do get in. Zimba can be seen saying this in the short movie "Building the Machine" starting at about 20:40 in.

Keep in mind what this means: no student who follows the Common Core’s pacing will be prepared to major in math, science or engineering in college.

When Jason ZImba was later questioned about his public statements that the CC math standards would not prepare kids for selective colleges or for STEM studies, he tried to say that he never said anything of the sort. Only when he was faced with the actual video of him saying exactly that, was he forced to address the issue. He continues to obfuscate and pretend that he didn’t really say what he clearly said.

Did he misspeak? Most people who look over the standards would say that he did not; the CC math standards are minimalist and aimed at making sure that everyone has a basic level of competence. They are not aimed at the high end of the spectrum or at future math and science majors. In addition, the Common Core documentation states that it prepares kids for the level of study provided at community colleges, and not for studies at more rigorous schools. - This brings up a semi-related point. I recently was talking to a parent in the Santa Monica school system. She has a daughter in 6th grade who is advanced in math. She is ready to take algebra next year. However, Santa Monica's adoption of the CC has included a jettisoning of all accelerated tracks of math study. Her daughter will not be allowed to take algebra in school until 9th grade. I remember when California passed the law adopting the CC, it did so in a rigid manner. The law said that what the CC says students should be taught in 7th is what
**all**students should taught in 7th--even if they are ready for advanced work. This eliminated the possibility of accelerated math. There was some talk about fixing this, and I know not all districts and schools have taken Santa Monica's position, but many have. Keep in mind, that in taking algebra in 9th grade, you cannot be on track to take calculus in high school--in a rigid system like this, high school calculus is not an option.

Can this interpretation of the CC standards be laid at the feet of the CC? In part, yes. The Common Core does not talk at all about advanced students or allowing an advanced track with calculus as an end-point in high school. That has given schools, districts, and states an excuse to eliminate or reduce math tracking. - On the other end of the spectrum, Common Core makes no allowances for students who are not developmentally ready for the work required in the given grade-level standard. A student with special needs must be taught the grade-level standard math even if they are years behind in understanding, or even in the
*ability*to understand the material. This is an "all students must be average" approach, which does not take into account the needs of learning disabled kids. Instead of giving those kids a curriculum which will advance them from where they are to where they can reasonably be at the end of the year, these students will be in way over their head with no chance of actually understanding the material and with little to help them catch up.

For example: Students who have not mastered counting to 100 might be required by the standard to do multiplication and division. How can they possibly progress when the curriculum is so far out of their reach?

- What is now happening, as the Common Core standardized tests are being taken in places like New York, is a massive upwelling of complaints about them.Elementary school teacher Ralph Ratto the day after administering CC math exams: I was angry that my students were victims in the abusive game to drive a political agenda.

I lost it today. I lost a little bit of my self-esteem. I lost my faith in my party. I lost my faith in my ability to protect my students. I lost my faith in our future.

I watched my students valiantly attempt math questions that most adults could not answer. These questions were wordy, and purposely confusing in a warped way to prove some point about our public education system.

Historically, my students excel on standardized tests, often finishing near the top of our district and state. Today I witnessed –, no I was part of!! – a situation in which students were forced to endure what amounted to what I would call an abusive situation.I can’t tell, without seeing the unpublished questions, whether he is complaining about how poorly-written these tests are, or whether they are testing math which is beyond the students’ learning. Is it simply the way they are asked to show their knowledge? Or are they being asked about things they haven’t been taught?Many of the complaints seem to be of the former variety: these tests are awful. That is a temporary problem, as the tests get better over time and as stupid questions and wording are removed. As I understand it, the NY exams were actually testing the tests, not the students. They were a dry run to see how well the tests worked. By the word leaking out about them, they seem to have failed in spectacular fashion.But, if it is a case of the students not having learned the material yet, then that might just mean that there will be an adjustment period. The new math standards are higher in many states than what was in place before, and it will take several years for the students to catch up to the standard. It should be that first graders starting out with these standards should do just fine. It’s only the older students who are being thrown in the deep end.

- In the only direct complaint against the actual standards I have seen, supposedly, the high school geometry standards came out of nowhere and embrace an odd view of geometry. I don't know if this is true or not, but I do know that the classic geometry of proofs and theorems and corollaries has been dying for a long time. Geometry was my favorite math class, and I loved the proofs-based course. If it has been dying for a while, it is hard to attribute that to CC.
- In fact, that's true with many of the complaints against CC: what critics are complaining about isn't really the CC, but the education establishment's strange ideas of how math should be taught, and what they are and have been teaching for decades. Many of the crazy examples of homework coming home supposedly “Common Core Aligned” are not any different than what was seen prior to the adoption of the Common Core.

- This includes the word-heavy explanations required in K-12 math today, and the belief that if you can’t explain something in words, then you don’t really understand it. Showing your work used to be enough to show understanding: if you could show the steps you took, you already showed your understanding. Now, even simple tasks have to be explained in complete sentences.

I’ve seen examples, including with our kids, of students baffled by how you explain why 5 x 6 = 30, or how you got that 3+3 = 6. My nephew, when asked to explain a simple problem this year, said: “They take something simple and make it so hard!”

One of the problems with this verbal-based math is that when kids are learning basic arithmetic they have not necessarily yet developed the linguistic abilities to explain things. You can fully understand that 5 x 6 = 30, you might even picture a 5 x 6 grid of objects, you might understand that this means adding 5 to itself 6 times, and might also understand that it means adding 6 to itself 5 times; and still not be able to put that in words.

As for explanations of the obvious, my favorite answer I’ve seen so far is: “my brain told me so.” At some point the language of mathematics becomes a real language and is sufficient to show understanding. Today’s math teachers don’t seem to agree.

This is especially hard on English-language learners, on kids whose brains take better to math than language, and on kids with learning/reading/writing disabilities.

It used to be that non-English speaking immigrants, in particular, could get ahead through math and science. Because language skills were less important than in other studies, they could become engineers, mathematicians, programmers, etc. Today, when everything has to be verbally explained in words instead of equations, students like this have less hope of advancement.

But, again, this is not necessarily to be laid at the door of the Common Core. These trends in mathematics education are long-standing and entrenched. What the Common Core adds to the problem is simply this: it locks the entire country down to this style of math education (and the accompanying documentation of the Common Core does do this, even if the individual standards do not) regardless of whether it is wise.

- As for crappy worksheets coming home with the Common Core label, I would say that math textbooks and especially workbooks are notoriously bad. My nephew came home with a worksheet last week which had only six problems on the whole page and with a “match each problem to its answer” format—in other words, the answers were all on the page, and you just had to link up the problem with the appropriate answer. But, for one problem the actual answer was missing. This was for finding the volume of a triangular prism, and whoever wrote the worksheet forgot that when calculating the area of the triangular face you need to divide by 2: b * h / 2 . Obviously, no one had bothered to check the worksheet for accuracy—including his teacher.

Math books tend to be written by freelance writers who are working on a rushed pay-by-the-problem basis. Editors prize speed over accuracy and don’t care if the books follow a coherent, systematic progression.

With the adoption of the Common Core, publishers sped to slap the label of “Common Core Aligned” on everything possible in their library, and commissioned rush-jobs of new material. Editing costs money and provides little, or no, return on publishers’ investment, so little editing took place. I don’t really see the Common Core texts and worksheets as being anything worse than what came before. It is simply that these things are now under greater scrutiny, and parents are wondering what the heck is going on.

- "Internationally Benchmarked" and "research based" claims about the Common Core are complete fabrications. The few attempts to compare the CC standards to our international peers fall into two camps: a) comparisons done by CC partisans which show some correlations and b) comparisons done by independent or anti-CC partisans showing no or negative correlations. Either way, the studies are few and far between and have been done *after* the standards were written.

Though the CC writing process is somewhat shrouded in secrecy, it does not appear that the committees that drew up the standards did so with an eye to our international competition. In fact, there is little research done about anything in the CC or about the CC in general. A recent study, by the Brookings Institution, showed that those students in states with a math curriculum most unlike CC did better than those states with a CC-like curriculum. The correlations were small, but the point here is that there is nothing out there which shows that CC is a superior (or even adequate) curriculum—or, conversely, that it is a bad curriculum. There is simply little out there to look at.

- Similarly, the claim that his was “state led” is bogus. This came out of the Gates Foundation and from a consortium of education think tanks that Gates had funded. Actual state involvement came after the fact when they were asked “hey, do you like this?” They were allowed no actual input during the writing process. So, yes, the promoters are lying about it, but that doesn’t mean the standards themselves are therefore bad. For a rundown of how the Common Core came to be written the movie “Building the Machine” goes through it.

- Prior to the adoption of the Common Core by 45 states, each state was on their own. At least two states, Massachusetts and California, are widely acknowledged to have had a better and more rigorous math standards before their adoption of the Common Core. Several states had to dumb down their standards to adopt the Core.

In fact, in this case, the rigidity of standards was also a routine complaint. California, in particular, required algebra in 8^{th}grade; this despite the fact that many students were simply not ready for it. Setting the bar that high meant that many students failed and hit the wall.

If anything, the argument should be made that it is not the grade level, which is largely decided by a student’s age, that is important, but what they are realistically capable of understanding given their prior learning. Common Core, like many standards before it, often does not take this into account.

The problem, as I see it here, is that the methods used by many teachers, and those they are led to believe in at ed school, simply do not work: Group math projects. Homework with only a handful of problems. No drilling of math facts. “Spiraling” curriculum, which believes in going over something lightly again and again every few months in the hopes that something will eventually sink in—instead of carefully, methodically, and systematically making sure the kids learn it the first time. The constant attempts to make every aspect of math class “fun” instead of addressing those aspects which simply take focus, work, and dedication.

This has nothing to do with the Common Core, and points to a deeper issue at the heart of education. Common Core, unfortunately, does nothing to negate, and often supports, these teaching methods.

- What was the rush? The Race to the Top program required states to adopt the Common Core standards by a certain date (if they were applying for RttT grant money, which most did). The final standards were only published a month or two beforehand. There was very little time for debate and for deep assessments to be made before it got passed. Once again, however, that doesn’t address whether the standards themselves are good or bad, just that the states which adopted them had very little time to review them. The RttT initiative dangled the carrot of grant money, and states signed on without really analyzing the standards.

- Just like anything else, the Common Core will obey the law of unintended consequences. If you ask any of the people involved in its creation, or in the government who pushed for, or who voted to adopt the Common Core, you are likely to hear some variation of the hope that this will help poor and disadvantaged kids get ahead; and moreover, that the Common Core should reduce inequality. In part, that might be true, but with a ceiling on these students’ aspirations.

Because in many states the Common Core is an improvement on what existed before, those students in those states who stick to the new program should come out the other side in a better position than their predecessors.

However, as I said above, the Common Core is not a selective-college or STEM-ready standard. Poor and disadvantaged students, or students with poorly educated parents, will be completely reliant on the schools to give them their math curriculum. On the other hand, students in the middle-class or better, and students with well-educated parents will get more.

The family in Santa Monica that I mentioned earlier will not simply have their daughter twiddle her thumbs for the next two years until her peers catch up with her and she can finally be allowed to take algebra. The family will hire the tutors necessary to make sure that their child continues to stay on the track she is on now.

There are six Kumon centers within five miles of where I’m sitting. There are two Mathnasiums in that same area. There is one Sylvan. There is one C2 center. There are many other smaller tutoring centers as well. In addition there are many people who tutor independently, including myself. We are in a middle class to upper-middle class neighborhood, and just to our east is Koreatown. All around us are parents who are not going to let their kids fall behind and who have the resources to make certain that they do not.

Poor kids have no such opportunity. Those students who are stuck in schools that are eliminating math tracking in the name of the Common Core, and who will only offer a single not-STEM or selective-college-ready curriculum, will bifurcate between those getting outside help and those who can only afford to be taught at school. To some extent, this has always been true. But with more systems eliminating tracking, more students will be denied advanced study.

- The effects on public colleges and universities should also be taken into account. As part of the push for the adoption of the Common Core, the Race to the Top initiative included a stipulation—signed onto by 45 states—that any student who completed the Common Core math curriculum in high school could not be placed in remedial math in public colleges and universities. They must be placed in non-remedial, credit-bearing classes. With current colleges often requiring 40-50% of their freshmen to take remedial math, this will require a great deal of shifting on the part of schools. This can take several paths:

a) They can just put students in the intro college classes and let them crash and burn. This one is highly unlikely to happen, especially when the kids crashing and burning are likely to be disproportionately poor minorities who went to crappy high schools.

b) They can dumb down the intro courses so that the students can pass. This is the most-likely scenario, and will result in the level of college math work diminishing for many.

c) They can remove the requirement to take math in order to graduate, depending on the major chosen.

This is actually not necessarily a bad thing. While I would say that the ability to do college algebra should be universal among college students, I would also wonder why someone majoring in social work needs to pass algebra? Or why someone majoring in early-childhood education (say preschool – third) would need to?

There are many college majors and post-college careers that simply do not require math at all. Many adults will never do another algebra-style problem for the rest of their lives. Apart from showing a level of mental discipline, why is college algebra required for these studies?

I know one former community college student who could not pass algebra to save her life. In the end she dropped out of school and never got her AB. I don’t know if that is a good thing or a bad thing. She went on to start a small business and is doing well—either way, she will never be called upon to do any algebra problem at any time for the rest of her life.

When college algebra puts up an impenetrable barrier to students who want to study something which has nothing to do with math, and in which they can do well, why is math a requirement at all? I would think it is quite likely that the math requirement will be removed from many majors and as a general requirement for graduation. It might be replaced with something like a statistics course, which would be much more useful to more students than college algebra.

- Some of the weakest critiques of the Common Core are about the process of its implementation and the knee-jerk reaction to nationalizing school standards.

a) To some extent this is justified. As Jay P. Greene, in particular, has tried to point out, there are at least two separate federal laws which explicitly prevent the federal government from creating or trying to implement a national curriculum. Race to the Top and the Common Core violate those laws.The intent of Congress is clear: The federal government cannot mandate, direct, supervise, or control curriculum or programs of instruction. Indeed, the legislative history of the DEOA [Department of Education Organization Act] underscores this, as does its statement of intent “to protect the rights of State and local governments . . . in the areas of educational policy” and to “not increase the authority of the Federal Government over education or diminish the responsibility for education which is reserved to the States and local school systems.” Yet…the Department is evading these prohibitions and using proxies to cement national standards and assessments that will inevitably direct the content of K-12 curriculum, programs of instruction, and instructional materials across the nation.

So, whether or not the CC is a good idea, it seems to be explicitly illegal according to several laws governing the Department of Education. It is reasonable to add this to the list of extra-legal legislation coming out of the current White House, and it is reasonable to object to the CC on this basis alone.

b) As I’ve said above, several states had**better**math standards pre-CC and had to jettison them to adopt the new standards; and previously, each state wrote their own standards (or in some cases*didn’t*write standards at all).

This plays to the old idea that states are “little incubators” of innovation. If one state has a better program, other states are free to use it as a model and alter their own in response. Hopefully the better states serve as exemplars until another state comes along and surpasses them. With a national set of standards, experimentation and change comes to an end. We will never know where that dynamic experimentation would have led.

- The weakest arguments of all, which I’ve seen too often, and which I think are things both my brother and I object to the most, are the “if it comes from Obama, it must be bad” mentality. A lot of the criticism starts with that idea, and searches for evidence to fit it. The standards themselves aren’t terrible, and aren’t even too bad. In some areas, they are quite good. Even if Obama’s name’s attached.

- At the end of the day, the people instituting the new standards, and the new curricula that go with them, are the same people who have been failing our kids for decades. The same mentality dominates in schools and ed schools. (Often against anything rigorous, and in favor of all things that are “fun,” and thus will make the children happy to learn. Not all that children need to learn can be constantly “fun”—you still have to learn how to spell, and you still have to learn your math facts.)

## 1 comment:

Very good analysis. I agree that the big problem with CC is its interpretation and implementation. The content standards are being interpreted in light of the nebulous Standards for Math Practice along the lines of reform math ideology--which has been going strong for 20+ years. CC is the gasoline thrown on the reform math ideological fire.

A group of us wrote comments on the CC standards, as part of the US Coaliti here.on for World Class Math (when there was such an actual group; now it is just a FB comment page). These standards can be found here.

We felt that the content standards themselves leant themselves to reform math interpretations--particularly the words "explain" and "understand" which occur often in the lower grade standards.

The standards CAN be interpreted sensibly and if the educationists truly believed in differentiated instruction (a term they bandy about, along with all their other pie-in-the-sky ideas like collaborative learning, "just in time" learning, discovery learning, etc) they would not insist on all students achieving the standards for a particular grade--which is a one-size-fits-all mentality. Ironic given that the reform math people tend to view traditional math as a one-size-fits-all approach.

I am in the process of putting together a document that offers sensible interpretations of the standards as an alternative to what school districts, publishers and PD vendors are saying the CC is all about.

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