Who needs math?

Some parents and a San Francisco Chronicle columnist flubbed the algebra and chemistry questions on California’s STAR exam. I don’t think it means much that people who haven’t used chemistry for several decades don’t know the material any more. Thanks to my tutoring of ninth graders, I could do all the algebra questions; I didn’t try chemistry, which I took in 1966-67. I question C.W. Nevius’ assertion that teaching to the test requires ignoring concepts.

Instead of critical thinkers, the ideal STAR test students would be multiple-choice experts who have memorized catch phrases and equations.

Finally, many of the questions in the math and science sections are incredibly obscure. Unless you are a mathematician or scientist, why would you need to know that information later in life?

So should we stop teaching algebra, geometry, trig, chemistry and physics to all but future mathematicians and scientists? That would require teen-agers to decide what fields — business, medicine, engineering, etc. — they want to remain closed to them forever. We can’t all be newspaper columnists. (And it would be nice if Nevius had the mathematical sophistication to understand the basic concept of “adequate yearly progress.” It’s not a fixed number.)

Here are links to state standards for various subjects — students must do more than memorize formulas — and sample questions.

About Joanne


  1. KateCoe says:

    My husband’s a chef, who last had math in college and he got all the algebra questions right. He got most of the chem stuff right, too. But then he went to Exeter and LSE. I’d say the only “fact” I learned is that you can be pretty dumb and write a column in SF.

  2. SuperSub says:

    I still don’t understand the problems with “teaching to the test.”
    A syllabus or other curriculum guideline is created to define the required course material to be covered. A test is made, by the state, to test that knowledge. Teachers, knowing the material that should be covered on the test, teach that material.
    I don’t see any difference than a teacher making up their own curriculum and tests… except that the control over the situation is with the state in the latter case.
    Personally, I believe that a lot of the opponents to “teaching to the test” either A) resent the control of the state, B) are themselves unable to meet the performance level required to cover the material, or C) are so trained in the ways of student-centered learning that they oppose any system which favors teacher-centered learning.

  3. Cardinal Fang says:

    Teaching to the test is not the same as teaching the standards, unless the test tests exactly what is on the standards. This is rarely the case, because some things on the standards are easy to test and some are quite difficult.

    For example, the history standards for California require that students analyze and discuss various historical movements: the ideological origins of the American Revolution, the great religious revivals in American, expanding religious pluralism, the social ramifications of World War I on the home front, and so forth. Yet the STAR test is a multiple-choice test that requires no analysis and no discussion. So in teaching to the test, that part of the standards would be neglected in favor of memorizing facts.

  4. KateCoe says:

    But how can you analyze the causes of the Am. Rev. if you don’t know many of the facts about it? Oh–wait–you can! It’s called bullsh*tting.

  5. Cardinal Fang says:

    But knowing the facts of what preceded the American Revolution is not the same as being able to analyze the causes. You could know the facts, but not be able to analyze. Knowing the facts is necessary, but not sufficient.

  6. Many journalists, like many “educators,” are anti-intellectual, in that they don’t believe knowledge has any value for its own sake, and they are too limited in their own life experience to be able to understand its practical value.

  7. Steve LaBonne says:

    Od course, Fang; but the trouble is that too many ed-school ideologues are reluctant (at best) to admit that it’s necessary. Whereas, who exactly is claiming that it’s sufficient? Nobody I know of.

  8. Cardinal Fang says:

    SuperSub wondered what the problem is with teaching to the test. I replied that if a teacher teaches to the STAR test in the case of American History, that teacher is teaching facts but not analysis, since that’s what the STAR test, a multiple choice test, measures.

    Perhaps some ed-school ideologues believe that one can ignore teaching the facts. I don’t agree with those people, if indeed such people exist. However, proponents of teaching to the test are implicitly in favor of ignoring analysis, at least in the case when the standards require analysis but the test doesn’t test it.

    The problem is that it’s hard to test analysis and easy to test facts. But we must not fall into the trap of only teaching what is easy to measure. That is the problem with teaching to the test.

  9. Steve LaBonne says:

    It’s still better then teaching nothing. And even worse than teaching nothing is teaching kids that venting their totally uninformed opinions constitutes “critical thinking”.

  10. SuperSub says:

    The STAR tests probably are designed to measure minimal knowledge since they are statewide… it still falls upon the district and administration to follow through with the standards placed forth by the state.

  11. Cardinal Fang wrote:

    But we must not fall into the trap of only teaching what is easy to measure.

    Well there’s more traps then that one, Cardinal. There’s the trap of not measuring anything. I’d say that’s a worse trap to fall into then just measuring what’s easy to measure.

    Also, there’s no analysis in the absence of facts. If the kids don’t know the facts of the American Revolution what context does any analysis exist within? The facts come first and then the analysis.

  12. “Finally, many of the questions in the math and science sections are incredibly obscure. Unless you are a mathematician or scientist, why would you need to know that information later in life?”

    Schools should be about opening doors, not closing them. Lower school math should be all about preparing the student to take a REAL course in algebra by 8th grade. Many schools have such dumbed-down and simplified math in the lower grades that it virtually guarantees that this will not be possible. It also virtually guarantees that these kids will not have a scientific or technical career without outside help. Unfortunately, most students will come to the wrong conclusion that they are just not (genetically?) good in math.

    High schools have honors and AP courses, but many of the kids are just not prepared properly. I have talked before about the quantifiable gap in curriculum I have seen between K-8 and high school math. Are there no working relationships between the development of high school and K-8 curricula? Do high schools ever go back to the lower schools to discuss problems in curricula and preparation? It seems to me that the lower grades are in their own pedagogical and philosophical dream world with no outside frame of reference or expectations. At least high schools have teachers who are trained in their fields and have AP courses defined by outside standards. Curriculum matters. It’s not just about the quality of the teachers and how you teach.

    The algebra test was easy, even for Algebra I. For those worried about teaching to the test, why would they worry about this test? What analysis or “higher-order” problem solving is possible without being able to answer these questions? There are some pedagogues who believe the proper way to teach anything is from the top down; from real world problems down to the basics. Unfortunately, this means that the basics never get mastered properly and that any analysis ability they might have rests on very shaky ground.

    If the student does well on this test, there is no guarantee that the student knows how to apply this skill to applications. However, if a student does not do well on this test, then he/she is nowhere. The former is a problem that can and should be dealt with. The latter can’t be fixed.

    Besides, who ever said that standardized tests define a complete curriculum? The problem is that there are many who feel that there is some “other” knowledge that makes doing poorly on these tests OK. The tests might not define a sufficient condition, but you will have a hard time convincing me that it isn’t a necessary condition.

  13. Cardinal Fang says:

    Besides, who ever said that standardized tests define a complete curriculum?

    If teachers teach to the test the tested material will be the complete curriculum.

    And if we pay teachers based on their students’ results in standardized tests, they will have an incentive to teach to the test and ignore those parts of the curriculum not tested- such as analysis.

    Steve, I agree with you that teaching to the test does not seem to be an issue with the algebra test. My concern is not with as much with math, especially in the lower grades, but with other subjects.

  14. hardlyb says:

    I looked at the Physics test a little, and the questions that I saw were actually surprisingly good at requiring an understanding of the material. The Algebra 2 test questions are less interesting, just routine, but if you think that kids should learn any math at all, they need to be able to answer the questions. I’m sure that I would do poorly on the Chemistry questions, since I’ve forgotten all of that in the 35 years since I took chemistry in high school.

  15. “If teachers teach to the test the tested material will be the complete curriculum.”

    Of course, and this is happening in our schools. The minimal state test expectations become the maximum that the school will aspire to. Our town receives “High Performing” marks. What more do they need to do? That is why so many students are leaving.

    Low expectations and bad curricula, however, won’t go away with no testing. They will get worse. Testing at least enforces a minimal level of accountability. Hopefully, parents will actually look at the tests, the grading, and the rating formulas and demand more. Maybe not.

    As for “other subjects”, you will have to be more specific. You will have to show how it it OK for students not to know the basic material on the standardized tests and how there is not enough time to cover more important topics. You have to explain how the basics are not necessary for this other kind of learning. I assume that each class has its own assignments and tests outside of the state’s standardized tests.

  16. Engineer-Poet says:

    I took the sample Algebra I and Chemistry tests (well, an hour and a half ago because the blog kept insisting I was NOT logged in and refused to let me post this) just to see if I was up to snuff or not.  I missed 2 questions on Algebra I (#15, which I wasn’t careful enough about, and #2, which I noted as “fucked” due to being nonsensical as displayed by XPDF – might be a PDF rendering bug, but I suspect not) and I found a question with faulty wording (#7).  I missed one question on chemistry – not surprisingly, the one about valence electrons, which I had not looked at in over 2 decades.

    I note that question #23 on the chemistry test would be likely to fluster Möbius Stripper’s ex-student Miss Needs-A-B.

    When I last took a chemistry course, Jimmy Carter was president.  I still would have kicked butt walking into those tests cold.  None of this material is particularly difficult; today’s students should be able to do this kind of thing in their sleep if they are properly motivated and instructed.  Failure to pass such simple tests should be considered shameful for student, school and family, and career-limiting failures in education should never be considered excusable.

    Education in math and science may lose relevance in work life, but it is more and more important for making political decisions.  One pol in the campaign is bullshitting or scaremongering on the subject of global warming, or mercury pollution, or Social Security.  The other is being truthful.  Are you going to vote for the guy who’ll tell the truth and make the difficult choices… and how do you know which is which if you don’t grasp the underlying facts?