Robert Berkman, who has been teaching math for thirty years, takes issue with the article by Elizabeth Green in the New York Times magazine called Why Americans Stink at Math. While he has great admiration for Green’s writing skills, he thinks she is an American who is not good at math.
He writes:
“The first place where Green goes wrong is when she cites “national test results” about mathematics achievement in the U.S.. First, I wonder which “test results” Green is referencing here (you have to be suspicious when, in the days of the omnipresent interweb, a link is not included to the data supporting this point.) It may be significant that 2/3 of all 4th and 8th graders are not “proficient” in math, but again, this is a national standard, not an international standard, so this only points to the fact that U.S. children are not achieving according to some standard that was created where, in some dark cave where Dick Cheney and his family reside?
“Green goes on to state that half the 4th and 8th graders taking the National Assessment of Educational Progress could not read a thermometer, or that 3/4 of the test takers could not translate a simple word problem into an algebraic expression. Note that this is the National Assessment of Educational Progress – it doesn’t say anything about whether U.S. children are better or worse than anybody else around the globe; for all we know, 7/8 of the children in Helsinki and 11/13 of the children in Ibaraki couldn’t successfully answer these questions either. Look, I’m not the sharpest pencil in the box, but even I know these numbers are insignificant without a context.”
If I may interject my view, NAEP proficient is a very high standard of academic proficiency, not a benchmark for what all students should know. Michelle Rhee constantly makes this mistake. It is like complaining that not all students are A students.
Berkman then chastises Green for comparing Massachusetts, a state, with Shanghai, a city (which excludes a significant number of students from the tests because their parents are migrants).
I confess I am tired of the constant barrage of articles and books about how terrible the U.S. is and how our public schools are the reason that we fail at this, that, or everything. I think this is a wonderful country, and I hope that one day soon we can take control back from the oligarchs that want to turn our children into standardized widgets (but not their own).
I like Elizabeth Green. I have known her for several years. I hope her next book will celebrate the success of American public schools in accepting all children and unleashing the genius of our best thinkers and creators, despite the contempt of the uber-rich and the war on the teaching profession. There is a reason that teachers say they work “in the trenches.” It’s time to celebrate their perseverance in the face of budget cuts and stupid federal policy.
Diane Ravitch's blog 
With this generation of students, more than any other, teachers battle with conveniences in order to teach critical thinking skills. Kids have iPhones that give time and temp as numbers. Many see no need to bother learning the logic behind reading a clock with hands or learning degrees and gradations on non-electronic measuring devices. As to research, they want google to do it all– even generate the keywords for a search.
Is it laziness? I think to some degree. However, the growing usage if technological convenience fosters this dulling of the struggle to master the life skill of situational application of critical thought.
“21st Century Skills” (gosh I hate that term) trumps critical thinking. Imagine that.
They seem to trump creative thinking, too.
Word.
Still, one must keep in mind that the needs of the students today are different from that of their parents and even their older siblings.
I’m not sure how many students have heard of a bushel or a peck. I don’t think all the teachers know what they are, either.
And Roman Numerals are just for crossword puzzles and copyright dates.
I’m not being critical, just realistic.
Ellen,
It’s been that way with every generation of children. Nothing new there.
Another difference with this generation of students is that the ease of communication provided by the internet means that teachers are not the only source of information about class material. I suspect that teachers will have to increasingly deal with mathematics students who are going well beyond the course material.
That would be nice. We’ll have to do a better job of inspiring students that the subject is interesting before that becomes a widespread “problem.”
I think it is already happening and making “the gap” larger.
I don’t teach math, but history. I have only ever had ONE kid who was reading and researching on his own and was beyond me in history. I’ve taught for 14 years. I think this is more rare than you think, TE.
Threatened,
I think it is much more common in math, in large part because the math curriculum is so confining. Your student may write a publishable essay in response to your assignment. No publishable work could possibly be generated as the result of an assignment in a math class.
That would be great. I always encourage students to try as many different sources as possible. I post supplemental links all the time. You are talking about a small percentage of students. However, Common Core limits the freedom in the classroom. For example, I can not spend a couple days demonstrating matrix math and computer graphics applications now without risking my all important VAM ranking – especially if those topics are not on the PARCC test.
TE – have you ever used the internet to teach yourself upper level math? Even Simpler math courses such as algebra and geometry can be confusing, let alone trigonometry, advanced algebra, and analytic geometry. We won’t mention calculus.
Even with a teacher’s help, many students have a difficult time with their math subjects. One must be truly motivated and have an innate skill to teach oneself math and deduce how to solve even the simpler word problems.
And I know this because when I taught Trigonometry and Advanced Algebra to children on medical leave, I had to reteach myself those concepts I had learned in high school and college using the Internet. (The textbooks were even less of a help). It took a lot of time and concentrated effort to relearn those skills. And I enjoy math. Actually I enjoy all puzzles.
There are not that many mathematical geniuses in the world – otherwise those ten (or are we down to nine) unsolvable math problems would have been completed by now.
Even gifted high school math students would have a hard time surpassing the knowledge of a competent math instructor, especially the ones I had the pleasure to work beside.
Ellen, you wrote in part, “There are not that many mathematical geniuses in the world – otherwise those ten (or are we down to nine) unsolvable math problems would have been completed by now.”
I think that with some reflection you’ll realize that this claim doesn’t really hold up. The problems on that list are such that no one even knows if they are solvable. Fermat’s Last Theorem, proved finally in the early 1990s), took over 350 years to be settled. And in that period, some of the greatest geniuses of mathematics lived, took shots at it, and failed to completely crack it. It is not unfair to suggest that it took the community of the world’s mathematicians biting off smaller pieces of it, developing new ideas and tools, for it to finally fall to Andrew Wiles. But he really stood on the shoulders of many, many others.
The Riemann Hypothesis has been around for 155 years. It is the last problem left from the ones proposed by Hilbert for 20th century mathematicians to solve, about 114 years ago and is on that list of $1 million prize problems. It might fall in my lifetime (I’m 64) or in my son’s (he’s 19) or it might never be proved. Other problems on that list include some that may well be not only not provable/solvable, but might be of the sort that we’ll never know. See Godel’s work for why that is possible. He proved that there are definitely false statements in mathematics that can’t be shown to be false and true statements that cannot be proved true. It’s the nature of mathematics and logic. So the failure to solve any one of those problems you mention tells us nothing about the number of geniuses (whatever that might mean) poking around in mathematics today, in the past, or in the foreseeable future.
Then again, neither do standardized test scores tell us much that is useful. ;^)
You are right Michael, it was an extreme example to make a simple point.
Still, our schools are not filled with budding math geniuses – either as students or as teachers.
And I am aware because, Yes, I happened to marry one (who does work on those remaining nine problems for fun), and I have a daughter who was a competent math major, but they are definitely the exception and not the rule. (Plus, if you are having trouble in math, it helps to have an inhouse resource to answer your questions – thus all four of my children had no trouble passing their high school or college math.)
However, that is a far cry from self teaching based on math concepts found on the Internet.
Ellen,
Here is site devoted to advanced mathematics for K-12 students: http://www.artofproblemsolving.com
And another site that is devoted to answering math questions: http://math.stackexchange.com
In the last decade or so at least three students from my local high school have taken graduate mathematics courses from the local university. Unless the mathematics instructors you worked with were well published Ph.D mathematicians, they would have had a hard time staying ahead of those students.
TE – I looked at both sites and found neither of them user friendly. They would not have helped me brush up on my trig.
That said, there are always exceptions to the rule. I’m sure those three students (over a ten year period) were exceptional. But the normal math student needs all the support they can get.
Ellen,
Three students a decade in one high school might suggest a student every year in four high schools (or perhaps one out of every 4,000 students).
TE – my daughter graduated with a degree in Math from SUNY at Buffalo. There were only nine graduates in the math department, 3 with a BS and 6 with a BA. There were two pages of psych majors.
My husband was the lone white male in the PhD Math Dept at UB. Everyone else was Asian.
There are exceptions, but there aren’t that many young math geniuses who can teach themselves college level math, even with the help of an online course or two. You know of three, I can’t think of one. Excellent students, yes, Einsteins, no.
And you sell our math teachers short. (Although my husband was called upon to solve the harder upper level math problems that they couldn’t figure out without help.) Over the years, there have been only a few high school math teachers I thought were in over their heads. The problem with math is that the teachers’ hands are tied by non mathematicians telling them what and how they can teach their subject area.
Ellen, we have a generally different set of experiences and draw some different conclusions from them. But my sense is that much depends on where we’re looking. In 25 years or so of teaching, coaching, supervising, working with student teachers, teaching math ed methods and content classes, etc,, I’ve seen a great deal of bad math instruction that looks very much like the bad math instruction I endured in 1955-1968. The culture of US K-12 math teaching is very resistant to change, and draws certain sorts of folks into it. I have had the frustrating experience of seeing more than a handful of secondary math teachers who have major league holes in their knowledge of K-12 math, not even including calculus as a high school subject.
And I honestly do not believe or have evidence to support the notion that the problem in most cases was that someone was telling them how to teach, but rather that their ideas about how to teach were far too much in keeping with a long tradition that has never served enough of our students well (I am skeptical, as are Henri Picciotto and many others, that this tradition serves most of those who do “well” in school mathematics particularly well. Quite the contrary, outside of the issue of grades, this system leaves many “achievers” with a lot of very false ideas about what it means to do and know mathematics or even what mathematics is. And therein lies a huge part of our struggle to improve the overall quality of math education in the US). My experience with preservice and inservice teachers suggests strongly that the biggest influence on how K-12 math teachers teach, particularly when under any sort of pressure, is the way in which THEY were taught mathematics, especially in K-12.
While many people both inside and outside the math teaching profession complain about “faddish” ideas that math education professors try to instill in them in methods classes, many of those ideas are sound and, sad to say, few teachers get them or try to use them once they’re on their own in their little closed-door fiefdoms. Since fewer still administrators are math educators, many of them don’t know how to critique a math lesson for content or pedagogy. If the kids are behaving, it’s all good. If they aren’t, or if they’re “too noisy,” “too active,” or otherwise APPARENTLY not sitting quietly doing work sheets, then the teacher is bad. A teacher can simply “mail in” a 30 year career with good evaluations from administrators by doing nothing different at all from what his/her teachers, and THEIR teachers, and THEIR teachers did, going at least as far back as when my parents were in school in the 1920s to early 1940s. Have we REALLY not come up with a single new idea worth doing in math classrooms since then? Well, according to some influential and vocal traditionalists like Wayne Bishop, that’s precisely true. He has said repeatedly about math teaching that there’s nothing good that’s new and nothing new that’s good. And he has ample company in that mindset. Which frankly makes me ill. Of course, “tradition” was bad enough for him, so it must be THE single way things should work for all. And he says so.
As for kids learning math at least through the end of the sophomore year of college without taking courses, I think it’s easier than you believe and will get easier still over time. The question isn’t how many geniuses there are, as it hardly takes genius or even close to get through two years of calculus, including a course in Differential Equations and Linear Algebra, since that one tends to be just as cookbookish as are the three previous semesters of freshman/sophomore math.
But then, as Henri Picciotto points out in his multiple essays on acceleration, should that even be a goal for kids, at least IN K-12 classrooms. He is skeptical, as am I. But I am not skeptical that many kids who choose to use the free resources that are out there can find good ones to deepen their math knowledge outside of school, if they aren’t getting sufficiently challenged in math classes. My bet, though, is that if there were more truly good teachers of K-12 math, we could be keeping all but the creme de la creme of students highly engaged in meaningful mathematics until they actually get to college. There’s nothing all that new about this. Read Richard Feynman’s autobiographical books and see what he did to get through calculus well before college. And there weren’t nearly as many good books out there in his youth as there are now, and obviously no computers or Internet sources. Still, he had to seek out resources on his own. He was motivated to do so. Yes, he WAS a physics genius, but he also had a dad who, though not highly educated, was a huge positive influence on his son’s curiosity and autodidacticism. We need more people like Feynman’s dad, on my view, and fewer people who either try to push their kids to take calculus in the womb or whine about the government conspiracy to “dumb down” math by bringing thought and conversation into the elementary mathematics classroom.
Michael, I bow down to your expertise. You are the scholar on this subject. I agree, if a talented individual is motivated enough, they can teach themselves anything (although guidance would be most helpful). And you, of course, have a wider range of experience with such advanced students. Perhaps TE has a valid point.
I’m sure there are many math teachers in this country who have gaps in their knowledge. And, with the current policies, I forsee the problem getting worse. What happens when TFAs start teaching Math, even to elementary students?
We do have reasons to be afraid, very afraid. We might just need a nation of students who are self taught.
Actually, I’ve had little opportunity to work directly with so-called gifted and talented kids. I prefer to think that there is not only a spectrum of math talent/ability, but also that most of us vary from day to day and topic to topic in how sharp we are, which is why heterogeneous grouping can be very productive. I don’t mind some homogeneous grouping, too, but am wary of it to the extent that I know too many folks who love the old-style tracking system mostly for reasons I can’t support.
My best guess is that if we had better early elementary mathematics teaching (and teacher training), we could make a positive difference in the overall mathematical ACHIEVEMENT of our population. Not that we would thus solve the many ills of an economically and socially inequitable society, but only that we could get more people to know more mathematics, which is probably a good thing. Unfortunately, I remain pessimistic about seeing a lot of change for the better in the immediate future. I was much more optimistic 22 years ago when I came to U of Michigan as a new (but middle-aged) graduate student in math education.
As for TFAers becoming math classrooms, I’ve worked with some of them in Michigan and in NYC. A few were good math teachers. A few have stayed teachers for longer than the requisite two years. I know of one in NYC and one in Detroit for sure who are still teaching. Some of them weren’t good teachers. Some of them might have become good teachers of SOMETHING, and a few could have become good teachers of mathematics at the middle school or high school level, but they never intended to be teaching for more than two years. The problem with some of them was that they’d swallowed far too much Wendy Kopp Kool-Aid. The problem with others was that they didn’t belong in a K-12 classroom no matter how well they did in college math or economics or what-have-you. And of course many just weren’t any more likely to become the sorts of mathematics teachers I want to see teaching kids, particularly those who have been least well served by the system.
Self-teaching isn’t for everyone, and virtually no one is going to learn mathematics without outside resources, be they actual humans, videos, or written sources in books, online, etc. Maybe there are a handful of people in history who were truly natural, unschooled mathematical geniuses, but most of the big names in the history of mathematics had mentors, teachers, professors, etc. that were important in their development.
But as to learning enough mathematics to do upper division STEM coursework without having sat in regular K-12 classrooms from start to finish? That’s not so implausible. Because the level of mathematical maturity necessary to thrive in school mathematics through the end of basic calculus (not undergraduate analysis/advanced calculus courses that are proof-theoretic and take a more mature understanding of knowing/doing/learning mathematics) is lower than we tend to think. As I tell students all the time who blanch at the mere word “calculus,” to learn it at the level most people who take a couple of classes in it in college actually do isn’t really so hard, by and large, if you’ve got a solid grounding in arithmetic, algebra, trigonometry, and geometry, and can grapple with only a handful of concepts that are new. Actually having a real understanding of what’s going on, however, is a more challenging matter entirely, but very few people need or want to “go there.”
Ellen,
I think that the way that math is taught turns many who would in fact be good at math away from it. If we can change the way it is taught, perhaps many universities can have a much large number if math majors.
Even in my public school classrooms there are children (mostly boys) whose parents have taught them the traditional algorithms for the four operations before they are required in school, according to the academic progression as outlined by the districts grade level curriculum. Except for a rare few (both boys and girls), who seem to have an innate talent for understanding how numbers work, most who excel in the early grades are average children who are good memorizers.
Even some teachers may consider these children advanced, or ahead of the other students in class based on the calculations that they can perform. The problem is, they are not more advanced, in their understanding of the structure and utility of the structure of our number system, than are many of the other children in class. In fact when memorizing process is not the criteria for success, they are merely good memorizers that can easily learn to apply formulas. They still have lots to learn.
There was a discussion the other day regarding this particular article. There were a few here that wrote about their own and their children’s successes in life learning math the old fashioned “vertical” way through memorization and application. One might also call that the ‘masculine’ way. They complained that having to work at a deeper level to problem solve and explain their thinking (feminine?) was too difficult and confusing.
Too many children (girls) have been convinced that they are not good at math precisely because they do not, or refuse to, memorize a process until they understand the underlying concepts.
Look at our economy. I believe that it is a result of having far too many people who do not understand how the numbers game is played, and as a result, voting against their own financial self interests. In particular, there are far too many women who are convinced early on that they are not good at math. I think that there might be a connection between how we teach math and the sad state of affairs we find ourselves in here in the United States.
We could do a better job teaching math in this country. Perhaps a more thoughtful, “horizontal” (feminine?) approach would be better for more students.
Robert Berkman says that Elizabeth Green does not offer links to give her claims context but his argument basically relies on defending against exploring questions regarding how math is taught in this country. His argument seems to rest on the idea that if it was a good enough for him, when he was in school, then why change things.
Betsy, are you sure you read my post carefully? I didn’t say anything about whether I was in favor of traditional vs reform math (I’m actually a rabid constructivist, if you must know.) My point was that here is an article about how Americans are bad at math, and wouldn’t you know, the writer consistently misuses statistics to support her point. In fact, she has no point, because her statistics do not prove that Americans are, in fact, “bad at math.”
If that’s all Robert Berkman got from the Green article, maybe he stinks at reading. Though it has a few flaws, on balance it’s an excellent piece, one of the better ones I’ve read in a major media outlet about math education issues. The test score stuff is predictable and has been debunked so many times by lots of very knowledgeable people, most noteworthy the late Gerald Bracey. And there is a particularly bad claim about multiplication being “just repeated addition” in Green’s accompanying piece, though I suspect that the vast, vast majority of Americans would have no argument with that notion, wrong-headed though it is.
However, there are so many good things in the article, from the material about Maggie Lampert and her work to the smart and fair treatment of Japanese mathematics education that to only carp about the flaws (she also is overly credulous about the birth of the Common Core Standards), that one needs to be blind, ignorant, or very biased not to praise her for the overall thrust of the article. She mostly gets it right, a VERY rare thing about math education these days.
Michael, you got there before me. Bergman misses the point. Most of the way math is taught in the US sucks.
I’ve spent a career teaching K12 and teachers. Middle school to AP. I’m a Montessori parent. I do statistics professionally.
With the NCTM Standards and other programs in the 1990s we were making progress. NCLB and the testing sidetracked a lot.
If Common Core were to be implemented in line with the NCTM position paper Principles to Action,, we might have a chance. But I doubt we will. We have too many teachers and parents who see math as the math of the 1950s, the Dolciani Algebra.
Yes, Americans do stink at math. And the fault is in ourselves.
Hi Michael – I agree with you: the description of how the U.S. research on mathematics learning ended up being perfected in Japan is excellent, and I liked the contrast she made with “school based” versus “real life” mathematics. Still, numbers are numbers, and Green’s use of them constitutes journalistic malpractice.
Green criticizes past scorched earth approaches, rightly including Common Core, but concludes with the same old idea of throwing out everything and starting over. All this means is we substitute one set of problems for another. Certainly, brushing the rhetoric and hysterics aside, there are methods currently working in the classroom. We need to indentify and refine those methods.
Second, I hesitate to reduce math to just concrete, real word approaches to problem solving as Green suggests. Green peppers her article with anecdotal stories of failure and success with math, but none of that is relevant other than for entertainment value. Math is steeped abstraction. The power of mathematics, more than any other field, is to model and predict based on pure conjecture and logic. Students need to be introduced to the “why” of math as soon as they are developmentally ready.
“Green peppers. . . ”
I’m not sure what capsicum annuum has to do with math teaching.
I think that the article was really, if taken in its entirety, against the whole Standardized Testing mania that is engulfing our country. Japan would never have been able to introduce this new way of teaching Math if the teachers didn’t have time to confer, time for staff development and a situation where they could absorb new ideas without the pressures of VAM. It is too bad that she didn’t make this clear in her article.;
I think Green consciously tried to resist the temptation to get overly-caught up in advocacy. The excellent practices she described from Japan speak for themselves to those with ears to hear, and it’s clear to any reasonable person who has experience with lesson study that the US isn’t ready for it on the whole. Why not? Because it’s “costly” and “fuzzy” and doesn’t appeal either to phony deformers or to the hard-line math professors, engineers, scientists and their parent allies who comprise groups like Mathematically Correct, NYC-HOLD, and other parents-with-pitchforks groups who hold the narrowest, most traditional ideas about K-12 math instruction. It’s just “too fuzzy” for them, because it can’t be simplistically quantified with test scores and feels too touchy-feely for their taste. Professionals having to open up their practices to other professionals? Collaboration? Just too expensive and “weird” for them. Which is one way to know it’s likely VERY worthwhile.
Michael, haven’t the practices that Green describes in Japan been covered before, like in “The Learning Gap” by Stigler and Stevenson, which was published 20 years ago? If so, where exactly is the “news” in this article? My point is that Green’s assertion that “Americans” stink at math may not be true – she hasn’t actually provided any reliable evidence to prove this. As the old saying goes, “the plural of anecdote is not data.”
Stevenson wasn’t inclined to talk about the downside of Asian math education at all. I wrote about that in grad school in 1993, but it isn’t like my essay made the NYT.
And we still don’t get math education here for the most part. So regardless of your dislike of Green’s stats, the article is mostly timely, useful, and on point. I think you are dismissing too much to get at what bothers you here. I had complaints, too, mentioned them here and elswhere, but chose to focus on the aspects of her message that I feel are vital and to praise her choice not to quote the usual Math Wars idiots.
I find the conversation that I hear in this teacher’s room, to be fascinating. So many of you are so intelligent, educated and experienced that to read your commentary threads is a delight. What I want to say, here I want to say to all, so the rest of this comment I will post to the blog as a whole.
Thank you for your perceptions and thoughts.
Michael, if Green asserts that Americans stink at math, and the data she uses doesn’t support her assertion, doesn’t the entire article kind of fall apart? While I don’t think our system is by any means perfect, if you consider the kind of social and economic issues that plague school-aged children, I’m inclined to think we get a lot of bang for the buck. An article that actually looks at the performance of U.S. students in the face of the poverty, bigotry, abbreviated school years and low regard for the teaching profession (especially the amount that they are underpaid), well, that would be a STORY!
It would be a story, and the way the professional teacher -practioner is treated IS the story. It would take an investigative journalist like Jack Anderson was or a real journalist.
I think it’s too easy to lose a bunch of important ideas someone illuminates or at least raises by focusing solely or principally upon what s/he leaves out or gets wrong. Sure, expose the errors, criticize the doubtful claims, point out key points not dealt with, but don’t dump the good stuff if it’s valuable, and don’t make it seem like the piece was a failure (unless it mostly was) simply for not focusing on what YOU might prefer.
I don’t see Green saying that poverty doesn’t matter, but it’s not her focus. She’s getting at some true and important things that most Americans still don’t get. If more do after reading her piece, she’s done us a service. And poverty certainly doesn’t account for bad math education in a host of places where there is very little or no poverty. Like the nice suburb in north Jersey in which I went to school in 1955-68. Poverty doesn’t in any way explain the brutally bad math teaching I increasingly slept through in 1964 – 68. That allowed me to graduate high school without the slightest clue what mathematics was about or interest in finding out, despite being able to score in the top 15% on mathematical reasoning on the SAT in Nov. 1967. It was not until my early 30s that I decided to go back to school for fun as a non-matriculating student at Borough of Manhattan Community College to repair the many holes in my K-12 math education and, as it worked out, go on to earn the equivalent of a BS in math, secondary certification in math, and, eventually, a masters in mathematics education from the University of Michigan. I am a relatively rare case: poorly served by traditional math curricula and teaching, but later going back to school to satisfy my curiosity. Good for me, but not so good for millions who didn’t have my lucky combination of friends, mentors, etc., that got me to go that way.
Good Points. I agreed. See my comment on the Nocera piece in the NY Times today, which I am posting here as a general reply
I haven’t read the piece yet. I do know lots of college educated people that cannot calculate how much of a tip to leave or even do very simple multiplication without a calculator.
It doesn’t help that it is socially acceptable to say that one can’t do math and that it is socially acceptable to treat STEM professionals as having no social skills
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Berkman’s advice to “hire a statistician” is something that many people (including those involved in education reform) would undoubtedly benefit from.
Some reformer/researchers not only don’t solicit review of and advice on their research by professional statisticians before they publish, but, worse yet, they essentially disregard such review and advice after the fact (when it has been offered unsolicited)
They could spare the public of lot of bogus claims and a lot of grief (and spare themselves a lot of embarrassment) if they actually sought out and took to heart expert advice on statistical matters that are well above their own pay grade.
I agree; the most egregious example is the use of VAM to evaluate the effectiveness of teachers. It has been so discredited that the American Statistical Association has written a position paper opposing its use.
Some DAM Poet & Robert Berkman: IMHO, the critical element holding together the public face of the business plan that masquerades as an education model [aka “education reform”] is standardized testing.
As I see it, once you begin to grasp the thinking and practice behind the design, construction, pretesting, administering and scoring of such numerical artifacts—
Many other things like VAM and international comparisons [based on test scores, of course] lose their power to intimidate and mislead.
Rather, it becomes clear that numbers and stats as used and abused by the typical self-styled “education reformer” is merely a restatement of Andrew Lang’s comment:
“He uses statistics as a drunken man uses lamp posts — for support rather than for illumination.”
Thank you for your comments.
😎
I couldn’t make it past the second paragraph, in which Berkman appears to scold Green for using the term “America” to refer to the United States (and presumably also her use of “Americans” to refer to United-Statesians), which to Berkman is an act of ignorance, or chauvinism, or hubris, or surely some character flaw that we must not abide. I say “appears to scold” because although I see none of the usual markers of satire, such as humor or wit or a point, I still find it hard to believe he’s being serious. And yet there it is:
“Me, I love a good screed disparaging Americans as much as anyone else, although I would like to point out to Ms. Green that ‘America’ is composed of two continents, North and South, and that even if she were referring to North America, we do share this continent with Mexico and Canada. Oh, and then there’s that issue about those people who were here before there was an ‘America,’but let’s not get technical, okay?”
Okay!
Oh, sorry you missed that: yes, the first paragraph was written with tongue planted firmly in cheek. Now that I’ve cleared that up, would you finish reading?
That depends on the point of the tongue-in-cheek. What’s the joke? The idea that anyone could consider the egregious use of “America” to refer to the United States to be a mere “technicality,” with the punchline conveyed through the tongue-in-cheek “but let’s not get technical”? (Ha, “technical” indeed!) Or the idea that anyone could be silly enough to actually take issue with the use of “America” to refer to the United States, with the entire paragraph delivered tongue-in-cheek? If the latter, I will absolutely read on.
Flerp – it’s the latter – read further and enjoy!
I think the New York Times reporter is too reliant on OECD reports. So is the Wall Street Journal. On July 18, the Wall Street journal had a sort blurb that caught my attention—a new report on education from the Organization for Economic Cooperation and Development (OECD). The OECD is the source of almost all of the reports about our terrible system of education compared with other nations.
I have looked at the executive summary of this report, “ Measuring Innovation in Education,” and a four-page summary on the US “innovations-in-education.”
The Wall Street Journal said that school systems do best with “rapid all-at-once change.” I suppose this is an endorsement of “disruptive” and “transformational” change for education (if there is plenty of room for tax-subsidized for-profit education).
Neither the Wall Street Journal nor OECD doubts that innovation is a great strategy for improving education. Of course, the prime measures of “improvement” in the OECD report are scores on the international math, reading, and science tests administered under the auspices of OCED, along with some additional data it collects about higher education for it new Composite Index of Innovation.
These international tests, with data from 2000 to 2011, are the major proofs that OECD offers readers for the success of “an innovation” and also, it seems, some sort of proof that an “innovation imperative” exists within the education sector of the economy.
In the four-page summary report for the USA, you will find a bar chart (17.1) that seems to place the US way, way, way behind in the innovation-in-education race—the sixth worst innovator in education among 29 entries.
Leading the innovation–in-education race are Denmark, Indonesia, Korea, the Netherlands, the Russian Federation, and Hungary (in that order).
A closer look at this chart reveals that the Index is picking winners among 22 nation-states, and all are in the same race with Hong Kong and Singapore, also three separate provinces in Canada, plus the United States, plus Indiana, Minnesota, and Massachusetts.
Massachusetts is not likely to pleased it is in actually in last place.
Here are few more of the amazing insights about our “innovations” in the United States offered in a bulleted list, as if all are perfectly wonderful transformations that somehow arose spontaneously from the ingenuity of teachers.
According to the OECD, “The top five US innovations in pedagogic and organisational practices (most between 2000 and 2009) ” are: (drums and trumpets please):
(1) More use of student assessments for monitoring year-to-year achievement.
(2) More use of student assessments for comparing school performance to district or national performance.
(3) More use of achievement data over time by an administrative authority. An increase for the USA from 76.2% to 96.9%…”the largest increase in this metric of any educational system analysed for this report.” (Notice the extreme importance OECD has attached to cut off scores with the difference of only .1%.)
(4) More frequent observations by inspectors or other persons external to the school to evaluate teachers (2003-2011).
(5) More parental invitations to join school committees (well above the OECD average).
Although the full report may tell a fuller story, the Summary is silent about the policies, politics, and money driving these “innovations.“ It is also silent about the history of test scores and why their many uses should be considered innovations.
There is no mention of OECD’s own role in creating rhetoric and policies that forward an international competition based on test scores and the consequences of that for well-informed and comprehensive thinking about education here and in many nations where educators are sick and tired of being subjected to OECD and other ratings.
Find this the US summary at http://www.oecd.org/unitedstates/Measuring-Innovation-in-Education-USA.pdf Other links to the full report and methodology are in this summary.
See also http://online.wsj.com/articles/report-finds-u-s-schools-rank-below-average-in-innovation-1405635683
Of the OECD report’s top five innovations the first three can be summarily dismissed as “vain and illusory” (Wilson’s term) as they are based on standardized tests that have so many conceptual and implementation errors that the whole test making, giving and disseminating of results COMPLETELY ILLOGICAL and INVALID and at best UNETHICAL and at worst harmful and damning to students.
To understand why read and comprehend Noel Wilson’s never refuted not rebutted “Educational Standards and the Problem of Error” found at: http://epaa.asu.edu/ojs/article/view/577/700
Brief outline of Wilson’s “Educational Standards and the Problem of Error” and some comments of mine. (updated 6/24/13 per Wilson email)
1. A description of a quality can only be partially quantified. Quantity is almost always a very small aspect of quality. It is illogical to judge/assess a whole category only by a part of the whole. The assessment is, by definition, lacking in the sense that “assessments are always of multidimensional qualities. To quantify them as unidimensional quantities (numbers or grades) is to perpetuate a fundamental logical error” (per Wilson). The teaching and learning process falls in the logical realm of aesthetics/qualities of human interactions. In attempting to quantify educational standards and standardized testing the descriptive information about said interactions is inadequate, insufficient and inferior to the point of invalidity and unacceptability.
2. A major epistemological mistake is that we attach, with great importance, the “score” of the student, not only onto the student but also, by extension, the teacher, school and district. Any description of a testing event is only a description of an interaction, that of the student and the testing device at a given time and place. The only correct logical thing that we can attempt to do is to describe that interaction (how accurately or not is a whole other story). That description cannot, by logical thought, be “assigned/attached” to the student as it cannot be a description of the student but the interaction. And this error is probably one of the most egregious “errors” that occur with standardized testing (and even the “grading” of students by a teacher).
3. Wilson identifies four “frames of reference” each with distinct assumptions (epistemological basis) about the assessment process from which the “assessor” views the interactions of the teaching and learning process: the Judge (think college professor who “knows” the students capabilities and grades them accordingly), the General Frame-think standardized testing that claims to have a “scientific” basis, the Specific Frame-think of learning by objective like computer based learning, getting a correct answer before moving on to the next screen, and the Responsive Frame-think of an apprenticeship in a trade or a medical residency program where the learner interacts with the “teacher” with constant feedback. Each category has its own sources of error and more error in the process is caused when the assessor confuses and conflates the categories.
4. Wilson elucidates the notion of “error”: “Error is predicated on a notion of perfection; to allocate error is to imply what is without error; to know error it is necessary to determine what is true. And what is true is determined by what we define as true, theoretically by the assumptions of our epistemology, practically by the events and non-events, the discourses and silences, the world of surfaces and their interactions and interpretations; in short, the practices that permeate the field. . . Error is the uncertainty dimension of the statement; error is the band within which chaos reigns, in which anything can happen. Error comprises all of those eventful circumstances which make the assessment statement less than perfectly precise, the measure less than perfectly accurate, the rank order less than perfectly stable, the standard and its measurement less than absolute, and the communication of its truth less than impeccable.”
In other word all the logical errors involved in the process render any conclusions invalid.
5. The test makers/psychometricians, through all sorts of mathematical machinations attempt to “prove” that these tests (based on standards) are valid-errorless or supposedly at least with minimal error [they aren’t]. Wilson turns the concept of validity on its head and focuses on just how invalid the machinations and the test and results are. He is an advocate for the test taker not the test maker. In doing so he identifies thirteen sources of “error”, any one of which renders the test making/giving/disseminating of results invalid. And a basic logical premise is that once something is shown to be invalid it is just that, invalid, and no amount of “fudging” by the psychometricians/test makers can alleviate that invalidity.
6. Having shown the invalidity, and therefore the unreliability, of the whole process Wilson concludes, rightly so, that any result/information gleaned from the process is “vain and illusory”. In other words start with an invalidity, end with an invalidity (except by sheer chance every once in a while, like a blind and anosmic squirrel who finds the occasional acorn, a result may be “true”) or to put in more mundane terms crap in-crap out.
7. And so what does this all mean? I’ll let Wilson have the second to last word: “So what does a test measure in our world? It measures what the person with the power to pay for the test says it measures. And the person who sets the test will name the test what the person who pays for the test wants the test to be named.”
In other words it attempts to measure “’something’ and we can specify some of the ‘errors’ in that ‘something’ but still don’t know [precisely] what the ‘something’ is.” The whole process harms many students as the social rewards for some are not available to others who “don’t make the grade (sic)” Should American public education have the function of sorting and separating students so that some may receive greater benefits than others, especially considering that the sorting and separating devices, educational standards and standardized testing, are so flawed not only in concept but in execution?
My answer is NO!!!!!
One final note with Wilson channeling Foucault and his concept of subjectivization:
“So the mark [grade/test score] becomes part of the story about yourself and with sufficient repetitions becomes true: true because those who know, those in authority, say it is true; true because the society in which you live legitimates this authority; true because your cultural habitus makes it difficult for you to perceive, conceive and integrate those aspects of your experience that contradict the story; true because in acting out your story, which now includes the mark and its meaning, the social truth that created it is confirmed; true because if your mark is high you are consistently rewarded, so that your voice becomes a voice of authority in the power-knowledge discourses that reproduce the structure that helped to produce you; true because if your mark is low your voice becomes muted and confirms your lower position in the social hierarchy; true finally because that success or failure confirms that mark that implicitly predicted the now self evident consequences. And so the circle is complete.”
In other words students “internalize” what those “marks” (grades/test scores) mean, and since the vast majority of the students have not developed the mental skills to counteract what the “authorities” say, they accept as “natural and normal” that “story/description” of them. Although paradoxical in a sense, the “I’m an “A” student” is almost as harmful as “I’m an ‘F’ student” in hindering students becoming independent, critical and free thinkers. And having independent, critical and free thinkers is a threat to the current socio-economic structure of society.
As someone who has proctored the 8th grade assessments (pre-CC), it is ridiculous to expect eighth graders to write algebraic equations when they don’t take Algebra until 9th grade. Only the advanced students take Algebra prior to high school. And reading a thermometer is not necessarily a skill taught in math, especially since technology has digital thermometers available at a low cost for everyone, not just hospitals, to use.
Perhaps the tests need to be updated so they reflect the 21st century instead of the mid 1900s.
Exactly. Those are ludicrous examples.
One of the issues that Ms. Green never addresses is the need for professional development for teachers. As a district-level administrator, I saw what happened during the recession. The first item to get cut in school budgets was money for PD. You cannot expect teachers to sit down at the end of a school day and learn new teaching strategies. Some of teachers in middle school teach 150 students in a day. They need to get papers graded and lesson planned.
What needs to happen is more intensive PD during the summer when teachers can devote their undivided attention to curriculum revision and best practices. Districts don’t want to pay for this.
Another issue with the Common Core Math is that it was introduced to all grade levels at the same time. If you are a fifth grade student (or fifth grade teacher), tackling the CC without the prior K-4 background, you are at a definite disadvantage. When my district introduced the Everyday Math program a number of years ago, the district started with first grade, trained the teachers during the summer and the next year moved to second grade. The curriculum was a success.
Details are sometimes overlooked when a writer has a narrow focus – bashing teachers.
Tom – what a common sense response. Too bad the right people aren’t listening.
And on p. 9 of the same magazine: a full-page ad for the New York Times “Schools for Tomorrow: Disruptions in the Lecture Hall” forum Sept. 8 & 9. The panel includes NYT conservative columnist David Brooks and…yes, Michelle Rhee.
I WISH I taught only 150 students a year. I taught 260 students in a core subject, grades eight and nine, last year. And we’re still expected to do PD for free. It’s getting to the point where I basically have to pay for the privilege of being a teacher.
In the district I teach in,here in Kentucky, our PD was on test taking skills and assessing data for the last ten years. Now we’re spending time figuring out common core plans from Bill and Melinda. Oh, we bought EVERY DAY MATH,but not the training component – then spent several PD days trying to figure what went wrong with our scores and blamed the math publisher.
She does mention most developed country teachers spend 600 hrs per year on classroom instruction as opposed to 1,100 hrs per year for U.S. teachers.
The problem with math instruction is we do not teach enough of the “why” behind the “how”. I do not see Common Core’s emphasis on standardized tests and rigid structure as any solution. Instead, math teachers must now focus on test strategy and mechanistic instruction.
Tom,
Thanks for the sensible comments. It is not very reasonable to expect teachers to be able to work on new ideas at the end of the school day (I have 185 students) with other things to think about. But I thought her main point was that it is ridiculous to ask teachers to completely revise the way they teach a subject without giving us the time and support to master new techniques. My district has a history of handing out a new curriculum two days before the start of school, which leaves me with the impression that they don’t think that it requires reflection or thought to implement lessons.
In the article, Green writes “…in Japan, teachers teach for 600 or fewer hours each school year, leaving them ample time to prepare, revise and learn. By contrast, American teachers spend nearly 1,100 hours with little feedback.”
She also writes about jugyokenyku, a type of professional development. It sounds like teachers in Japan get a lot of support.
I didn’t agree with everything about the article, but it was nice to read about a place where teachers are respected and supported
I thought the NY Times magazine article was interesting -maybe because I don’t teach math….and never really liked the subject, either.
But….. then I couldn’t stop thinking about the fact Elizabeth Green cites about educators in Finland and Japan teaching so many fewer hours than teachers here in the U.S. , -allowing them time to collaborate and learn. (Now there’s some important numbers!)
It’s difficult for me to believe that our government (and the Robber Barons that are too often controlling our legislators) are going to suddenly devote the sort of funding that would free up teachers and other school staff for the sort of work that Elizabeth Green advocates. I mean, c’mon, really? We’re talking about a lot of money if you’re going to do it right. And, I can just imagine some of the comments that would come from the public in our country.
I wish Ms. Green would have pursued this angle further. It seems like she just left that very important fact hanging there.
I finished the article feeling a little bit cheated. I got into it but by the end I had the sinking feeling that, yup, here’s the Times flogging the common core again. The thing’s going south, support is withering…..so let’s devote an entire magazine piece on a Sunday in July giving the common core yet another advertisement.
And, instead of blindly citing research from the Bill and Melinda Gates Foundation, how about a real, in depth Times piece about how Gates has manipulated the reform process from the start, as so wonderfully documented by sources cites here on Diane’s blog?
-John O. (Still a disappointed Times reader)
Hey, “A”…..
I was typing for a while then saw your comment above mine after I hit “post comment”.
We must’ve been thinking the same thing at about the same time.
You nailed it. I like the way you put it!
-John O.
Missing the most important point… which is that this incarnation of the new math is thrown at teachers with no support. Missing the reality of the way teachers in places where a new paradigm for the teaching of math is accompanied by collaborative activities so teachers know what is working as others struggle to learn it. We teachers only ‘teach’ what we ourselves know. While I was a cohort for the standards research, the word ‘teach’ was replaced by the words ‘enable’ and facilitate. Practitoner of a new procedure in medicine and science ar given access to all they need to enable them to pass on what they know.
What exists into days schools are administrative who are punitive in their actions. The principals that I have met, and i have meet dozens in NYVC do not assist teacher to do anything. In fact, when 80% not the novice practitioners discover the culture of deceit and hostility, they run.
All the the esoteric conversations that deal with the statistics, are missing the OBSERVABLE REALITY… THAT THE NEW MATH IS FAILING because teachers are isolated and given no access to the kind of professional staff development that is needed to SUPPORT their practice… and by the way… there were FOUR principles of learning in the Pew funded , authentic standards research, that WERE FOR THE PRINCIPALS… to support classroom learning… and in every one of the thousands of classrooms in this third level research, when the students succeeded it was not merely that the teacher-practitioner met the 4 principles that must be in practice for learning to occur…. THE ADMINISTRATION WAS SUPPORTING THEIR PRACTICE.
THE AMERICAN EDUCATOR is filled with articles on the successful schools, and one and all they discuss the collaboration that makes it work.
For the hundred thousand teachers who were sent packing in the first assault on public education and for those of you who are presently working in schools where top-down management makes the rules, issues the mandates, and not only fails to support the teacher, but actively impedes real learning with dictates that are anti-learning, the CRUX OF THE MATTER IS YOU ARE ALONE IN YOUR DEDICATION to enable those kids… you care, and given the support, including smaller manageable class size, and texts, materials and staff development you would FLY… AND SO WOULD YOUR KIDS.
THIS IS THE REALITY that took working schools and created failure.. in the largest school district of the “15,588 districts, even as they do their think in LAUSD, promoting kids with 2nd grade skills and blaming the teaches.
I do not agree with everything Ms. Green said, but the crucial truth was the way the failing schools lack a culture that respects the dedication and talent of the professional practitioner, and is willing to help the teacher to do the job. THAT is why the school fails..
And by the way, my niece ran a successful elementary school in San Francisco. She new the teachers who were fine practitioners, and she helped them. Her success led her to become the principal of a K to 8 school, which is doing very well too.
I am NOT anti principal despite my experience with the failed human beings who got to run the show…. into the ground. In my 40 year career I met the real administrators and in every one of those schools the teachers depended on them, and the schools functioned.
Then when the assault began, everything changed, as Lorna Stremcha describes in her new book. (title is in flux….used to be called “Sins OF THE SCHOOLS, but the editor is changing that. Here is an excerpt:
“My book is now in the hands of editors and I’m hoping it will be on bookshelves soon. It describes what happens when bureaucratic bullies try to cover up, intimidate and harass a tenured school teacher. Following is an edited excerpt from “Sins of Our Schools: After the Bell Rings” that describes what it sometimes takes to fight bullies in powerful positions.
Looking at all the boxes stacked in my basement, I still wonder how I survived four years of legal wrangling. Many attorneys feel that this part of the law is all a “game”. It wasn’t a game to me. It was a pursuit of justice. Thanks to my family and faith, we survived it all.
My book only described some of the more important events that happened during this four- year period. There is no way I could convey the mind numbing details that dominated every day of my life.
The administration’s response to my complaint before the Montana Human Rights Commission eventually caused me to pursue multiple legal avenues. I had to file specific grievances against the school, additional complaints before the Montana Human Rights Commission, and finally State and Federal law suits. That’s the way the system works. It’s difficult and complicated. When dealing with our public schools, you can’t just file a lawsuit. There is formula for everything.
In today’s world of high self-esteem, it’s sometimes difficult to determine when (and if) you have a case. Many of us don’t take criticism well and are very thin-skinned. The first step I recommend is to take a good look within. Ask yourself if your boss or coworker is truly a bully, or if he/she is offering what they think might be constructive criticism about your work or professional abilities.
Study numerous books and articles concerning bullying behavior. Make some lists and determine if you are truly the target of a bully. If that is the case, your next decision is whether or not it’s worth it to stay in that toxic environment. Would you and your family be better off if you left and found another job? If that’s the case, move on. If you are in a job that you love and want to stay, then it’s time to fight.
Learn about the laws in your state. There are numerous laws on the books about various kinds of harassment. In many states the law hasn’t caught up with the bully. It is critical to build a case by documenting everything.
Journals and notebooks are valuable tools. Even events that might seem unimportant now could become critical in a legal action. When keeping records remember who, what, when, where, and how of reporting. Dates are especially important.
Keep all your documentation in a safe place and keep it organized from the start. Never give anyone an original. Make copies and keep originals and copies in separate locations.
Speak out! Tell others what is happening. If you are fortunate enough to have a trusted friend or coworker ask them to write down their impressions. If others have witnessed events that you describe in your journal, ask them to sign and date the documents.
Remember the human resources person has the same employer as you do. It’s only natural that their first loyalty will be to the source of their paycheck. Do not consider them a friend who is there to listen, comfort, and console. In this case try to leave your emotions at the door and discuss only the events in question. Be brief and to the point. Not everyone will believe you. No matter what you say, many will choose to believe those in authority.
Know the contents of your collective bargaining contract. If your employer has a list of employee rights, get and keep a copy. Ask for your personnel file and insist that they provide the entire file, not selected pages. Check the file on a regular basis. Make copies each time.
Even though it seems futile, continue to scrupulously follow company policy. Use the state and federal laws that pertain to employee rights. If you don’t know the laws, find someone that does. Work with them. Obtain legal counsel before filing any complaint.
Before hiring an attorney evaluate your financial situation. Almost every legal battle costs more and takes longer than anticipated. Ask yourself if this case is so important that you are willing to mortgage your house, dip into the children’s college fund, and take every dollar from the savings account in order to possibly obtain satisfaction and justice. There are some legal aid organizations that might be willing to help, in certain situations, but the sad financial fact is that you will be on your own.
Once you decide to fight here are some things you need to know:
Know that your battle will be long and arduous.
Know you will have enemies.
Know that some friends will become enemies.
Know you are not crazy.
Know you will feel alone, even when the room is full.
Above all, take comfort in your friends and your family. They will provide security and strength in what will probably be a long journey. It won’t be easy. If you are following the right path, you will hopefully reach a safe end to the journey.
Working with my attorneys I learned there are different components to discrimination, hostile environment, bullying, and sexual harassment cases. The information I provide is based on my experience. Again, I encourage you to seek legal counsel. Find someone experienced in employment law.
In some states there are no laws concerning bullying. You must learn the language of your laws and find the best tools with which to fight your own case. It might be age discrimination, sexual harassment, or a hostile workplace environment. Sadly, just because you have been bullied it might not mean you have a legal case.
Sexual harassment can be the result of a single incident. Individual incidents of bullying tend to be trivial and often are not enough to merit disciplinary or grievance action. Bullying is an accumulation of small incidents which slowly grow over a long period. Bullying occurs usually, but not always, when one person (or many persons) in positions of power or authority feels threatened by another person or subordinate that displays qualities or abilities which the bully believes he/she can never possess.
Workplace Bullying is the repeated mistreatment of one employee targeted by one or more employees with a malicious mix of humiliation, intimidation, and sabotage of performance. Bullying crosses the boundaries of race, religion, gender, sexual orientation, and age. Anyone can be a bully and anyone can be bullied. Those who are bullied often find themselves with little, if any, support. If it goes on long enough, job performance suffers and that may often lead to job loss.
Bullies prey on those weaker than themselves. Often their targets are employees under their supervision. That makes it easy for them. Their goal is simple: to make everyone around them look bad while they look good.
We can all recognize a bully. I have described several in my book. The Internet is full of discussions concerning this problem. Always remember it is up to you to prove that you are being bullied.?
Susan,
What is “third level research”?
Thanks in advance!
Duane
Gee, Duane, scientific theory must be researched, but unlike the kind of research that pharmaceutical companies of to ‘prove’ their expensive medicine works, third level research uses a statistical base that is huge, and representative…. in plain words for those who did not study statistics in college…. it gotta work everywhere, not just in Oshkosh or FOR EXAMPLE, some school district in Detroit, that thinks 100 kindergarteners benefit from such a huge class.
For the zillions they would spend…. Pew chose 12 representative school districts from the 15,880, and studied THOUSANDS OF CLASSROOMS, IN LOW, MIDDLE And HIGH PERFORMING SCHOOLS.
After five years of filming, studying what teachers use and how they plan and implement, how they evaluate, they validated the theory that the FOUR PRINCIPLES OF LEARNING for the practioner, if present, showed SUCCESS.
THIS ‘theory’ that Harvard’s Lauren Resnick said operates in all classrooms where CHILDREN LEARN worked — (notice the absence of the word “teaching’ ”
This theory, therefore, was VALID, and thus, in all classrooms, with low or high performing kids, if there was genuine success, as indicated by authentic performance assessment ( authentic and genuine were BIG words in the research) these principles were in play.
IN all places where kids are ENABLED to learn, (another favorite word that replaced the Duncan rant about ‘teaching’) the teacher FACILITATED (another word to replace teaching) learning if the four principles were in play… there were over 20 indicators for each principle, by the way).
Also, BTW, there were FOUR PRINCIPLES For PRINCIPALS… pardon the wordplay.
They all involved the SUPPORT of the practitioner, such as:
* supplying current and important materials and texts, and (hold onto your hat)
* a safe, quiet environment (with removal of disruptive elements & class size being a key component, and
* the hiring of SUPPORT staff to ensure that the practitioner meet learning goals, AND
* it is the principals job to ORGANIZE the plant, so that things move well, and to schedule and create collaborative efforts were the teacher isolation is mitigated.
** Included in this support were the workshops that PRECEDE the introduction of NEW mandates, AND the implementation of programs that ASSIST the less abled novice to learn and correct deficiencies in instructional technique.
That YOU don’t know about the REAL New Standards, is no surpass and not your fault… no one does… no educator, no blog, NO WHERE, not here or from the NRA or AFT, does anyone describe or refer to it, as they push the Duncan narrative.
Into the trash went the GENUINE, AUTHENTIC research out of Harvard and the LRDC at the University of Pittsburgh, who sent the ‘tools’ folks, the observers and the staff developers who went into the districts in this HUGE sample, and gave workshops for all teachers, but who studied and reported on the Cohorts!
They, by the way, were the ones CHOSEN AT THE START because by all measures of achievement and success (standardized tests, parent satisfaction, student accomplishments and acceptances to top schools, etc) the teacher was doing something right.
What that was, according to the indicators were simple things that the human brain must have present in order to ACHIEVE… LIKE
1- clear expectations.
2- rewards for achievement (an this was NOT test scores, by the way)
3- Good planning based on AUTHENTIC ASSESSMENT and GENUINE EVALUATION (gotta love those woods)
The fourth one, was the presence of a practitioner who knew the content COLD, who was educated and experienced and dedicated to learning. The teacher had to know her/his stuff…cold, and have that indefinable talent to motivate kids to learn what she/he knew… as long as the administration supported her/his practice!
I hope it is clear now.. oh, and by the way… at the end of all the filming, and the interviewing of my students, and the perusal of every single piece of curricula that I wrote (and mailed), and the materials I used, AND the student work…. I WAS ONE OF SIX WHO MET THE STANDARDS IN A UNIQUE CURRICULA, which they showcased at the LRDC in their seminars for THE SUPERINTENDENTS from districts across the country, and then sent my work on tour…
I received the prestigious NYS English Council’s “Educator of Excellence award for this work, on this 3RD LEVEL RESEARCH and Ihave letters from the lRDC calling gym work BRILLIANT…. and within 4 months I was in a rubber room on bogus charges, and then real charges were put out… FOR INCOMPETENCE.
I mention this for one reason only, you see, IF the real STANDARDS WERE USED, then teachers would be IN CAHRGE OF THEIR PRACTICE as in the past WHEN THE SCHOOLS WORKED. Thus teachers like me, the genuine pedagogues would not accept test-prep as THE classroom REFORM. For the schools to fail, we had to go, and for 20 years before VERGARA DEALT THE FINAL BLOW with the BIG LIE. they desolated the lives of teachers and brought down the road to opportunity that had created our great land of dreams.
The real standards disappeared along with over one hundred thousand teachers like me, so Gates could substitute his ‘standards’ and VAM could replace genuine assessment of teacher performance, and then, Koch and Broad and Walton could build a charter network that produced a citizenry ignorant of the past, so they had no ability or facts to compare the utter bullpoop emanating from the media….like this, today.
Hope you get it now.
So “third level research” is a statistical model used in “meta” studies??
One point Ms. Green overlooked was the parallel to Deming’s experience, which mirrored that of Takahashi and Matsuyama and continues to limit our ability to innovate. Like Deming before them, Takahashi and Matsuyama implemented recommendations of US experts, recommendations that our country rejected because they did not fit the hierarchical “factory model” of management that blinds us to new and different ways of thinking.
As one who led school districts from 1980 through 2011 I saw two other factors that Ms. Green overlooked or underemphasized: our country’s obsession with standardized tests and the unwillingness of parents and school boards to accept “non-traditional ways” of teaching mathematics and scheduling teacher time… and, as noted in a blog post I wrote yesterday, one of the limiting factors for school boards is the budgetary impact because new programs when they are implemented well DO cost money.
We need to stop thinking of our schools as factories that pour information into students who progress along an assembly line in lockstep based on their age and whose progress is measured by standardized tests and hours spent in the classroom.
See http://waynegersen.com/2014/07/27/changing-gears-in-mathematics/ for more.
Be careful in throwing out the baby with the bathwater. While I would agree with the misuse of testing data, Green does point out an essential truth of failed efforts to teach implement conceptually based pedagogical models—in this case conceptually based mathematics. These models never gain traction because teachers lack the proper content background to teach sophisticated concepts in math–the same could be said about other subject areas (e.g. teaching of science). This is not meant to be a diatribe against teachers or their efforts in difficult classroom situations, but it does point to gap in our training regimes. In countries, like Japan or Finland, etc. the subject matter background of their teaching force surpasses what we require of teachers in this country. All the jokes that are being made about the new math (which we called modern math in the 60/70) gets a laugh, but the last laugh are in countries where students focus on conceptual understandings of a subject, rather than the endless repetition of mathematical routines/procedures/ on worksheets that are then replicated on Friday’s test —While our students in the U.S. do all the even problems tonight, and the odd tomorrow, other countries ask their students to think about and develop a strategy for solving ONE problem –for the week.
xxxxxxxxxxxxxxxxxxxxx Hear, hear on the conceptual vs regurgitation approach, particularly as regards Asian vs American pedagogy. As a non-math-brain bystander interested in pedagogy, I can tell you I’ve read detailed expositions of this stark difference K&up, comparing America’s methods to those in both Japan & China, a number of times, starting with 1980’s worried treatises regarding the tech challenge from Japan. The info has been out there for decades.
Though I agree the baby to be saved from the bathwater is teacher-training, just upping the game in college won’t do it. Curriculum is huge (sorry I can’t see Everyday Math or CCSS as anything but a toe dipped in the water, to mix the metaphor)– and would have to be supported with the sort of ongoing & collaborative PD we don’t see here (for obvious reasons).
I actually found Berkman’s article helpful. At the heart of the matter, it is all about instruction. Change requires investment of both time and resources. In education, we tend to come up short on both counts when it comes to preparing teachers and supporting them in the classroom.
When I read the article (which I am still reading) I was irritated also. She made so many assertions with no research to back it up. Thanks for this analysis because we need to stay focused and diligent in refuting these articles when they spring up. I will finish the article but know that you have clearly answered and pushed back against these statements so that they don’t stay in the collective memory.
Dear Friends – I’m glad this article inspired such vigorish discussion about the state of mathematics education in the United States of America (yes, I do use that term – referring to us as “Americans” is a bit chauvinistic in this day and age.) My original intent was not to criticize the “story” part of this article, which I thought was pretty good (with the exception of trotting out th at old idea that Common Core was initiated by math professionals and state governors: it is well documented that it was paid for and promoted by Bill Gates…)
However, how do we know that the headline is true, if all the statistics that Green uses are next to worthless? Perhaps our fellow citizens are actually better at math than has been previously thought? What does “mathematical proficiency” look like in this country? Sure, we all have anecdotes about the 8th grader who didn’t know his multiplication facts, but you could probably hear the same story in any other country. Green did some fine research on the actual practice of teaching of mathematics, needed a headline to get us to read it (even though much of that information was already covered by Stigler & Stevenson), and then conjured up some silly statistics to support it. Isn’t it ironic that Green is decrying our poor understanding of mathematics while abusing statistics so blatantly?
BTW, I actually just completed a post that once and for all proves that the U.S. totally rocks when it comes to achievement and innovation in mathematics: http://bltm.com/blog/2014/07/28/do-americans-really-stink-at-math-lets-check-the-numbers/
We who actually do statistics cringe when we hear words like “that once and for all proves …”
Unless they are spoken in jest.
Moi, jest? Ce n’est pas possible!
Yes, well maybe we should look at “Fields medals per billionaire” or “Fields Medals per New York Times columnist” or “Fields Medals per Statue of Liberty” or “Fields Medals per nuclear submarine” or “Fields Medals per Olympic size swimming pool” or “Fields medals per Fahrenheit thermometer” or some other more appropriate measure than just the raw number of Fields medals.
Then I bet the US wouldn’t look so good compared to the rest of the world, now would it?
Based on the Fields Medal, virtually everyone stinks at math. And based on most professional or academic criteria, nearly everyone does in fact stink at math. So…?
Not going to take that blog piece seriously and assume it wasn’t intended to be. But it is worth noting that many Asian educators and psychologists envy aspects of our schools that we undervalue. And there has been concern in Asia for quite some time about turning out exam geeks who mostly can’t cut it when it comes to creative, original mathematics. As usual, the issues are more nuanced than what most experts seem to focus upon with their ideological blinders on.
I’m glad you folks caught the irony in my piece; yes, Michael, I agree: we all essentially “suck” at mathematics. But, as my friend & math geek Joe Zipoli observed, “if you work really, really, really hard at it, you’ll suck a little less at mathematics.” True words, indeed.
“This is because no matter whether CCSS sticks around or dies a slow death, the future for our children is going to suck, and when our grown children are fending off the marauding hordes and baking away during the 140º summers, the issue of the viability of the Common Core State Standards is going to be as relevant to our survival as the current size of a Kardashian butt.” -Robert Berkman
That’s brilliant! Thanks so much for reminding me that I penned those very words. Does this make you one of my followers?
http://atthechalkface.com/2014/07/28/revisiting-the-common-core-math-content-and-practice-standards-sort-of/
Well done. Not just because you are stating what should be more obvious but also for the way in which it was done. 🙂 Thank you for being part of the solution and for teaching our kids. We do have a great country.
I’m not so sure if I agree that teachers do not know how to teach the “new” math. What I have found in my area is the parents of (K-2) students being very vocal because they “can’t help their child with CC math”.
One thing that I think would help everyone in the USA is if it were possible go to the metric system (SI units). When I was in elementary school decades ago, there were rumors of a conversion to SI units and we were learning it, but then it never happened.
@concerned mom: you’ve hit on something that actually addresses the other issue pretty well. I often cite the example of the (actually) centuries-long failure of the US to convert to the metric system as evidence of why efforts to reform math teaching and learning fail so consistently and miserably. Without taking the adult population of the country, putting them on a gigantic raft, dragging it out to the middle of the nearest ocean, and sinking it to the bottom, change of things onto which the vast majority of the populace clings so desperately is effectively impossible. Parents don’t want to change, and so they don’t want their kids to either. Which means they don’t want the teaching of their kids to change at all. After all, kid might come home with some work mommy and daddy can’t do or understand.
There is also the fraternity hazing aspect of education: parents who hated math will nonetheless cling to the notion that “If it was bad enough for me (and I survived it), then it’s certainly bad enough for my kid.” Crazy? You bet. But quite deeply ingrained in American psychopathy, on my view.
Twenty-five years of trying to convince parents and far too many educators that “the bad old way” of teaching math that failed to reach a truly enormous proportion of kids in any meaningful way really wasn’t all that great, regardless of whether the individual(s) to whom I’m speaking got through “okay” or not. Take a few minutes and look at James Tanton’s free video course on quadratic equations or combinatorics (permutations/combinations etc.) and tell me you couldn’t have been taught vastly better than you were (the collective “you,” not you personally). And that’s just one guy with some innovative approaches that actually are grounded in sense-making. We’ve simply not yet tapped the potential to make mathematics vital, powerful, and gripping to children because we’re trapped in doing quite the opposite: making it deadly dull for all but a tiny elite and those who enjoy doing mindless calculations that are better performed by machines.
Even where we have converted, we try to ignore it. My son runs the “mile” and the “2 mile” in track, but he is really running the 1,600 and the 3,200.
Exactly so. I think that minimally, every baseball field, golf-driving range, etc., should post distances in both English and SI units to give folks a prayer of connecting the two. I have only one unit fairly clear on a regular basis, and that is kg => lbs because I worked in food importing for three years in the mid-’80s and many of the exporters I dealt with only sent shipping weights in kilograms. So 1 kg = 2.2 lbs because ingrained in my head. And that’s an easy conversion. With a little thought, I could do the reverse conversion if I needed to , as 2.2 = 2 1/5 = 11/5, so multiplying pound by 5/11ths to get kilos is doable, though not as “clean” a mental calculation.
I also know that 1 inch = 2.54 cm., but I can’t say it’s truly ingrained in my thinking. Just a fact I know but don’t really use. As for km miles? No dice. Ditto meters and feet, meters and yards, etc. Just never got integrated into my thinking. Don’t use those things, don’t have to. I suppose if I had take physics or the like, and if I used it regularly, I’d know those by now. But there has to be something vital in one’s day to day life or work to make that sort of thing really meaningful, at least for me.
Interestingly enough, even in high school,beyond “2 miles” is the cross country distance of 5k. Of course running in general beyond 10k the units become half marathon and marathon.
Michael,
I just went on an internet search for Dr. Tanton and here’s the link for anyone else who is interested:
http://gdaymath.com/
I am bookmarking that and plan to do a little review myself and hopefully, this will still be available when it is time for my children to learn these topics. I just watch the intro on quadratics so far and it looks very exciting!
I am happy there are others who see the value in SI units. Thanks for sharing your thoughts.
Thanks for putting up that link, which I meant to do but got distracted. Dr. Tanton has a couple of web sites. The other one is http://www.jamestanton.com/ and that contains information about his Thinking Mathematics series, links to his YouTube video channel (separate from the G’Day Math course stuff), and other publications of his. He has two monthly newsletters (free) with loads of great things. You can subscribe to them through the website listed above. You can Google his videos, search for them on YouTube, or find them via his site.
As long as I’m recommending great math videos, search for Numberphile on YouTube, and also for The Singing Banana and/or James Grime there or on the web. A lot of fabulous, fascinating stuff.
Ms. Green’s article, read completely, speaks to my own experience. I taught Mathematics in California in 1986 when the standards changed toward “teaching for understanding.” I am still working to help teachers do that. It is hard work to teach children to find mathematical understanding; it is much easier to “find answers.” For Americans to be smarter at math, we need to help our teachers understand mathematics themselves and support them as they teach children. This means lesson study, observing other teachers teach, and common prep periods. It means teaching fewer classes and learning to teach them well. Instead, current dissatisfaction with test results blames the teacher. Is that a better plan than supporting their development?
And then there’s THIS:
http://digg.com/video/this-is-without-a-doubt-the-worst-way-to-teach-kids-math?utm_source=digg&utm_medium=email
Well, I won’t say it’s THE worst, and I even am familiar with mnemonic systems similar to the one he’s using, but this is, frankly, really antithetical to pretty much everything I do as a mathematics educator. There is simply no good reason for the vast majority of people to try to “learn” even basic arithmetic with a system like this. Perhaps someone with cognitive issues in math that prevent any sort of sense-making approach from sticking in long-term memory (I’ve worked with a few students like that over the last 35 years or so) would benefit from this approach, but otherwise, it seems pointless and completely disconnected from mathematics and numbers.
Just as a simple alternative to learning that 9 x 4 = 36. Learning the multiplication facts for 9 can be bolstered by realizing that, for example, 10 x 4 = 40 and you’ve gone one too many four times that way, so subtract 4 from 40 to get the correct product: 36. That sort of “compensation” approach is mathematically sound and works every time if you understand addition/subtraction and have those facts well in hand. With practice/ experience, you will almost assuredly not have to go through that process each time and will get “automaticity” with the facts in question. But it’s nice to have fallback approaches other than counting or doing repeated addition, etc., that are tedious and potentially error-prone.
Of course, if you’re obsessed with rote, insist that students just use flash cards and similar things until they “get it.”
If we’re going to talk about things like multiplication facts, it actually helps to know the science involved in learning: multiplication facts are not mathematical, they are linguistic. That is, when you “retrieve” 9 x 6, no numerical or quantitative areas of the brain are involved. In fact, if you can learn the end of “hickory, dickory dock….” you can learn the multiplication facts.
The reason that some students don’t learn all the multiplication facts has more to do with how we assess and remediate those who take longer to learn them: many teachers shame their students when they forget the 5 – 6 facts that they haven’t memorized yet, and then give “mad minutes” for practice. This is all quite foolish and counterproductive, and ignores the reality of how multiplication facts are actually stored and retrieved.
It is foolish to hold up the failure to memorize multiplication facts as an example of mathematical inadequacy. It’s like saying that Herman Melville was a bad speller or that Mahatmas Ghandi couldn’t throw a curve ball…
While memorizing multiplication facts and retrieviving by rote is not mathematics, learning, understanding, making connections, and using them in context do comprise mathematics.if we teach that way, memorizing becomes moot.
Of course we don’t assess for these things.
It’s a combination, Peter: you need quick access to factual information to decrease the load on your pre-frontal lobes, because taking time away to figure out the answer to 6 x 7 does use up the energy to do the things you describe. But, alas, you are correct: what we value is what we assess, and thinking doesn’t seem to be one of them…
I guess I am not quite as big a believer as some people in the vital nature of cognitive load for elementary mathematics. If I blank out on a multiplication fact, as I used to do with a couple of them as a kid and even later in life, I have back-up strategies that take almost no time at all and don’t cripple me for dealing with all sorts of high-order problem solving and thinking. I used to struggle for some unknown reason with 7 x 8 and 7 x 9. But since I knew that 8 x 8 was 64 (squaring single digits is one of those things a lot of kids learn before it comes up in school, and without necessarily making a conscious effort to do so), I just subtracted 8 from the result to get 56. I could also say that 7 x 7 is 49 and then add a 7 to get 56.
And since I knew that 7 x 10 is 70, I subtracted 7 from that to get 63. I don’t think these “nonstandard” approaches to fix a lost or missing fact cost me anything and may in fact have built some useful connections that I use elsewhere. What bugs me about the “cognitive load” argument is that I see it used often by educational conservatives to “prove” that teaching or promoting the development of alternative algorithms for young children is dangerous because they clearly can’t be as “efficient” as the “standard” algorithm and hence increase “cognitive load” for kids who should have achieved automaticity with arithmetic, freeing up those allegedly limited mental resources for other things. Only I don’t see much of the “other things” going on in our math classrooms, and I know that historically at least on “standard” algorithm, the one we use for multi-digit multiplication, is pretty much an artifact of limitations in the early printing press. Had that not been the case, it’s quite conceivable that most of us would have learned lattice multiplication and never thought twice about another way of doing things. And I’m convinced that both the multiplication and long division methods we teach in school harm a lot of kids because they by their very nature as “efficient” algorithms compress and mask how place value contributes to the processes, leaving those kids who don’t get it completely at sea, and the vast, vast majority of those who do master it equally ignorant of what’s going on. Seems like efficiency might be the wrong value to be worrying about in K-5 math, at least as the first and main goal.
I find the conversation that I hear in this teacher’s room, to be fascinating. So many of you are so intelligent, educated and experienced voices.I have one thing to add to your discussion about Green and New Math, which are 2 distinctly different subjects. I think that Green purposely stays out of the judgmental political conversation. If she wants a voice in the public forum, to speak or publish, she had best refrain from anything that seems like advocacy, and thus, she ignores the cons of a methodology/philosophy… for that is what she is presenting. MP Goldenberg and many of you make good points about what was missing.
To me, The most serious problem with the NEW math, is the implementation and the lack of a helping hand.
Here is a MUST READ piece by Joe Nocera that illustrates MY point in this comment; I write here about HELP for teachers. Throwing the best teacher into an entirely new paradigm of instruction, with no training, no materials, the wrong textbooks and in literal isolation — no collaboration with other teachers— NO HELP is typical of teaching in most big systems today. The grunt on the line, the teacher who is responsible for imparting the knowledge/skills… and who will shoulder the blame when it fails, is on her own!
“Teaching Teaching” by Joe Nocera: “Teachers shouldn’t be learning on the job as they go.”
I would like to elaborate on MY point, using my experience in that classroom with almost 40 kids in each of four classes, looking to me to show them how to do something difficult. These are emergent intelligences, adolescents, each with its own learning style and capacity, and it was my job to show them how to do the work… and the parents’ expected that I could do this, but they had no idea that I had no help and little support.
Now picture me, 50 years old, an experienced teacher of literacy in primary grades, sent to a new middle school where I will instruct the entire 6th and 7th grade, with not a shred of curricula or materials. Not even a blackboard in the room that was originally re-modeled to be a dance studio… no closet or shelves. Luckily for all concerned, children, parents administration and that teacher, I held several degrees, knew my subject and pedagogical principles (methodology) , and had subbed in 3 middle schools in a real school system, in which the state curricula GUIDE/ SYLLABUS was de rigor in every room, and used to plan the year’s objectives by all teachers.
So, there I am, with all those children, and I create the curricula from scratch, because no one gave me anything! No help! Nada! I also supply the books for individualized reading, xerox the stories from literature books that I used in East Ramapo and created all the materials that I needed.
The only ‘help’ came from a teacher in Vermont, who had written a book that I had read that summer to INFORM MY PRACTICE. She had a small class and I had an entire seventh grade, but Nancy Atwell’s idea of creating a tool which helped kids to talk (ON PAPER about books), was fascinating. I adopted her “Reader’s Letters” , even using her ‘skills sheets;’ each night, reading the kids’ letters, and writing a response to EACH child regarding what they actually discussed,
I would insert a ‘skills sheet’ into the left-hand part of their folder, which said at the top, “Here are the skills that……. needs to improve.” A parent would sign it, so that they knew the progress and the criteria for improvement. On that skills sheet I would show a better way to construct a sentence, or use a vocabulary word, or explain that , “there, their and they’re,” are not to be used interchangeably (as autocorrect is want to do here.)
The letter-writing curriculum made the school famous when my practice became the cohort for the standards. And EVEN THEN, the administration did NOT support my practice, they actively undermined me, moving behind the scenes, unknown to me, to break my tenure. The administration had a ‘fit’ when Harvard said, “SUSAN LEE” is the cohort in District 2, but the money poured in for the standards workshops and they bided their time. You must understand that for 2 years in the ‘real’ standards workshops, there was actually genuine help to improve teaching for the entire district; the jargon was about ‘learning’ and what it looks like, and how to “ ’enable’ and ‘facilitate’ learning”, AND to do the WORK. Today, with the new Core Curricula “standards’” where are the workshops that teaches teachers?
Last point, regarding the Nocera article with the title that says it all, for me, at least: who will teach the teachers once they graduate? Doctors hone their skills in PRACTICEs; my son attends conferences and training courses as a cardiologist in his 20th year of applying what he learned in college. Who teaches teachers, and who helps them to acquire the skills needed to show kids something difficult? With the veteran teacher gone from the schools, and teachers isolated in their classrooms, and no one shows teachers how to motivate and manage the kids, today! Management is key. Huge class sizes show the contempt that administration has for the children and the teachers… it sure ain’t HELP! No one shows struggling teachers how to manage the 20th century NYC kids !
You see, I was the old lady on the small magnet school’s staff, and the novice teachers — all educated, very bright and talented, committed to kids— looked to me for many things, but mostly for classroom management, because they noticed that the same kids in MY room were well behaved and engaged in instruction. So, because we worked as a TEAM, I assisted my younger colleagues to manage their classrooms, and they became valuable members of a real collaborative team.
The presence of a veteran teacher as a mentor in that new school was a benefit.The school became well-known for its excellence, but of course, in a few years, everything that worked, was undone. VANISHED. Like so many successful education experiments, it was doomed to disappear when some new reform or magic elixir was sold to the public.
http://www.opednews.com/articles/Magic-Elixir-No-Evidence-by-Susan-Lee-Schwartz-130312-433.html
And when I was hounded out, my celebrated curricula was NOT passed on to a single teacher. The book that Stenhouse publisher asked me to write, about my philosophy of education — which might have helped to inform the practice of other teachers ,as Atwell’s book informed mine was never written when I went to a rubber room !
THAT, is the point. When nothing that SUCCEEDS in a school or institution, is celebrated, and everything that teachers accomplish is disregarded and even discouraged, then there is nothing handed down, and thus, teachers teaching teachers what works best — BEST PRACTICE as they did it ) — is lost.
Few got the help they needed to teach the new math, including collaborations with parents so everyone was getting HELP in order to show the kids how to think in this new way about numeracy.
HELP, not rhetoric, promises and mandates is what creates best practice and successful teachers for any subject.
I too though that Green’s article was great – a real support to teaching math conceptually. I think the author of this piece did not read the whole article.
Liz, consider that, sadly, there are teachers who oppose teaching math conceptually. Or doing anything differently from what they’ve always done or the way they’ve been taught math.
It may not be that they are teaching badly; they’re just teaching a different mathematics.
Liz, your assumption is incorrect: I read the piece very carefully, and praised the excellent comparison between the practice in U.S. and Japanese schools (which was actually covered about 20 years ago by Stigler and Stevenson.)
The point I am making is that Ms. Green’s assertion that “Americans stink at math” is not at all valid: the data she cites is either irrelevant or unreliable. Ms. Green is a journalist; her job is to make headlines. At the same time, if she is going to make a bold statement such as this, she must use evidence to back up that statement: without real evidence, the whole story falls apart. Her playing fast and loose with statistics may get her a lot of clicks, but her readers are being played.
Robert,
I am interested in your take on a slightly different question. My families experience suggests that the way we teach mathematics stinks for students that are good at mathematics. At my institution (a public research university), students who were very good at high school and engineering mathematics are shocked when they reach the real analysis class to find out that they are not very good at mathematics (though of course some overcome this). Meanwhile, some who are in fact good at mathematics as mathematicians understand it, dropped out long ago because they were not good at K-12 “math”.
Precisely my view, TE. Thanks for saying it.
So Americans DON’T stink at math, Robert? Really? Somewhat ironically, Harold Stevenson gave a talk at the University of Michigan School of Education in fall of 1992 to launch the new academic year. As a new graduate student in mathematics education, I attended because I was told about his focus on international comparisons of math teaching and learning. He was quite adamant that American students by and large stink at math compared with Asian students. He also claimed that part of the problem was that on the whole American students assert that they are good at math, whereas Japanese students mostly say that they are not good at it. Another key difference seemed grounded in widespread cultural beliefs: Americans believe for the most part in talent, IQ, inborn mathematical ability or lack thereof; Japanese people believe in hard work. If a Japanese student does poorly in math, his parents feel responsible for not helping that child work harder.
My sense is that there are bits of truth all over the above claims. If we’re talking about “school mathematics,” I’m willing to entertain the notion that a lot of Japanese kids learn more of it and perform better on tests designed to reflect that knowledge than do American kids by and large. But of course, that hardly tells “the whole story.” Both stories are worth considering, however: we really do a vast national disservice to the majority of our kids when it comes to mathematics, particularly to those children living in poverty. But we also do a vast disservice to nearly all kids in what and how we teach in K-12 (and probably K-14) mathematics classrooms.
Furthermore, it sounds like Japanese kids get a more interesting and, probably, useful, mathematics education into the middle school years, and then they get pretty royally screwed over by high-stakes exams in ways that the education deform crowd must envy. There, certain realities about the number of prestigious universities and colleges, coupled with cultural ties between certain industries/companies/corporations and given post-secondary institutions makes the stakes in those college entrance exams vastly higher than they likely ever will be in the US as far as individual students are concerned. One’s future is tied to those exams in Japan in ways it would be hard to bring about here.
We also have repeated evidence from Asia that there is SOMETHING we’re doing over here that math educators and educational psychologists like, because they come here to study it. I had the good fortune to meet one such fellow, Dr. Hiroshi Usui, a professor of ed psych from a university in Sapporo who was actually at U of M studying US math education via the institute that was headed by. . . Harold Stevenson. I was able to get Professor Usui into a number of elementary and middle school classrooms in the area with which I had connections through my own research, and we had a number of long conversations about what he observed there and his feelings about the Japanese system. With a son just starting the exam grind, Dr. Usui confirmed some of the negative things I’d found in researching a paper I’d recently written for a graduate class in which we compared national math standards/curricula for a variety of European and Asian countries. And I must emphasize once again that Harold Stevenson never spoke about the downside, never spoke about secondary math education in Japan, never addressed issues of serious concern in Japan about difficulties many graduate students in mathematics had doing original research, etc. I suspect but can’t claim that Jim Stigler had then and has now a broader perspective than did the late Professor Stevenson, who seemed to me to have some definite political agenda about American vs. Asian math education that today’s ed deform crowd would be able to use for propaganda purposes.
What makes this whole issue far more nuanced than I think you make clear in things I’ve read of yours, Robert, is that I believe a number of seemingly contradictory things about what goes on here (and in Asia) are true. First, I think most people stink at math, myself included, despite the fact that I teach mathematics and have studied and continue to study far more mathematics than the average American imagines exists, let alone that s/he ever looks at. As far as “school math” goes, I’m not the most knowledgeable person out there, but I make most Americans look pretty ignorant, which is far easier to do than it should be. But the real difference between me and most Americans is that I actually have a pretty fair inkling of what actual mathematics is about, and a big piece of that inkling is that it IS NOT school mathematics. And it is along these lines that the Math Wars were and continue to be fought, only now we have the Common Core Initiative obfuscating the debate in ways I doubt many people dreamed of in 1989 or so. Anti-Obama sentiment and Teabilly paranoia now allow the Beverly Eakmans and Charlotte Iserbytes, the Glenn Becks and Rush Limbaughs, etc. to support the views of the Sandy Stotskys, Wayne Bishops, R. James Migrams, David Kleins, attracting new hosts of parents to swallow and repeat, with the power of social media that wasn’t available when the Math Wars started flaring up in the early-to-mid 1990s, and gaining support, too, from “progressives” like Louis CK, Stephen Colbert, Mercedes Schneider, and many other less well-known people who oppose the Common Core “from the Left,” but whose take on math education leaves a lot to be desired, on my view.
You asked me personally yesterday why I was, supposedly, ignoring you. I wrote a lengthy response to which you’ve yet to reply. I suggest you add to that my comments above. I have long agreed with people like the late Gerald Bracey that much of what’s published about US education is a combination of bad statistics and willful propaganda. But were he alive now, I’d be talking with him about the issues at hand here and the fact that when all is said and done, we’re still failing to do a good job at promoting numeracy in our citizenry. And of course, that’s one of the reasons the bad statistics and propaganda so easily takes root in the populace.
What bothers me about your take on Green’s article remains that you seem blind to the overall thrust because you see errors in her statistics. I come away from the article pretty happy because she still manages to provide mostly good ideas about how to make things better. It doesn’t really matter if her evidence that things are bad is flawed, because the reality remains that things actually ARE bad. Americans (and many other people) stink at math. And her examination of some of the reasons and what alternatives exist is better than much of what I’ve seen in the NY Times or other mainstream media in over a decade. Since the NYT dumped Richard Rothstein as a contributor to education writing, the good reportage on these issues is hard to come by. Green’s magazine article gets more things of importance right than not, and I really think we should be focusing on those things. You’ve made your point about her statistics, but still, I fear, missed the bigger point. I’m not sure why you are still harping on a narrow view on this article, why you apparently think that Harold Stevenson got the Asian thing right (when he failed to tell at least half the tale), and why you appear to have no interest in talking about the pedagogical issues Green’s piece looks at that we’re going to be continuing to have to deal with when this latest Math Wars phase (“the Common Core War”) is dead and buried, probably in January 2017 when the Tea Party and GOP don’t have Barack Obama around to blame for everything.
First of all, Michael, I appreciate your taking an interest in my work and actually reading what I have to say. Your long and thoughtful responses are very interesting and helpful. At the same time, I hope you understand you’re preaching to the choir here: I’m in agreement with 99% of what you say, and at this point, we’re just re-arranging a lot of the same words. I was a victim of the HOLD ideologues back in 2001 (in the New York Post, no less!), so I can claim a few bruises in the “math wars,” as they were.
But I won’t stand down on Green’s article: she gets an A+ for narrative, but an F for statistics.