Algebra = ‘most failed’ college class

Math 111 —  intermediate algebra — is the “most failed” class at Oregon State.  Students aren’t prepared, says an instructor.

“If you never had to memorize your times tables, how do you factor a number with a calculator?” (Peter) Argyres said. “I see people fail Math 111 for arithmetic issues all the time.”

When students never learned the basic information appropriately in high school, or earlier, it is significantly more difficult for them to succeed when they get to college algebra.

Only half of incoming students place into college math.

OSU Frosh Gettin’ Suspicious They Ain’t Learnin’ Much in High School, summarizes the Two Million Minutes Blog.

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Comments

  1. So, the cited paragraph demolishes the idea that calculators make arithmetic passé. There are other problems with the course, though. Is it possible to learn math with 280 students in the course, especially if many of the students have never experienced a class larger than 25? If you’re accustomed to working in “learning groups” of 3 or 4 kids, at small tables, how long does it take to adjust to a strict lecture format, in a traditional lecture hall? I think attention issues may come into play. I’m not making excuses for the students; I do think that certain types of academic skills need to be practiced. Lecturing has a bad reputation in K-12 schools, which may not prepare students for college. (Just a thought.)

    Also, there’s an interesting comment from the instructor about the effect of budget cuts on teaching. Is anyone surprised that electronic course materials are expensive?

    “With budget cuts still continuing, there is little hope that the classes will get any smaller.

    The textbook froze about five years ago to get the price down for students, but this has caused the class to lose online support.

    “Now, we’re re-looking at the text, trying to see if we can get a better text that moves in a more linear fashion as far as the structure of the course, along with online support,” Argyres said.

    This may cost more money for students, so the math department is looking at doing an “e-text” where students can download homework in PDF form, but nothing has been determined yet.”

  2. I teach college algebra, and have some reason to believe many students are not learning arithmetic the way they should. It was about a year and a half ago that I was trying to explain a factoring problem to one of my students. I explained that we were looking for two numbers that multiplied to 72 and added to 17. She replied, with a bit of exasperation, “I know that! I just don’t know any two numbers that multiply to 72!”.

    I like to be very careful about concluding that students are not being taught well. I’m sure there are many middle school and high school teachers who feel they are doing the best they can with the material they have. I wouldn’t pretend to tell them how to do their job. However I certainly would argue, and have argued, that in the last few decades the NCTM (National Council Of Teachers Of Mathematics) has been much more a part of the problem than a part of the solution.

    I haven’t investigated how well my students know the times table, but I have looked into what they know about fractions. I describe what I am doing in an article “Fractions My Algebra Students Can’t Do” on my website. Over the past year I have realized more and more that knowing fractions is not just a matter of computation. It is a matter of understanding our number system. There are many topics in algebra that cannot possibly make sense if you don’t know and understand fractions with a high level of fluency. Here’s a link.

  3. If we don’t solve the major, serious education problems in this country, and soon, the U.S. will not be a global leader in anything in the near future. Culturally and economically, we’re already less than two generations away now from becoming the world’s first country to go from “1st World” back to “3rd World”… 🙁

    How long are the students who begin college in Intermediate Math going to be in college? 6 years? It will take them two years just to get to Calculus I – which I always thought was the ‘ideal’ freshman year college Math class.

    What is the usual pattern of Math classes in most colleges? Intermediate Math, College Algebra, College Geometry, PreCalculus, Calculus I (Derivatives) & II (Integrals)… (and from that point on branching off into classes for Math, Science, and Engineering majors?)

    The first three (and in my opinion, four) classes on that list are classes that the students *should* have learned in high school. But I guess our K-12 education system in the U.S. is so broken at this point, that universities are having to pick up some major slack.

  4. Mathematics–basic operations such as multiplication, division, addition, and subtraction, fractions, decimals, and such–is easy. Algebra is a lot harder. I’m not stupid, but I couldn’t ever really get equation manipulation. And it was just made harder with “real world application” word problems when I didn’t understand what to do in the first place. Nor did I have a math teacher that understood anything but teaching to explain it to me.

  5. Golobulus,

    Despite the “sky-is-falling” commentary of people like Thomas Freidman, we are not going to revert to a third world country. We have problems with our education system, but they are predominantly with the bottom third of academic achievers. Many failing college students have simply been misled to believe they need college, when we are at a historic high of 29% of the population holding four year degrees.

    Our top third are still the best in the world, and the United States is still leading the world in innovation. The growing number of AP/IB programs nationwide have hundreds of thousands of high school students achieving success with college and even graduate level material by the age of seventeen. Two students, juniors, at my high school were featured on ABC News for their breakthrough in finding a new treatment for muscular dystrophy. Clearly, many of our students are on the cutting edge of progress, and the U.S. is still the best market for that sort of person.

    Additionally, the United States is still the primary choice for graduate level schooling for the entire world, and while many return home, as many choose to put down roots here. Thus, I would argue that our system is anything but “broken.” There is much we are doing quite well.

  6. Cardinal Fang says:

    Oregon State’s Math 111 is entitled College Algebra. As with other courses called “College X,” it’s a high school level Pre-Calculus course, although Oregon State offers college credit for it. The worst is, Math 111 is the third course in their math sequence. The two lower courses, neither of which earn college credit, are Elementary Algebra and Intermediate Algebra.

    I volunteer in a community college Elementary Algebra class. At the beginning of the class, most of the students have trouble with arithmetic involving fractions, decimal numbers or negative numbers. I often see them pulling out their calculators to do arithmetic with single digit integers.

    Rather than spending the whole class section lecturing, in my algebra class the teacher gives a short lecture explaining a topic, then hands out problems for the students to solve. After a few minutes, she’ll go over the solution with the class and introduce a new topic. Students are allowed to collaborate on their work in class, which sounds like a bad idea but isn’t.

  7. Cardinal Fang says:

    Globulus, the students who pass Oregon State’s College Algebra can move right on to a wierd kind of Calculus for Social Science that doesn’t include trigonometric functions, or they can take a trigonometry class and then normal calculus. My guess is most of those students don’t take any calculus, but instead go for statistics.

    So if a student passes Math 111, she can take her calculus or statistics and be done with math at the end of her sophomore year. Too bad so many students place into a lower level than Math 111 or don’t pass Math 111 the first try.

  8. I am not an algebra teacher, but I have taught enough 1st-6th grade math to know that if my students didn’t know addition, subtraction, multiplication, and division facts automatically, they struggled with higher level math. After students can demonstrate what the computation means, they need to memorize the facts. This is why I am so passionate about getting the word out about how to teach math facts. Give them strategies to learn the facts, and then lots of written practice. If they didn’t learn facts at an early age, then take the time to teach the facts now. One is never too old to learn. Math facts are the keys to everything in math!

  9. ” We have problems with our education system, but they are predominantly with the bottom third of academic achievers.”

    If so, why do I have students in college with ACT scores in math from 20-25 who cannot do basic arithmetic, including long division, fractions, and decimals, without a calculator? There are indeed strong achieving students in math. But, this problem is a systemic one and it will not be solved by citing anomalous examples.

  10. Math is hard!

  11. Anon,

    When someone is declaring our “system is broken” and warning of our future as a third world country, I hardly see it as anomalous to argue that the fundamentals of educating our populace are sound and our top third are excelling beyond anyone’s expectations of high school students.

    There is no doubt students will come to rely on calculators if they are allowed to use them in class and on exams. If they ACT/SAT forbid it, the students, especially the top two-thirds, would quickly adapt. Yet, there is no evidence this is necessary, as the quality of our innovation and scientific progress did not diminish in the past three decades as calculators became more common.

    Additionally, we should argue over the validity of memorized knowledge and skills. Certainly, there are no working engineers or scientists out there refusing to use technology to make their job more efficient. Professional writers use spell check and look words and rules up. The military uses maps with the names already printed on them.

    Now, I am a proponent of people having in long-term memory as much knowledge and skills and possible. Willingham’s argument about the necessity of knowledge from a cognitive scientist standpoint is valid and should be integral to any k-12 curriculum. I do expect my students to simply have knowledge.

    However, I am not going to extrapolate that into believing the country is in crisis because a kid who received a 25 on his math ACT needs a calculator. That’s simply not a reasonable position.

  12. michael mazenko – your claim that the top third of American students are the best in the world is very surprising, and you don’t cite any data for it, while there is a chunk of data failing to support it.
    Look at the TIMSS international results and at the percentage of fourth- and eighth-grade students who reached the TIMSS advanced international benchmark in mathematics, by country in 2007.

    In this study, for grade 8, the USA came 10th in the included countries. More students reached the advanced benchmark in mathematics in countries as diverse as England, Hungary, Japan, and Singapore.

    In terms of the advanced mathematics benchmark, the USA came 11th in the world for 8th graders. Again countries as diverse as Hungary, Singapore, Japan and England surpassed the USA.

    At my NZ high school we started doing calculus in fifth form, when I was 15. This was the standard maths course for high school students. By the time I started university I had already been studying calculus for three years. This was ordinary. I got my engineering degree, accredited by the US-based IEEE, in 3 years.

    Clearly, many of our students are on the cutting edge of progress, and the U.S. is still the best market for that sort of person.

    The US may be the best market for that sort of person, but I suspect that is because of the US’s economic policies, history (basically the Nazis drove a lot of people like Einstein out of continential Europe, many of them went to the USA, people who wanted to learn from the really top minds followed them, and it’s snowballed since then) and the sheer number of people in your country, nothing to do with the US primary and secondary education system.

    I agree with you that it’s silly to worry about economic collapse in the USA, but there is still a problem with primary and secondary education in the USA. It’s fine that American universities can attract the brightest minds around the world, but a lot of born-and-bred Americans are being unnecessarily prevented from being the brightest minds in maths and science because of inadequate primary and secondary teaching (as of course is true of many other countries in the world, American’s problems are not unique nor particularly bad by international standards).

  13. Homeschooling Granny says:

    Many basic math facts can be learned to the point of being automatic through the use of games, rather than drills. Joan Cotter sells math games by the box at RightStart Mathematics.

    Or simply take a deck of cards, remove the face cards, and play War. Two play. Deal the deck. Each player turns over 1 card, higher card captures the other. If both turn over the same value, declare war. Turn over 3 cards (spelling w-a-r) and the fourth card determines who captures all. When the child learns to add, each turn over 2 cards and add. With subtraction, each turns over 2 cards and subtracts. Same with multiplication. Then comes fractions. Turn over 2 cards, place lower number over higher and compare to see who has larger fraction. Finally, do improper fractions with the higher number over the lower number.

    My granddaughter squeals with delite and has no idea math is either dull or boring.

  14. Tracy,

    Perhaps I should have said “among the best,” as I see the quality of education at the top American students in the top American schools as every bit as successful as the top students I taught when I taught in Taiwan. Additionally, I always view these rankings with a skeptical eye – as we all should – for a series of standardized assessments are hardly the definitive factor in identifying “best in the world” or “cutting edge of progress.” My Taiwanese students were incredibly skilled at test taking. However, that in no way automatically translates into skilled and innovative producers. In fact, the opposite is very often true.

    As I’ve noted here before:

    A telling comment on the differences in the Taiwan system and the US came from Dr. David Ho, the researcher credited with coming up the “AIDS cocktail” which was the first and most effective treatment for lowering HIV to undetectable levels in infected people. Dr. Ho was born and raised in Taiwan where he went to school for his formative years – elementary and middle. He then moved to the US where he did high school and college. He has noted that if he’d stayed in Taiwan his whole life, he never would have made the discovery. Likewise, he explains if he had been born in the US and always educated here, he never would have made the discovery. It was the rigid style of the early years in a Confucian system that gave him the discipline he needed, as well as the more “open” and diverse style in the US that encouraged questioning and creativity (yes, through electives) that allowed him the solid foundation and insight necessary to make one of the 20th century’s most significant medical breakthroughs.

    Thomas Freidman has argued passionately about higher level math jobs moving abroad. However, that has little to do with the math/engineering skills of our top students. Firms move these jobs abroad, not because the Indian or Chinese or Singaporean workers are better. They are comparable, but cheaper.

    Thus, I would again simply assert, that talk of “crisis” and a “third world” future because many of our mid -level students are struggling with college math and using calculators is misleading. And ranking students and education systems based on international standardized testing and competition is somewhat useful, but myopic at best.

  15. Michael said, “When someone is declaring our “system is broken” and warning of our future as a third world country, I hardly see it as anomalous to argue that the fundamentals of educating our populace are sound and our top third are excelling beyond anyone’s expectations of high school students.”

    Michael, I didn’t say that the system is broken nor did I warn about our future as a third world country. I just want to know the following: If our problems with math achievement are primarily with the bottom third of students, then why can’t my students with ACT math scores of 20-25 (who are NOT the bottom third of achievers) do basic arithmetic without a calculator?

    Having said that, we have grave problems with our elementary and secondary education system in ALL subjects and a few platitudes about high achievers will not make those problems disappear.

  16. ” We have problems with our education system, but they are predominantly with the bottom third of academic achievers.”

    I don’t know about this. I’ve had to tutor kids who were taking calculus in high school (and getting good grades) and for some reason didn’t know how to solve SAT math problems without calculators.

  17. Another reason too many are failing college algebra is that too many are being pushed into college in the first place.  This happened because the high school diploma is essentially worthless as a measure of achievement.

    Right now, the USA is importing millions of illiterate farmers and herders (many of whom have never learned a European language, despite hundreds of years of living in a nation where it was the official language).  We are further encouraging them to “maintain their culture” rather than to become literate and numerate.  Who in their right mind thinks that these people, or their children, will supply the ranks of students to fill freshman classes?  This can only end badly.

  18. Cardinal Fang says:

    It may be that too many students are pushed into college, but “College Algebra” is not a college class. Students should have learned that material in high school.

  19. superdestroyer says:

    How many of those doing poorly in algebra took agebra in 8th or 9th grade and did not even take many during their senior year. Maybe part of the problem is that the freshmen have actually not seen a math problem is almost two years.

    Image how many more will fail if more middle class white Americans adopt the year off before college idea. The would give them almost three years off between taking algebra classes while the harder working, achievement oriented Asian-American students take four years of math in high school and go straight to college.

  20. It seems much of our arguments are anecdotal – we know students who can’t do the math – or they are generalized outside of practicality in the workplace and everyday life – our rankings behind Hungary in a standardized ranking. Ultimately, my initial objection to the issue was the idea that the education is in a state of decline and the country faces a future crisis because kids can’t do math without calculators. Both cases, in my opinion, are drastically overstated.

    Ultimately, I agree that I would certainly like students to have more core skills and knowledge – math, English, science, and government – committed to memory. However, there is valid criticism of those expectations. Engineer-poet and Superdestroyer have made additional insightful comments about the necessity of many of these students needing to go to college or studying math when they get there. While I landed in the 20-25 ACT range in math (twenty years ago BTW), I still needed the calculator. I had taken little higher level math, as I was destined for writing and English teaching. Do I wish I was more skilled? Sure. Is it integral to my success? No.

    As an English teacher, I am constantly frustrated by the writing skills of adults. Friends at numerous Fortune 500 companies regularly comment on the poor writing and speaking skills – and lack of literary/historical/cultural knowledge – of their superiors (managers, vice-presidents, CFOs, CEOs). Yet, these people and companies manage to survive and even thrive. NASA and our tech industry continue to lead the world. Our engineers are still designing buildings and bridges, all the while using calculators and computers.

    In terms of real world experience, this concern over calculator usage is over-valued. As I noted before, if we required that students do the math without assistance, our top third to half would respond. But to what end? We might shoot into the upper rankings in international tests, but would we suddenly produce even better buildings and software?

    That’s more of an academic discussion, than a practical one.

  21. As a former teacher of college freshman mathematics, I’d like to share my observations with you.

    First, while we see a lot of high school students taking classes with names like “calculus” and “geometry”, if you actually look at the content of these classes, it is substantially watered down from what classes with these same names used to contain. There is much more emphasis on training students how to punch buttons on their calculators than on having them learn concepts. One time I got curious and took an informal survey of students in my Intermediate Algebra class. I was shocked to discover that most of them had already taken a course in high school that was supposed to have the exact same content as the college course I taught (determined by comparing the state core curriculum to my syllabus), and most had taken at least one high school math course after that, and yet had placed into Intermediate Algebra by examination. Also, the recentness of the experience was not the problem; most had taken math recently (before enrolling in my class). So when you hear that X% of high school students are taking “calculus”, be very suspicious that they are taking a course that is only *named* “calculus” and would be more properly named “Advanced Calculator Techniques.”

    Second, there really *is* a disconnect between the level of math functioning of today’s high school graduates and those of yesteryear. My husband, for example, is not particularly math-oriented, but when I tell him that only 18 out of 35 of my students passed the test, he immediately comes back with “That’s a little more than half!!” How many of today’s average high school graduates can even do that? I would speculate not many. When I worked as a supervisor at a craft store, one of the requirements for a job application was to pass a brief test of basic arithmetic of the “60 clothespins at $1 a dozen costs how much?” type, without recourse to a calculator. Older applicants who had been out of school for 20 years or more never had a problem passing it. High school students rarely passed it; one of the worst failures came from two girls who failed despite being currently enrolled in a class called “calculus” AND cheating off each other.

    Third, I believe there is a special place in hell for elementary school teachers who skip the computation and go straight to the calculator, especially for teaching fractions. I have seen what happens to their students once they hit adulthood. They have dreams of being a scientist or an architect or an engineer or even just a college graduate, but their dreams are dashed on the rocks of the reality of their ignorance of math. Because you can’t build on a missing foundation, ever since 5th or 6th grade (or whatever grade their teacher failed to educate them) these students have borne the burden of thinking they must be stupid because they don’t “get” math. By the time they get to college, they’re so convinced of it that they defeat themselves whenever a number pops into view. Teachers who don’t teach fractions ruin lives, plain and simple. They kill dreams and banish future wealth and productivity.

  22. Charles R. Williams says:

    Back to the original point. Yes, many students are unable to pass Intermediate Algebra – which is basically an 8-9th grade high school course – because they have not been taught arithmetic properly. Certain skills have to be learned to the level of automaticity to permit a student to move forward in algebra. I suppose you can do it with games. You can certainly do it with worksheets, hours and hours of practice on worksheets, to properly lay the foundations for algebra.

    Well, many students in these courses lack this experience. It is not just a matter of their having forgotten it, they never learned it in a way that assures retention.

    We cannot make up for this in a 3-4 semester hour course at the university level. So the courses are continually being watered down and students are being passed on without mastery for the sake of improving the university’s retention rate.

    So should a BA imply mastery of high school algebra? Today, outside of technical fields it certainly does not.

  23. Let’s face it. Students don’t know how to do basic arithmetic because our schools don’t teach it very well nor do they expect very much from the students. The same holds true for reading, writing, grammar, speling, science, history, foreign languages, etc. Our students are in deep trouble, in part, because our schools are in deep trouble and have been for some time. From what I see at our teachers colleges, there is little reason to expect that situation to change in the near future.

  24. I agree with the last post and I lay most of the blame on the education establishment, both college-level and k-12.

    First, ed schools admit very weak students and they do nothing to remediate their academic deficiencies; they don’t even make an attempt because they don’t feel that academics are important. Their focus is all on process; the guide on the side, not the sage on the stage. They provide their graduates with neither real academic knowledge nor the ability to teach, although some learn it on the own.

    Second, the k-12 schools do not focus on serious academic knowledge and skills. Too many teachers, especially at the elementary level, don’t have the requisite knowledge and skills and they don’t have the interest. They are also unwilling/unable to demand serious attention/effort of their students, so that they MASTER the fundamentals of reading and math that enable all further learning. The plague of journal-writing – never corrected for content,grammar,spelling, punctuation etc – is emblematic. Learning to write well requires extensive reading of GOOD LITERATURE (presented orally in younger grades) and frequent/regular correction of student writing, just as real math skills are built on a solid foundation of arithmetic, fractions, decimals etc.

    The schools have decided that students’ egos are too fragile to support serious effort and serious correction of errors. I’m sure that another elephant in the room is the racial/ethnic differences in achievement, which (at least until NCLB) could be papered over with differentiated instruction and group work. There is no acknowlegement of the possibility that real study skills and real subject-area knowledge make teaching to the test unnecessary and that it is the kids at the bottom that need them the most, because their families (unlike those at the top) are unable to compensate at home.

    Again, I don’t see much changing in the near future.

  25. Michael Mazenko’s comments above have helped me clarify my thoughts about these things. I have long felt that it is not helpful to say American education is “broken”, or is failing. I agree with Michael that there are many reasons to say that American education is doing what it should be doing. It is, by and large, educating young Americans. We are not in crisis, and we are not going to become a third world country.

    But that certainly does not mean we should not be concerned. I think we should be. But the reasons to me seem more humanistic, or even aesthetic, than economic or practical. What ever happened to the idea that a “liberal education” is valuable because it liberates the mind? I remember hearing about that when I was young, but not in recent decades. Our country will not go bankrupt if factory workers cannot solve quadratic equations. But wouldn’t it be better if they could? We’re not going to become a third world country if the less talented half of our students can’t tell an participle from a gerund. But wouldn’t it be better if they could? We’re not going to lose our auto industry because our engineers can’t put the Civil War and the Revolutionary War in their proper centuries. But wouldn’t it be better if they could?

    Self esteem has a history of being important to educators. But somehow that is often seen in a very shallow way. Getting praise from a parent or teacher for minimal accomplishment may be better than no praise at all, but it is a very pale imitation of the self esteem that comes from genuine accomplishment.

    I believe that when a subject is well taught it has intrinsic value to the learner, and this intrinsic value can be very satisfying to the learner. This satisfaction can very well repay the learner for all the effort, struggle even, that is required to gain that learning. I have long been aware that most students come to my college algebra class with a rather commercial perspective. They are willing to put in money, time, and effort to learn algebra, and in return they get a grade and credit on their transcript. They don’t expect anything more. It seems a fair trade. This is not an ideal attitude, but I do not lament it so much as simply accept it. Indeed that was pretty much the attitude I brought to the history, English, and perhaps a few other courses I had to take as a young college student. But sometimes we get more. Sometimes we get a bonus of obtaining something that has intrinsic worth, something we are glad to have, even if we didn’t ask for it or expect it. I had two semesters of English composition as a freshman. The first course was a fair trade. I wrote the essays and got a C and three hours credit on my transcript. The second semester, as I recall, gave me something more. I don’t remember what grade I got but I remember that course as being something better than just a fair trade. I recognized that I had gotten something that I valued. I also took, for some mysterious reason that I have forgotten, a literature course. It was considerably more than a fair trade. I got something that I genuinely valued from that course, though I would be very hard pressed to define just what it was. I cannot explain just what I mean when I say that it was well taught, but I have no doubt that it was. My one history course and my two political science courses were again fair trades. They were required for a degree.

    The world is a better place when students get more than a fair trade. But I cannot give students in my algebra classes more than a fair trade if their mathematical background is so compromised that they must struggle hard with ideas that they are not equipped to understand in the way that they should. I have become more and more aware in recent years that you can’t understand algebra in the way that it should be understood if you don’t know arithmetic to a high degree of fluency. Indeed for a fair number of my students the “fair trade” is a failing grade. They don’t complain. They recognize that their money, time, and effort (and that time and effort is sometimes is pretty minimal) is just an entry fee. It doesn’t guarantee them anything. These students sometimes just go away. Often they are back next semester to try again. What percentage of these students were doomed by arithmetic? I don’t know. But whatever percent it is, wouldn’t it be better if we could reduce it? Wouldn’t it be a lot better if more students took away a genuine appreciation of algebra and math in general?

    I realize that the plural of anecdote is not data, but I think it is also true that when anecdotes accumulate they do have meaning. Every semester, every day in some ways, I make adjustments in how I teach what I teach, and these changes are based on what I experience with students. I cannot avoid forming opinions and theories of causation from what I observe and deal with. My opinion now is that you can’t understand algebra if you don’t know arithmetic to a pretty high level of fluency.

    But I want to be very careful not to blame math teachers at lower levels. I don’t know what goes on in K-12 math classes, though I would very much like to. I have two hypothesis.

    Hypothesis number one (the grim one): The human brain is not built to do math. Only a minority of the human race can understand arithmetic. The best teaching in the world will never change that. We are becoming aware of this grim fact in recent decades only because so many of those untalented students are now coming to college.

    Hypothesis number two (the hopeful one): A substantial majority of the human race is quite capable of understanding arithmetic, and by extension a whole lot more. (Is algebra harder than arithmetic? Maybe, maybe not. Is calculus harder than algebra? Maybe, maybe not. I don’t know.) If this is the correct hypothesis then we would have to conclude that we must be doing something wrong. What are we doing wrong? Well, I have my opinions, and have expressed them at length here.

    And the really sad part of all this is the depressingly common attitude that it’s drudgery to memorize the times table. I don’t remember it that way. I don’t believe it is that way when done under the direction of a skilled teacher (or even a semi-skilled teacher who uses her common sense and learns from experience, not the latest educational fad). Flash card drill is not drudgery if done right. Going to the board and racing your classmates to get the right answer is not drudgery if done right. Worksheets and homework assignments are neither busywork nor drudgery if they are done right. Rather they are the tools and materials with which to construct learning, real learning. (I wrote about that too, here.)

  26. Well said, Mom of 4.

  27. If American education is failing to teach basics such as reading and arithmetic today, but it largely succeeded before, then that is certainly a failure.  That in turn means we need to fix it.  If we have to demand arithmetic fluency from K-6 teachers so we can be certain that they can at least model competency (preferably as an entrance requirement for ed school, not a graduation test), we should do so.

  28. michael mazenko Perhaps I should have said “among the best,” as I see the quality of education at the top American students in the top American schools as every bit as successful as the top students I taught when I taught in Taiwan.

    Top students at the top American schools is a lot smaller group than the top 1/3rd. And is it not entirely possible that those top students would do as well if there were no schools at all in America?

    Additionally, I always view these rankings with a skeptical eye – as we all should – for a series of standardized assessments are hardly the definitive factor in identifying “best in the world” or “cutting edge of progress.”

    Okay, you think we should regard these rankings with a skeptical eye, I can agree with that, I’m generally in favour of skepticism. But what’s your rationale for failing to apply that skepticism to your own claims? You only mention the American and Taiwanese education systems as ones you have worked in, but in the rankings I provided 9 other countries had more 8th grade students performing in the top grades than the USA. And I’ve never heard of English students being described as incredibly-skilled at test taking, the English education system is very different to Taiwans from all acounts, yet they also did better in those tests than Americans did.

    Furthermore, when you observed the education of those top students at top American schools, and the top students and Taiwan schools, how did you control for your own biases? For example, did you blind yourself as to which students were American and which Taiwanese? This sounds like a minimum necessary to do the comparison.

    If you’re going to be skeptical, try to be consistent.

    Furthermore, when you say “for a series of standardized assessments are hardly the definitive factor in identifying “best in the world” or “cutting edge of progress.””, are you crazy?
    If you don’t have standardised tests (or assessments), then how can you possibly identify the best in the world? It’s the apples and oranges question – if you assess people differently, if you say test Americans on their geometry skills and Taiwanese on their calculus and Brits on their trignometry, then you can’t make any sensible comparisons at all.

    And if you don’t know that two markers, given the same set of test results, will wind up with roughly the same set of marks, then you have to have one marker mark every single test, which is ridiculous for any sizeable international comparison, unless the single marker is a computer, in which case you have to standardise the marking anyway.

    Standardised tests may not be sufficient for identifying “best in the world” or “cutting edge progress”, any standardised test used for that purpose needs to be validated, and there are always going to be philosophical arguments about how “cutting edge progress” should be defined, but standardised tests are vital anyway.

    Incidentally by standardised test I am referring to any test for which reasonable inter-marker validity has been established, not merely to computer-marked multi-choice tests.

    And ranking students and education systems based on international standardized testing and competition is somewhat useful, but myopic at best.

    At least myopic people can see things nearby. The same can’t be said for people like you who don’t use standardised tests at all.

  29. Anonymous10 says:

    Mr. Mazenko
    Thank you for pointing out that Indians and Chinese aren’t necessarily superior to Americans, just cheaper. Indeed, having worked for years with these people (both in academic and industry settings), I’ve concluded that nobody who talks about the virtues of foreign education knows any foreigners.

    In particular, I work in Redmond, WA (yes, Microsoft-Land!), and I know plenty about Indians and Chinese. Chinese work incredibly hard, and are sometimes innovative. Interpersonally, they are argumentative, contrarian, and often very, very caustic, especially with suboordinates, making them difficult managers and directors. They are exquisitely skilled at finding other people’s mistakes (indeed, observe Chinese interacting with their children, and you’ll hear endless shrieks of the phrase “BU DUI!” meaning, “You’re wrong!”), and are therefore excellent software testers, but a Chinese worker will never, ever make a mistake himself. Despite their reputation for docility, Chinese take criticism and correction VERY badly, making them far less teachable than American and Indian counterparts. However, they are often broadly knowledgeable outside their fields of expertise.

    This last statement can almost never be made of an Indian; indeed, I’ve encountered many Indian computer “geniuses” who take their computers to The Geek Squad and Office Depot for servicing by low-level technicians. These people, although very pleasant to work with, are not “traditionally” or “liberally” educated, as some people on joannejacobs.com seem to believe. Anyone who desires to observe staggering ignorance would do well to ignore American college grads and discuss history, politics, theology, literature, etc. with an MCSD (MS certified software developer) from India. These people were the super-elite back home, so what gives? India has a standardized national curriculum with ferociously tough standardized tests. That means they should know just about everything right? Or at least more than a lazy, American clod like me….

    I hope I haven’t offended any Indian or Chinese people, or shattered any treasured illusions. At least in my field (computers), formal education still isn’t that big a deal unless you’re in the Finance Department. Some of the best programmers I’ve seen were high school grads who had only a few months of high-intensity training at a local tech school, sometimes not even that. (But most American college grads are actually very good, too. I’ve heard the horror stories about newly-minted Bachelors’ of Science who can barely do fractions or compose a sentence, but I’ve yet to encounter such an animal in almost ten years. None of my colleagues or friends has ever met one either, not inside or outside the software business. Possibly this is an urban myth?)

    And please remember: the Great Masters in computers are college dropouts, one and all: Gates, Jobs, Wozniak, Ellison, Dell, Joy, and all the rest. Self-Education still seems to be the best of all.

  30. I’m all in favor of entrance exams for ed school, and for all college. These could be waived in certain circumstances, such as AP scores above 3, but it’s long past time for colleges to stop remedial courses. That should be done in community colleges, with some exceptions in western states where geography limits access. Even in that situation, successful completion of remedial courses should be required BEFORE college acceptance and those credits should not count toward graduation. Also, the percentage of graduates needing remedial courses should be immediately available online, broken down by college and high school. Any interested person could check the website and find that (x) percent of (y) HS graduates required remediation before being admitted to (y) State. Those two changes should increase the pressure on the k-12 system to ensure that their graduates have real knowledge and skills. That should also apply to graduates going to vocational programs, the military or to work.

  31. Tracy W.,

    Ouch!

    While I don’t put extensive faith in the significance of international standardized test rankings, I certainly wouldn’t say I have no faith in or use for the tests. In fact, in my district and state, I am generally one of the more vocal defenders of testing – CSAP and NCLB, as well as AP/ACT/SAT/PSAT. And I do apply my skepticism to my claims about the top third, knowing many of my AP students arrive ready to get a 4 on the exam, though I am pretty effective at giving my borderline students an edge. Additionally, I wasn’t conducting an experiment to establish a position on these rankings – I was using anecdotal evidence to provide perspective on the issue.

    I can only speak personally of two systems, as I did, and then I use that perspective to evaluate the rest. There are numerous other variables to consider, such as the restrictive nature of higher education in Europe and Asia. The English – and, in fact, many European schools – use these tests as gates to higher education. They have far greater incentive to do well. That’s much less true in the US. American students can go to a four-year college after graduating with a D average in high school, or not graduating at all, and performing below average on ACT/SAT. That is true nowhere else in the industrialized world. Thus, the stakes on these tests are much different for US and foreign students. As I said, if the ACT/SAT forbid calculator usage on their tests, it wouldn’t take long for US students to catch up to that expectation. But to what end? To do better on a test and a ranking? How does it correlate to success in the marketplace?

    The foundation of my skepticism about the test rankings is the increasingly dubious correlation between those tests/rankings and success in work/life. And to answer the question, no, that’s not “crazy.” Colleges and businesses are seeing less correlation between high standardized test scores and actual success in college and the workplace. I don’t have any article titles at the point, but I could look some up. Of course, the top tier of test takers are most likely assured of success. When I point to the top third, I’m also noting that America currently has about 29% of its population with a bachelor degree. However, I continue to read anecdotes like that at the start of Wagner’s “The Global Achievement Gap,” in which he conveys the comments of CEOs who argue they will teach “the skills” they want their workers to have. The people they are looking for are the ones who “ask the good questions” and use their “imagination to solve problems.” That is not quantifiable by a test. Many CEOs have spoken of their lack of interest in what their candidates learned in college. They just want to know what college they got into and that they graduated. Thus, the skill on the ACT math section is of little considerable value or interest to many employers.

    That difference is to what I attribute my skepticism about the rankings. The ultimate test, at least from my point of view, is what I see happening in the marketplace. Where is the innovation and the progress? That quality, which is omnipresent and foundational, in the US, is not at risk – at least not from what I hear and read of corporate America. The tests matter to me – they really do – but I am as interested by what’s happening at our engineering firms and NIH and CDC and NASA and IBM and Google, etc.

  32. michael mazenko – What bothers me is not lack of faith in standardised tests, but lack of skepticism on your part in your anecdotal evidence. Anecdotal evidence consisting merely of two countries does not justify such an extreme statement as the top third of American students are the best in the world. You still have supplied no evidence to support that statement, especially as you have apparently used absolutely zero measures to control for any biases you may have.

    As for standardised tests, if you want to use success-in-life as your basis for international comparison, then to do so you need some standardised test of what success-in-life is. Perhaps GDP per capita, or happiness on those global surveys, or rate of mental illnesses, or some combination of all of those and other things. People have attempted to construct many standardised tests aimed at measuring sucess-in-life, for example the Human Development Index. I am in favour of being skeptical about every standardised test, but if you don’t use some sort of standardised test you can’t make any sort of reliable international comparison. That’s why I asked if you are crazy.

    American students can go to a four-year college after graduating with a D average in high school, or not graduating at all, and performing below average on ACT/SAT. That is true nowhere else in the industrialized world.

    You use this to argue that American students will do worse on standardised tests. Okay. But this argument also implies that American students on average will do worse at their schoolwork overall – they lack the same incentive. So therefore this argument undermines your claim that the top third of American students are the best in the world.

    I also note that in the link I provided to the maths international comparison, only 6% of American students made the top level on the test. Do only 6% of American students care about getting into selective high schools?

    The people they are looking for are the ones who “ask the good questions” and use their “imagination to solve problems.” That is not quantifiable by a test.

    Then the school system shouldn’t waste its time teaching it. If we can’t test the difference between someone who has been educated to “ask the good questions” and someone who hasn’t, or between someone who is creative, and someone who isn’t, it’s foolish to waste money on teaching it. Spend the time on something where schools can make a detectable difference.

    However, I don’t actually believe your assertion that creativity or question-asking is not quantifiable. Options for creativity testing – give students a box and ask them to write down as many different uses for it as possible. Next item, give them a variety of shapes and ask them to draw an object including as many of those shapes as possible. Etc. Test on a test population to develop inter-marker reliability.
    Want to test question-asking? Set up a set of scenarios and ask students to write down as many questions as occurr to them. Use experts in the fields related to those scenarios to assess the questions – allow them to discuss anomalous results. Develop from this a standardised marking protocol.
    People have already made standardised tests of creativity.

  33. Tracy,

    I see your point, though it seems we simply disagree on what “best in the world” means and how these tests measure it. Are they the best students? Are they the best test takers? Are they the fastest readers? The best at math with a calculator? The best at math without a calculator?

    The more important question, for me, is will they become the best doctors and lawyers and engineers and scientists and producers and programmers and technicians and historians and writers and musicians and humanitarians and citizens. I don’t believe the international tests are great predictors of this. The market/workplace is the predictor of this, and I’m simply pointing out that American companies still “hold their own” and even dominate many areas, and they predominantly employ American citizens who were educated in American schools. That’s the comparison I am making – it’s one outside of the test. If our students perform poorly on these tests in comparison, is there a correlation to a negative impact on American business and society. I’m not seeing it. Where is the impact?

    The tests on creativity are fascinating, though I don’t see them being used currently in the type of ratings and rankings which prompted this discussion. In terms of “best in the world,” I would simply argue that our “top” students are as effectively serving our society as the Japanese and Hungarian and English and Taiwanese are serving theirs. I don’t put our “top third” on top of any others, but simply note that it’s possible they only thing trail in is the test ranking.

    I completely agree that their “rankings” should be a concern, just not the primary concern. I guess I might ask what your criteria are for determining that these tests/rankings are indicative of anything other than the ability to do the test.

  34. I see your point, though it seems we simply disagree on what “best in the world” means and how these tests measure it.

    Neither of us have defined “best in the world”, so I wouldn’t say we have gotten to the stage of disagreement. All I have been doing is casting doubt on your assertion that the top third of American students are the best in the world.

    In terms of “best in the world,” I would simply argue that our “top” students are as effectively serving our society as the Japanese and Hungarian and English and Taiwanese are serving theirs.

    Okay then, argue that. Present your evidence.

    I’m simply pointing out that American companies still “hold their own” and even dominate many areas

    You have set yourself another problem here. If American companies are “holding their own” this may be for reasons entirely independent of the education system, such as the USA’s system of business law, or accidents of history (as I stated earlier, Nazi persecution leading to an exodus of many of the best scientific minds in Europe to the USA). You haven’t supplied any evidence that the performance of American business is because of the performance of American schools with the top third of students.

    I guess I might ask what your criteria are for determining that these tests/rankings are indicative of anything other than the ability to do the test.

    The assessment framework developed for the 2007 TIMSS is available at their website.

    The tests on creativity are fascinating, though I don’t see them being used currently in the type of ratings and rankings which prompted this discussion.

    This may be because you didn’t use any rankings in your initial statement in this discussion. I used the TIMSS to question your assertion because it was conveniently to hand. I don’t know of any sources of international standardised tests of creativity, so I don’t think we can say anything one way or another about the relative international performance of American students in terms of creativity.

    I don’t put our “top third” on top of any others, but simply note that it’s possible they only thing trail in is the test ranking.

    Michael Mazenko, to quote you:

    Our top third are still the best in the world, and the United States is still leading the world in innovation.

    You most definitely did put the USA’s “top third” on top of any others.

    It may be possible that the only thing that American students trail the world in is test ranking. All sorts of things are possible. I note however that American students were about the top 10 or 11 in the eighth grade tests I linked to, well above the average of the countries’ tested, which does cast some doubt on this possiblity you describe here.

  35. Because, as I noted before, most of the commentary here is anecdotal, I don’t see providing the sort of “statistical evidence” that would satisfy you. And that was never my point. It’s simply not “testable,” and my point is you are putting far too much emphasis on the performance of students on these tests. The burden of proof on TISS is for you to provide evidence that the top students in other countries are superior to US students in terms of anything other than these tests. Are they more effectively serving their society? Are they producing better citizens and employees as a result of their education system and their performance on these tests? These are questions you haven’t answered because you can’t with statistical data.

    Additionally, you argue that America’s greatest assets might be indicative of cultural, socio-economic factors, and despite our education system. That is absolutely valid, but you can’t definitively parse it out, and it is indicative of the strengths of American students. The areas in which America leads the world – production, business administration, technical innovation, teamwork, critical thinking – are reflective of American society, which includes (but cannot be exclusively linked to) its education system. Most European and Asian systems, which rank higher than we, do not, at the high school level, offer the diversity of extra-curricular activities – athletics, clubs, music, student government, internships – that develop the qualities which lead to our strengths in innovation. Therein lies much of your difference, which belies the validity of using these tests to compare systems.

    As you noted, there are many ways to measure “best” (GDP, production, health, investment, “happiness,” etc.). The evidence you seek is American society – production, technology, medicine, engineering, global leadership, citizenship, and social/civic stability.

  36. Because, as I noted before, most of the commentary here is anecdotal, I don’t see providing the sort of “statistical evidence” that would satisfy you.

    What I am curious about is how *you* could be satisfied making the claim:

    “our top third are still the best in the world

    without using any statistical evidence at all, and only based on an anecdotal comparison of two countries, without you using any methods to control for your possible biases.

    I know that there’s not the sort of statistical evidence that would satisfy me, but how can you be satisfied without any either?

  37. As I noted initially, I can look at the “statistical data,” and then I apply that to my existing knowledge to determine my position on the validity of these tests. One example is: having experienced Taiwanese society and its students and compared that to American society and its students, I draw personal conclusions about how much “weight” to give these rankings where American students are outperformed by Taiwanese. I am not more impressed by their system, and higher rankings on these tests don’t equate to “better students” or a superior system/society for all the reasons I previously mentioned – all the variables that aren’t measured by these tests.

    Because I am not in the midst of conducting educational research, but merely engaging in a discussion about the quality/effectiveness of the education systems, I don’t seek to control for my biases, though that doesn’t mean I don’t understand or acknowledge them. The criticism of American society and the American system, based on these tests, is, in my opinion, extremely limited, and it overstates the validity of these tests. While you apparently place great significance on these results, I know of no economic models which would do the same.

    If there is no “statistical data” you know of to satisfy your concerns, why would you not look outside of this limited measurement. I am quite “satisfied” by the quality of education my children and students receive. So are 3/4 of Americans who, when polled, are “satisfied” or “very satisfied” with their children’s schools. Additionally, 80% of Americans are satisfied with their own education. If I weren’t I would make a change. Not being averse to living, teaching, and raising my children in the U.S. or abroad, I made an educated decision to raise and educate my children here because I believe it is the best place to do so. Certainly, some of that is cultural, but that bias works both ways.

  38. “The market/workplace is the predictor of this, and I’m simply pointing out that American companies still “hold their own” and even dominate many areas, and they predominantly employ American citizens who were educated in American schools. ”

    Hmm. Want to try again? Because that statement just isn’t true. Look into the public debate on the need for HB-1 visas. Increasingly, the top students in other countries are the top students in US universities. The US depends upon the K-12 systems of other countries to meet our economy’s need for competent graduates in science and engineering.

    “In many fields of science and engineering, foreign students make up the majority of doctorate recipients,” Finn said. “Universities, research labs, and other high-tech employers have become dependent on these scientists and engineers.” (http://www.orau.org/media-center/news-releases/2008/fy08-16.aspx)

    This is not an endorsement of a wonderful, creative US system. To me, this means that many students are not adequately prepared after high school to complete an S&E degree at the college level, nor to pursue a graduate degree in science & engineering.

  39. Parent2,

    Or, from the standpoint of Fareed Zakaria in “The Post-American World,” this not about the demise of the US, but about the “rise of the rest.” Certainly, both our universities and corporations are going to seek the best people, and those “best” won’t always be Americans. In fact, it would be rather ego-centric to think so, though many countries and cultures often have. American society it simply more open to opportunities for all. Additionally, I argued that American companies “predominantly” employ Americans, and that is, of course, true. Tracy W. pointed out that I have implied, or even stated, that Americans students are “best” across the board, though I merely meant to imply our best can and do compete with everyone else’s “best.” Perhaps I’ve overstated my optimism about our top students, but that only qualifies overstating the significance of American students trailing other countries’ students in international standardized tests.

  40. Because I am not in the midst of conducting educational research, but merely engaging in a discussion about the quality/effectiveness of the education systems, I don’t seek to control for my biases, though that doesn’t mean I don’t understand or acknowledge them.

    Okay, so you’re engaging in a discussion about the quality/effectiveness of the education systems. What’s the point though of engaging in this discussion if you don’t care whether your opinions are right or not? Even in the context of this discussion you are happy to be skeptical about the quality/effectiveness of standardised tests, but oddly not about your own potentially-biased observations. Why not? Why the one-way skepticism?

    I made an educated decision to raise and educate my children here because I believe it is the best place to do so…

    You are free to do so. However, I do not consider comparing merely two countries’ education systems a valid basis for claiming that the top third of American students are the best in the world. You may choose not to be skeptical about your own beliefs, but I am most certainly skeptical about your beliefs, particularly when you expand them beyond the two systems you know about to the rest of the world.