Discover Project Follow Through

[ Times Colonist ] Many Canadian provinces adopted discovery-based curriculums about 15 years ago. Newer curricula and textbooks appeared, advocating the use of multiple strategies in the classroom, replacing more conventional methods for teaching arithmetic. The result of this phenomenon has led to a remarkable decline in math skills, and a proliferation of children enrolled in costly learning centres to achieve knowledge of foundational math facts.

These centres and private tutors use more conventional and traditional methods to teach their students, because they have been proven to work. This is something to which our policy-makers must pay attention.

Gee, it didn't work! Project Follow Through came out in the early 1970's--that's fully 40 years ago, which means pretty much every single teacher currently trained and working has been trained after its findings were known...and utterly ignored.

The world has known what works and what doesn't in math education for four decades. Educrats continue to ignore it.

Education in a panic

From a comment of mine, posted to the FreeRangeKids.com website and discussing how the Common Core is taking away recess and free play time for kids:

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Common Core is being used as a scapegoat for every problem in education today. If anything, the Common Core and the Race to the Top initiative overturned some of the heavy testing requirements of the previous No Child Left Behind Act--which was very heavy on "accountability" and accountability at the classroom and teacher level: which meant testing. This is why states have been reluctant to jettison the CC, even with major backlashes against it: without the Common Core (or a set of standards so similar there's little difference) states have to return to the No Child Left Behind requirements which are much heavier on the testing, and require serious--and probably unreachable--results. (All children must be above average sorts of results.)

I think much of the education world is in a panic and reaching for ideas to improve educational outcomes. Spending on education has skyrocketed in the last few decades, with little or nothing to show for the extra money in terms of results. (Though, a large chunk of that money is being spent on special-needs kids who in the past were either not mainstreamed or were stuck off in a corner and ignored.) Class sizes have been shrunk with little benefits seen. "Technology" and computers have proliferated with little in the way of benefits. "Reform Math" replaced "New Math" replaced "traditional math" with little benefit. "Whole Word" replaced "Phonics" and failed miserably. Everything they've tried has failed.

With little in the way of results, schools are eliminating anything that isn't 3-R related: art, music, even academic subjects like history and science have been put on the back burner. Free play time was often the first to go.

This isn't the result of Common Core, this is the result of decades of failure in our education system. (And even schools which we consider good schools, like the nice suburban ones which we don't consider a problem, often stack up poorly to schools around the world.) They don't know what to do, and don't know how to fix the system.

If they are once again turning to a system which will backfire--less free time for squirming children, it is entirely in line with most of what they've tried over several decades.

Common Core

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:

1. 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.
2. 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.
3. 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?
    
4. 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.
   
   
   The weird thing about this, is that many of the complaints against the Core are of the “it’s too slow” variety, but here, it might be too fast. Is this just because there needs to be a period of adjustment, or is the standard really too high for the average student?
   
   
5. 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.
6. 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. 
    
7. 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.
    
8. 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.
   
    
9. "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. 
    
10. 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.
     
11. 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.
     
12. 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.
     
13. 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.
     
14. 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.
     
15. 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.
     
16. 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.
     
17. 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.)   

I often liken the implementation of the Common Core to the whole country throwing all its educational balls up in the air at the same time. Considering how bad the system has been, you would think that whatever gets reassembled would be an improvement; but, the same people who were in charge before are the ones now catching the balls, and they will do their utmost to try to put them right back where they were.

Education spending is not the same as educating

This study by Andrew Coulson (or, perhaps I should say: Andrew, Son of Coul) at CATO is an impressive piece of work. A few years ago, he published a study showing how test scores in math and English have been completely stagnant (I believe using the NAEP) since the 70's, while at the same time the inflation-adjusted money we are spending on education has skyrocketted. In short, he showed how spending on education is not the same thing as actually educating, and did so in a spectacular fashion.

Now, he is out with a more-detailed study (using the SAT--but washed of any socio-economic or "who takes the test" baggage, then compared to the NAEP), which shows the same results on a state-by-state basis.

Here's his graph for Massachusetts. Most states are similar.

Building the Machine

Highly recommend that you take 40 minutes and watch this film on the development of the Common Core: Building the Machine.

It details how the Common Core got made, and how many of the things said about it ("internationally benchmarked", "state-led", "college and career ready", etc.) are hokum.

It covers a lot of ground, but I particularly like the interviews with two of the people who were asked to participate in the reviewing of the Common Core: James Milgram--the only mathematician or math teacher involved in any stage of the creation of the core, and Sandra Stotsky--who wrote the excellent pre-core, Core Knowledge-based, Massachusetts standards. Both of them refused to sign off on the Common Core standards.

Another critical moment, is when they show video of a hearing with a core participant who says flat-out that the core is not for STEM-oriented students and not for students aiming at selective colleges.

It's not as if the lead mathematics standards writers themselves didn't tell the public how low Common Core's high school mathematics standards were. In 2010, Jason Zimba, a lead writer, said the standards are "not only not for STEM, they are also not for selective colleges." [ Common Core Fails To Prepare Students For Stem (Denver Post) ]

Retread of a retread.

Yet another article about how traditional classroom suck, and how we should be encouraging kids to learn through self-study.

This is just the same repackaging that's been going on for over a century. Dewey railed against the classroom structure at the end of the 19th Century--and he was hardly the first. "Gradgrindian" is often the word used for traditional classrooms, and that comes from Dickens in 1854.

I'm always amazed that these types of stories pop up every *#$%^* year and are treated like a great breakthrough in educational thinking, when they are actually retreads of over a century of commentary. This has been the standard theory of education, taught at ed schools, since the 1960's. Nearly everyone educated today is being educated on the theory 1) that kids learn best when they learn through self-discovery, 2) teachers shouldn't be in front of the classroom giving lectures (these things even have cute nick names: "sage on the stage" is this one), but should be allowing kids to find things out on their own ("guide on the side".)

Every generation rails against the educational system of the day, yet the reforms always seem to result in degenerating results; with fewer competent, educated adults who can read, write, and cypher adequately.

I remember an old episode of either "Leave It To Beaver" or "Andy Griffith" where the kid was in a class and they were discussing some odd event in American history that no one today has ever heard of. That isn't really a problem, we emphasize different historical events differently as time passes. What really stood out was the level of knowledge 3rd graders were expected to master and be able to discuss. There is no where near that level of learning today, as teachers have been taught for decades to teach kids "how to learn" instead of actually teaching them facts, skills, writing, grammar, spelling, etc. Those kids were learning things that would allow them to think critically later in life.

Basic modern neuroscience is showing that we need information to be able to think about something and analyze it properly. Here's an simple-stupid example: a baseball manager pulls his pitcher even though he's still doing really well. If you don't know that the pitcher's arm was still sore from straining it at practice, or that the manager was worried about damaging it further, you might scream from the stands at the manager's stupidity. You can not analyze the manager's decision without the facts.

The same goes for history, economics, science, politics, etc. Uninformed people can not think critically, yet schools are doing little to inform students.

There is little doubt that kids do actually learn better when they learn through self-motivated self-discovery, but how many second graders walk into the classroom really, really turned on by learning about past participles. Or eighth graders taking a gee-whiz-this-is-fun! attitude toward working to master factoring polynomials. And yet we need just about everyone to learn how to write at a basic competence level, and we need a substantial number of people to excel at factoring polynomials. I'm sure teachers live for the moment, the eureka moment, when a kid figures it all out and finally understands something they've been working on for weeks, and excitement gets kindled--they take ownership of their learning; but I wouldn't want to develop a curriculum based on those moments. The idea that all kids can, or are going to be self-motivated and propel themselves into becoming educated adults is silly, and the fact that it has been the dominating philosophy in ed schools is at least partly to blame for the lack of educational progress in recent decades.

Florida's Charter Schools

A study by Florida's Department of Education shows that:

The achievement gap section of the report contains data that are used to analyze the gap between white students and African American students, and white students and Hispanic students, in reading, math, and science. This section of the report includes 18 separate comparisons of current achievement gaps. The achievement gap was lower for charter school students in 18 of the 18 comparisons.

The learning gains section of the report includes 96 comparisons. The report compares the percentage of students in charter schools making learning gains against the percentage of students in traditional public schools making learning gains, by subject, grade level, and subgroup. The percentage of students making learning gains was higher in charter schools in 83 of the 96 comparisons. The percentage of students making learning gains was higher in traditional public schools in 6 of the 96 comparisons. There was no difference in the percentage of students making learning gains in 7 of the 96 comparisons

Bottom line: cut it any way you want it, cut it 96 different ways, and public schools beat charters in only 6 of those ways; charters beat publics in 83 of those ways.

Student Achievement in Florida's Charter Schools - Charter_Student_Achievement_2012.pdf

New law dumbs down Calif. math performance | CalWatchDog

This is horrible. What it boils down to is this: not only has the adoption of the Common Core slowed down California's math curriculum by a year (algebra in 9th instead of 8th,)  it destroys the possibility of a calculus-track for top math students.

New law dumbs down Calif. math performance | CalWatchDog

Furthermore, SB1200 is so poorly drafted that it doesn’t just roll back the expectation of Algebra 1 in grade eight. It does more than that by requiring “one set” of standards “at each grade level,” and precluding typical mathematics course options for students in high school.

California high schools have always offered different math classes to students in the same grade who have different levels of preparation. Accordingly, California historically has adopted course-level math standards for high school — preserving local control at the district and school level to decide when it would be best to offer rigorous courses to each student based on the student’s ability. But SB 1200 would outlaw that practice by mandating only one set of mathematics curriculum- content standards, textbooks and training and teacher materials for all students in each K-12 grade.

Officials of Brown’s administration have offered rhetoric about how they will not have to implement the plain language of the law. But they do not have the statutory authority or capacity to violate the law’s provisions. Efforts to get around the wording of the law will lead to confusion about policy on curriculum, textbooks and testing — and hence invite lawsuits and re-ignite the math wars.

You must be joking!

Large excerpt from interview with on Education Next Stephen Wilson is: "a professor of mathematics at Johns Hopkins University, served on the National Governors Association-Council of Chief State School Officers “feedback group” for the Common Core standards, and was mathematics author of Stars by which to Navigate? Scanning National and International Education Standards in 2009: An Interim Report on Common Core, NAEP, TIMSS, and PISA."

My comment notes follow.

[Education Next]: Will the Common Core put an end to what has sometimes been termed the “math wars”? In your view, do the math standards resemble those recommended by the National Council of Teachers of Mathematics (NCTM), and what do you make of that similarity (or lack thereof)?

[W. Stephen Wilson]: The end of the math wars! You must be joking.

There will always be people who think that calculators work just fine and there is no need to teach much arithmetic, thus making career decisions for 4th graders [1] that the students should make for themselves in college. Downplaying the development of pencil and paper number sense might work for future shoppers, but doesn’t work for students headed for Science, Technology, Engineering, and Mathematics (STEM) fields.

There will always be the anti-memorization crowd who think that learning the multiplication facts to the point of instant recall is bad for a student, perhaps believing that it means students can no longer understand them. Of course this permanently slows students down, plus it requires students to think about 3rd-grade mathematics when they are trying to solve a college-level problem.

There will always be the standard algorithm deniers, the first line of defense for those who are anti-standard algorithms being just deny they exist. Some seem to believe it is easier to teach “high-level critical thinking” than it is to teach the standard algorithms with understanding. The standard algorithms for adding, subtracting, multiplying, and dividing whole numbers are the only rich, powerful, beautiful theorems you can teach elementary school kids, and to deny kids these theorems is to leave kids unprepared.[2] Avoiding hard mathematics with young students does not prepare them for hard mathematics when they are older.

There will always be people who believe that you do not understand mathematics if you cannot write a coherent essay [3] about how you solved a problem, thus driving future STEM students away from mathematics at an early age. A fairness doctrine would require English language arts (ELA) students to write essays about the standard algorithms, thus also driving students away from ELA at an early age. The ability to communicate is NOT essential to understanding mathematics.

There will always be people who think that you must be able to solve problems in multiple ways. This is probably similar to thinking that it is important to teach creativity in mathematics in elementary school, as if such a thing were possible. Forget creativity; the truly rare student is the one who can solve straightforward problems in a straightforward way.

There will always be people who think that statistics and probability are more important than arithmetic and algebra, despite the fact that you can’t do statistics and probability without arithmetic and algebra and that you will never see a question about statistics or probability on a college placement exam [4], thus making statistics and probability irrelevant for college preparation.

There will always be people who think that teaching kids to “think like a mathematician,” whether they have met a mathematician or not, can be done independently of content. At present, it seems that the majority of people in power think the three pages of Mathematical Practices in Common Core, which they sometimes think is the “real” mathematics, are more important than the 75 pages of content standards, which they sometimes refer to as the “rote” mathematics. They are wrong. You learn Mathematical Practices just like the name implies; you practice mathematics[5] with content.

There will always be people who think that teaching kids about geometric slides, flips, and turns is just as important as teaching them arithmetic. It isn’t. Ask any college math teacher.

The end of the math wars! You must be joking.

[1] " making career decisions for 4th graders "

This is one of the big problems I have with the kids' school. Their curriculum makes it almost impossible to follow a path towards a STEM career. Our school uses the weak "Everyday Mathematics" curriculum, but even does that poorly--every year, they only get through about 2/3rds of the material. Year after year, those 1/3rds left behind add up. The entire 6th grade math curriculum is a review of 1st-5th grades, because the kids are so poorly prepared for pre-algebra. And even there, they are already 60% of the way through their school year (even counting the week-long trip that is coming up in March) and are only through chapter 5 of a 13 chapter text. Chapter 6 is the always-exciting "Using Multiplication"!! This is supposed to be 6th grade, third trimester work, and these kids have no idea how to work with fractions, calculate the area of a circle, or the volume of anything! This is simply not a track that will allow kids to take calculus senior year of high school, which is what many STEM majors in college need.

[2] "The standard algorithms for adding, subtracting, multiplying, and dividing whole numbers are the only rich, powerful, beautiful theorems you can teach elementary school kids, and to deny kids these theorems is to leave kids unprepared."

Try the lattice method with large numbers or decimals! At open house for 4th grade this year, the parents were doing a good job of eating the teacher alive. Sure enough the lattice method came up, and someone asked about doing it with bigger numbers. My sister piped up and asked about doing it with decimals--The teacher didn't know how to do it! Another parent, with an older kid, started to explain, and my sister said--"Yes, we know how to do it; the point is she (the teacher) doesn't know how to do it!" Yet, they still spent several weeks doing it this year, and if you used the standard algorithm on your homework, you were graded down.

I remember when the 3rd grade teacher wanted to show his students how well and quickly the lattice method worked. He had someone come up and do the standard algorithm on the board while he did the lattice method. Lo and behold, the teacher won! Our kid came home defending the lattice as "quick!" I had to point out to him that the teacher had cheated; he had drawn the lattice in advance—the most time-consuming part was thus ignored. I showed our kid how long it actually takes to do the two methods. But it's a strange thing, kids can get very defensive about their teachers, even when the teachers are full of … The kid got mad at me for showing him the teacher was wrong.

[3] " you do not understand mathematics if you cannot write a coherent essay "

This is actually a bigger problem than it seems. There has been a push for many years to drive reading and writing into every class, including math. No similar push has been made to get math into reading and writing classes—leaving less math time for actual math. But that's not even the big problem.

Some kids excel at language, some kids excel at math. Not all the kids who are good at one are also good at the other—though many are. In particular, many boys hate the language parts of school (especially when they are forced to write or read self-reflective pieces about emotions, hopes and dreams—sometimes it's better when they are allowed to blow things up with words and read snot jokes.) For many of the boys who struggle with language (and it can be something as simple as have slower-to-develop fine motor skills which makes writing a (literally) painful chore) math is their salvation. They can be good at math without having to put any of it into words.

At least, they used to be able to. Now half the problems are word problems, and half their answers have to be too. This is one of the reasons boys are having so much trouble in school. For the more math-oriented boy, they no longer can escape their weak language skills.

Also, ask yourself this: which do you think is easier for kids to master, a set of 26 symbols with 42 different sounds, joined together in increasingly complex and confusing ways. Or a set of 10 well defined symbols that always mean the same thing and follow simple and easy to experience rules. "Wind" can be something that blows, or "wind" can be something that rolls up. 10 is always 10, 15 is always 15. There is some evidence that pushing arithmetic at an earlier age and backing off on the language skills could be beneficial for a non-negligible segment of kids. In essence, kids can develop a natural and strong understanding of numbers before they develop a similar understanding of phonics, vocabulary, language and the motor skills needed for reading and writing.

[4] " you will never see a question about statistics or probability on a college placement exam "

I'm not so quick to dismiss statistics. I think it is the most-important worst-taught subject in school. If it is not part of the regular math sequence, I think it should be a separate semester-long class at the high school level. Every single day we are bombarded with statistics, and without learning how they can be manipulated, exaggerated, and misused, we are all apt to fly off the handle when we hear our (completely insignificant) RISK HAS DOUBLED! Or 50% of people polled think you're an IDIOT (when they only asked your best friend and your twerp of a brother.) People need a far better understanding of statistics than they currently have. My high school required a one-semester economics course; they should also have required one semester of statistics.

[5] " You learn Mathematical Practices just like the name implies; you practice mathematics"

Amen. I keep telling the kids this one. You can only get good at math and science by doing as many problems as you can get your hands on. If the teacher assigns the even problems, and the book has the answers for the odd in the back, do the odd too! The more, the better.

This is also the biggest problem with the ALEKS online math program. They give a kid three problems, and if they get them right, that's it. Eventually, the kid will be given a test on whether they've really learned it or not, and often will have to repeat the section, again and again—with a feeling of failure instead of mastery. It would have been better to be given many more examples before letting the student cross that topic of their list. It takes a lot of practice to really learn long division or how to find a least common denominator. Practice makes perfect.

Jobs Machine

Dan Mitchell at his "International Liberty" blog showed a graph charting education spending with achievement of 17-year-olds since 1970. The original graph was from a blog post by Andrew Coulson at Cato's "Cato@Liberty" blog. Here's the graph:

The steep blue line represents all education spending. The flat little lines at the bottom shows the percentage change in achievement. For all the spending, we got bupkis...except for the steep dotted line. That's the percentage increase in the number of education employees.

The bottom line numbers are:

Spending on Ed: +140%
Math scores: 0%
Reading scores: 0%
Science scores: -3%
Ed Employees: +75%

Our schools are worse, but they employ more people than ever. Increasing proof that the national education system isn't about education, it's a jobs machine.

Low-hanging fruit

Valuing Teachers : Education Next

Eric Hanushek presents the case for eliminating the lowest performing teachers. He believes that simply replacing as few as 5% of the worst teachers with only average teachers would pretty much eliminate the education gap with other high-performing countries and would result in a massive increase in our long-term economic outlook.

The key paragraph is this one:

Admittedly, these estimates are subject to some uncertainty. So if you think those that are given here are too high, even though they are based on the best of contemporary research, then just cut them in half. You will still have effects on growth of one-half of 1 percent per year, which produces impacts of $56 trillion over the lifetime of today’s child. In other words, to make the very large effects disappear, you have to make either the very strong assumption that student learning has little effect on the U.S. economy or the equally strong assumption that teachers have little impact on students.

Which is it? If a good education makes a difference, then having a bad teacher also makes a difference. The teaching profession is not a magical Lake Wobegon. Not all teachers are above average.