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  • Mathematics versus The Blob

    Posted by David Foster on November 17th, 2009 (All posts by )

    (…and so far, the blob seems to be winning)

    Here’s a New York Daily News article on mathematical ignorance among City University of New York students:

    During their first math class at one of CUNY’s four-year colleges, 90% of 200 students tested couldn’t solve a simple algebra problem, the report by the CUNY Council of Math Chairs found. Only a third could convert a fraction into a decimal.

    And here’s Sandra Stotsky, discussing some of the reasons for poor math performance in America’s schools:

    But the president’s worthy aims (to improve math and science education–ed) won’t be reached so long as assessment experts, technology salesmen, and math educators—the professors, usually with education degrees, who teach prospective teachers of math from K–12—dominate the development of the content of school curricula and determine the pedagogy used, into which they’ve brought theories lacking any evidence of success and that emphasize political and social ends, not mastery of mathematics.

    and

    Classroom practices follow logically from these theories. Teacher-directed learning goes out the window, despite its demonstrated benefits for students with learning problems; instead, schools should embrace “student-centered” math classrooms. High-math-achievement countries teach arithmetic in the elementary grades in a coherent curriculum leading, step by step, to formal algebra and geometry in middle school. The progressive educators, by contrast, support “integrated” approaches to teaching math—that is, teaching topics from all areas of mathematics every year, regardless of logical sequence and student mastery of each step—and they downplay basic arithmetic skills and practice, encouraging kids to use calculators from kindergarten on. The educators also neglect the teaching of standard algorithms (mathematical procedures commonly taught everywhere, with only minor variations, because of their general applicability), insisting instead on the value of student-developed algorithms—this despite research by cognitive psychologists strongly supporting a curriculum that simultaneously develops conceptual understanding, computational fluency with standard algorithms, and problem-solving skills as the best way to prepare students for algebra.

    Read the whole depressing thing.

    I think much of the problem with math teaching, and with K-12 teaching in general, stems from the fact that many of the people dominating our public schools are highly anti-intellectual, in the sense that they themselves do not put much value on knowledge, and don’t really believe that anyone else does, either. (Ironically, many of these individuals probably view themselves as intellectuals, are very very proud of their–often very lame–college degrees, and love to sneer at what they view as the “uneducated” mass of Americans.)

    For decades, educators have been justifying their even-increasing demands for money by talking about how we live in a scientific society, or a technological society, or a “knowledge economy.” It’s pretty clear, though, that the controlling forces in public education have no serious interest in providing the kind of education that is actually relevant to science and engineering. This practice of demanding money for one purpose, and then actually using the money for wholly other purposes, constitutes fraud on a very large scale, in a moral if not in a legal sense.

    Is there any hope for major improvements in this situation? Despite all the speeches about “reform,” much of public education in America remains tightly controlled by the aggregate of interest groups that has been referred to as the blob.

    And, given that the blob is a major constituency of the Democratic Party, I don’t think there is likely to be much improvement unless and until the power of the Democrats is decisively broken, in states as well as at the national level. People should still work to improve things at the local level when they can, of course: getting a good math education for 100,000 kids is worthwhile even when millions are still being mis-educated. But from the standpoint of the overall country and its economy, these mammoth educational failures should be of major concern. To quote again from Stotsky’s article:

    A form of mathematics stripped of much of its intellectual content has obvious repercussions for higher education and the American economy. Hung-Hsi Wu, a Berkeley mathematician, expressed the view of many of his peers when he wrote in 1997 that the brand of mathematics purveyed by the NCTM’s 1989 report “has the potential to change completely the undergraduate mathematics curriculum and to throttle the normal process of producing a competent corps of scientists, engineers, and mathematicians.” And Larry Faulkner, the panel’s chair and past president of the University of Texas in Austin, warns that if national policy doesn’t ensure the development of a large domestic workforce with first-rate technical skills, we risk “technological surprise to our economic viability and to the foundations of our country’s security.” If the bleak math statistics in the United States don’t change soon, such “surprise” may well be imminent. The math wars, which started in debates about pedagogy, may end in questions about the long-term prospects for American prosperity.

    (both links via Erin O’Connor)

     

    15 Responses to “Mathematics versus The Blob”

    1. Daran Says:

      I like to put it as ‘conservatives are anti-intellectual; liberals are anti-intelligent’.

    2. onparkstreet Says:

      Do you really think that is the case? That it’s about anti-intellectualism? I’m not sure of this.

      I think many of the problems in math education have to do with academic fads (student centered learning – I always want to ask, but how is the student to know best?) and the fact that the teachers themselves may not have mastered the material. The second point is key, I think, well, that’s what my math professor father thinks, anyway. He deals, occasionally, with the problem when he teaches undergraduate classes. A certain percentage of students who will go on to teach math, among other subjects, at the K1-12 level, and don’t have a mastery of the subject. To be blunt: they don’t do well in his classes.Isn’t the KIPP program based on teaching teachers, and helping them so that they can better transmit information? I know, I know, transmit information is so old-school. I also know I am painting with a broad brush, but I do think poor education of the educator is a part of the problem.

      Hmm, you have given me an idea for a new post…

    3. RJO Says:

      > many of the people dominating our public schools are highly anti-intellectual

      On this point, I strongly recommend an old classic that people ought to dust off: Richard Hofstadter’s Anti-intellectualism in American Life (1963). Three chapters focus on education in particular: “The appearance within professional education of an influential anti-intellectualist movement is one of the striking features of American thought.”

    4. onparkstreet Says:

      OTOH, maybe I need to read the book highlighed in RJO’s comment….

    5. David Foster Says:

      OnParkStreet…the educators I am talking about seem to think that every subject is inherently so boring that kids will only be interested in it IF it is somehow spruced up…for example, combining two different subjects in strange ways. I saw one lesson plan which attempted to combine math (graphing, in particular) with WWII and Holocaust history by assigning students to graph the number of Holocaust murders on a year-by-year basis.

      I am all in favor of making subjects interesting in ways which are reasonably integral to the subject: math, for instance, is probably much more interesting to most people when taught with reference to actual applications. (I was helping a nephew with linear equations (which required a little refreshing my part) and he asked if there were actually any uses for these things. Why in the world wouldn’t the textbook/teacher say something about this?) But many of the attempts by the education establishment to make subjects “relevant” remind me of the stuff one gets in the mail from frantically incompetent direct-mail people (IMPORTANT! DO NOT DISCARD! SERIAL NUMBER 3143431432)

      I’m probably using “anti-intellectual” in a different way than it is typically used.

    6. Shannon Love Says:

      Modern educators are definitely “anti-intellectual” in the sense that they oppose the enlightenment concept of the intellectual as someone who used reason and empiricism to examine problems.

      Instead, leftist today use “intellectual” in a manner very close to that of the Communist. For Communist, an “intellectual” was someone with the proper ideological indoctrination. For leftist, to “think” is to conform to the tenets of the ideology. The same fate has befallen the concept of “education” itself.

      This is why so many people in the education field believe themselves intellectuals, believe they think and believe they are educated. They’ve change the meanings of the words without telling the rest of us.

      My own experience with math education with my children was horrible. My daughter had a teacher who panicked if my daughter did algebra problems the way I taught her instead of the exact method the teacher used. After talking to the teacher, I realized she simply didn’t understand how to do the math and was instead relying on rote.

    7. Michael Kennedy Says:

      I think there may really be a role for paying math and science teachers more. Unions fight that, of course, and are in control. My ex-wife, who has a lifetime elementary credential, taught 2nd and 3rd grade in the 1960s when I was medical student. Years later, she was a VP of a big bank and got eased out in a merger. She got a job as a substitute teacher when California hired a huge number of new teachers. She took the CBEST test that was the subject of many complaints by applicants for those jobs. She told me it was 8th grade math. She taught for about 6 months and after her first month, the principal was trying to get her to sign a year contract. She got another bank job and moved on. He lived near her and she used to see him in the market from time to time. He would always come over to talk. He told her she was his best teacher.

      She had not taught in 30 years at that time. She was appalled at what she found after 30 years. The teachers were contemptuous of the kids. It was a middle class area but they would make fun of the kids when they were in the teachers’ room. She complimented a second grade teacher on the job she did with reading. The woman burst into tears. No one had ever told her she was doing a good job. This is a national collapse of education training. They are the bottom of their college classes and they are not motivated to do a good job. Some still try but do not get reenforcement. In the 1960s, lots of smart young women went into teaching because that and nursing were the careers for women. No more.

      She was always very pro-public school when our kids were growing up but she told me she would home school them now.

      This has got to get fixed early or we will lose a generation of kids. Larry Elder used to talk on his radio show about the library in Hollywood near his home. Outside on the sidewalk, minority kids were doing skate board tricks. Inside, Korean kids were studying with their mothers standing over them. The economic status of those kids was no different. I agree about math but this is much more than math.

    8. David Foster Says:

      Michael K…”paying math and science teachers more”

      If qualified math & science teachers are scarcer (because they have more job alternative, for one thing) and they *don’t* get paid more, then they are *automatically* going to be in short supply.

    9. Dove Says:

      I always thought a big piece of the problem was that the teachers generally didn’t understand the math.

      Not only is teaching a relatively low-paying job for someone who understands math well, it comes with a lot of other drawbacks: it often requires a (relative content-free, if you’re used to studying things like math) education degree, comes with a lack of creative and intellectual control over your own work, and requires putting up with a great deal of administrative nonsense on a daily basis.

      Small wonder they can’t get qualified applicants, and depend heavily on the altruism of the ones they do get.

    10. Laura(southernxyl) Says:

      “(I was helping a nephew with linear equations (which required a little refreshing my part) and he asked if there were actually any uses for these things. Why in the world wouldn’t the textbook/teacher say something about this?)”

      David, I use them all the time on my job. One way that you can test the purity of a solvent is to make solutions with varying concentrations of your analyte, then inject them on the GC (or whatever) and plot concentration against response. The closer your best-fit curve is to going through the origin – that is, the closer the y-intercept is to zero – the purer your solvent is. Also, if you use the standard-addition method of analysis, you find the best-fit curve and then the result is the negative x-intercept. (I love Excel, by the way. Used to have to do this stuff by hand on graph paper, or with HP calculators and the weird RPN or whatever it was.)

      I also used them to explain to my daughter why she traveled through elementary school always the size of the kids two grades behind her. It’s your growth curve, I told her – your slope is good, but your y-intercept is off.

    11. david foster Says:

      Laura…meant to say “SIMULTANEOUS linear equations”…of course, there are lots & lots of applications for these.

    12. Laura(southernxyl) Says:

      Ah.

      I’ve had to do that lately too but can’t remember why. Job-related, b/c I was sitting at my desk at work.

    13. UNRR Says:

      This post has been linked for the HOT5 Daily 11/18/2009, at The Unreligious Right

    14. sol vason Says:

      href http://www.nytimes.com/2009/11/15/education/15plans.html

      Here is an article about teachers selling lesson plans and tools/ideas they use to cause children to learn. It doesn’t turn bad teachers into great teachers but it does make the better teachers. It seems there are some bad teachers who want to get better. The only people who are opposed are the politicians and the union leaders.

    15. TMLutas Says:

      A good chunk of the problem is that parents and students do not realize how much they are being robbed and how to get a good education anyway. This is fixable.

      Thanks to George W Bush, we now have an imperfect measurement system for our primary and secondary schools. It could use some work but it’s better than what came before.

      Our very best schools get their heads handed to them on international education competitions, a sad state of affairs that has persisted for decades. We make up for that poor education in having superiority in other areas but those other areas only get you so far. The hierarchy of educational results counts too.

      Our children are being robbed. They are being robbed of better jobs and a better life.

      The people in the community are paying for that robbery.

      This is evil.

      This is unfixable from the inside.

      I had a friend, a professional political operative. He ran for school board, got a slate in so he had a majority to back him. He informed the teachers that the days of fat raises for mediocre performance were over. The board stuck firm even after the union surrounded the school with tens of thousands of chanting teachers. The teachers union pulled in resources from all across the state to defeat him. He survived but he lost his majority after one term.

      Unless you have a coordinated campaign of tens of boards all rising up at the same time, any state union is going to be able to put down any reform effort. Very unfortunate, but it’s true.

      The only solution is escape, education, and when the alternate system is sufficiently robust, defunding. Private schools are an escape for the wealthy, tutoring for the upper middle but for the middle and below, it’s rough going. We need a radically cheaper solution.

      When the task is getting something done cheaply, it means an online solution. This is doable and very likely there will eventually be an open courseware solution to provide the curriculum. There is a worldwide open courseware consortium that is handling higher education but it’s of limited use if the foundations are not there.

      Eventually, those in higher education will “get it” and add in materials for the lower grades and we will have a solution. All that can be done in the meantime is to fight for our own children and to assist where we can in limiting the damage.