William M. Briggs

Statistician to the Stars!

Can you do these math problems? If not, you can still go to college

Here are four problems, published by the New York Daily News, that high school graduates attempted as they entered the City University of New York (CUNY) system. The percents are those who answered correctly.

  • 64%: 5 + 3 (4+6)
  • 44%: How much is 0.2 divided by 5?
  • 34%: Write 3/8 as a decimal
  • 10%: Solve the equation x2 = 9

Note again that these are the results from fresh high school graduates entering college. These are not older people coming back to school after many years, nor are they the folks who eschewed college. These are people who should know these answers.

I can just see—maybe—that knowing the answer to the fourth question should not be a requirement for a university education. But one-third could not accomplish a simple addition/multiplication problem.

As I’ve argued before, that’s about the percentage of people who do not belong in university. For an interesting debate of this subject, head over to Chronicle.com. Our pal Charles Murray is there.

I’ve told this story many times, but when was an undergrad I was in an intensive mathematical program. Five days a week, tons of homework every night, oral quizzes—-oral quizzes! A lot of people washed out after the first year, even more the second. One first-year washout was a female who we can call Jenny. I met Jenny again in our senior year and asked what was her new major. “I’m going to be a math teacher,” she said. Those who can’t do…

Here is an article from City Journal on math education. Perhaps I’ll give away the punchline when I tell you that “educators” spoken of in the article invented the phrase “deep conceptual understanding.”

Try not to read this article with any sharp objects in hand or within reach. You have been warned!

Some schools acknowledge that a large proportion of kids will do poorly on math, and will hence have lower GPAs. Solution? Have them donate to the school. 20 points for each $20 on the final exam. Full story here; sent in by long-time reader Ari.

30 Comments

  1. Most students (in my experience) have a tougher time with word problems than with simple equations.

  2. a) 35 b) 0.04 c) 0.375 d) 3

    How’d I do?

    MrC

  3. d) -3 and/or +3

    In Texas the standardized (multiple choice) tests in reading and math pose a challenge to the system. For a given grade level, the reading comprehension level required to understand a math “word problem” is higher than the reading level required to pass the reading test. That is, a tenth grade student “successfully” meeting minimum reading standarss as measured in reading tests may not read well enough to understand tenth grade math test questions.

    This is widely interpreted to men the KIDS are stupid …

    I might suggest an alternative interpretation.

  4. Briggs

    14 November 2009 at 10:47 am

    Speed, that’s true of everyone, but of course that’s how all real-life problems come at you. Except for the highly artificial setup of school exams, most of the effort of solving a problem comes from setting it up correctly using only the vague and imperfect English language.

    MrCannuckistan, see pouncer’s answers.

  5. These are easy:

    1. Trick question, since the answer is right there in the parentheses: 5+3 = 4+6

    2. You can’t divide 0.2 by 5 since 5 is bigger than 0.2.

    3. 3/8 = 3.8, simple substitution.

    4. x^2 = 9? Bad test design – you gotta give us the #2 footnote (also, I didn’t see any footnotes before this one – is this just an excerpt of a longer test?).

    Now, where’s my New York State high school diploma?

  6. Any right thinking person knows that math is just a tool used by the evil white man to oppress women, minorities, people of color and gays.

    Newton’s Principia was declared a rape manual by the feminists.

  7. Briggs

    14 November 2009 at 3:33 pm

    Ray,

    After reading

    Lemma V.

    Similium figurarum latera omnia, quæ sibi mutuo respondent, sunt proportionalia, tam curvilinea quam rectilinea, & areæ sunt in duplicata ratione laterum.

    how can you doubt it?

  8. I blame out of date text books. For example, the ancient Egyptians would have “expanded” 3/8 as 1/4 + 1/8.

    I do think there is more going on here than math illiteracy (which I agree is shocking among high school and college graduates). But over 1/3 of the students couldn’t be bothered to count on their fingers to come up with an answer to the first question. I suspect that there is an instinctual knowledge that this test doesn’t matter so they don’t bother. As the test got “harder” more stopped bothering.

  9. It’s not fair! They thought they could use a calculator and a formula cheat sheet.

  10. And the sad irony is that “Jenny”, a faithful member of the NEA, has probably been promoted even further past her competancy level and is now a middle school administrator. “Primoris operor haud vulnero”, etc.

  11. FYI: City Journal Link is broken.

  12. Briggs

    15 November 2009 at 6:05 am

    MrCPhysics,

    Whoops. Thanks, it’s now fixed.

    49er,

    Let’s hope so.

    Joe,

    You’re probably right.

  13. Once per year I teach a Statistics for medical sciences course (nurses, pre-pharmacy, etc.), and two sections of physics without math, or maybe it’s physics without tears, and for my own information I give a mathematics test early that contains four sections that depend on pre-algebra (signed number calculations), algebra I, algebra II, and college algebra. All students had taken college algebra already. The average grade earned on the signed numbers end of the test is 70%, and that earned on the college algebra material is as close to zero as one can imagine. These students are already in college and nearing graduation at the A.Sc. level.

    As to the charge that they just stop bothering with a test that they know “does not count”, their preformance in class matches the test nicely. With enough effort on my part they will get back to a passing level of competency at the college algebra level at the expense of other material in the course, but it doesn’t stick, and in a few months they can’t calculate anything once more. The community colleges are now filled with the ranks of incapable students who were not college material in the first place, and we don’t do much for them except give them a certificate of some sort. I fear we are becoming a highly credentialed nation of nincompoops.

  14. Who needs math when you’ve got R? Just use the read.WordProblem function (optional parameter: answer.everything=TRUE). Available in the dumbdown package downloadable from failures.org.

  15. Joe,

    If one expands as you suggest (3/8 = 1/4 + 1/8) then a very large proportion of (community) college students, those taking a 900 level remedial course, will calculate as (1/4 + 1/8=1/12) so 3/8=1/12! The inability to handle fractions is the single worst barrier to students being able to do algebra.

  16. My fear is that this reflects the level of the student’s critical thinking. I am depressed.

  17. Oops. it should be “Students’ critical thinking”

  18. From the article ( http://www.city-journal.org/2009/eon1113ss.html), this should leave a mark:

    “Baseless pedagogical theories mean that the educators’ long-term captive audience—K–12 teachers, most drawn from the middle academic tier of our high school population and the bottom third of our undergraduate population—will know even less about authentic mathematics than they do now. Alas, so will their students. And even if a new Congress or Secretary of Education were to support the panel’s recommendations, it will be essentially business as usual in the public schools so long as math educators, joined by assessment experts and technology salesmen, continue to shape the curriculum.”

  19. “I can just see—maybe—that knowing the answer to the fourth question should not be a requirement for a university education.”

    That sort of statement coming from a self-stated mathematical pedant like yourself is an eye-popping revelation for a foreigner like myself.

    Can’t think of any school system I have become familiar with (a few) where that would be acceptable for a 14 year old.

  20. What do we need math for?

    You can clearly become president without any.

  21. Sometimes the best players do not make good coaches.
    What if Jenny decided that (failing the test) was an indication that her math teachers had failed her?
    What if she decided that by studying hard and working diligently she could become a better math teacher than those that had taught her…… and therefore her students would have a better chance of passing the test than she did?
    Teachers who cannot teach well, or in some cases even do/understand the stuff they are supposed to be teaching, is not a modern phenomenon.
    Some of us were just plain lucky to have good teachers at important stages in our education.

  22. Briggs

    16 November 2009 at 3:54 pm

    Tony,

    Hear, hear! But, in this case no. “Jenny” was a dope.

  23. d) don’t forget x also equals ((root 3) * i )squared

    I went to my 40th HS reunion last summer. I am still the only one who knows any math at all. Yet my class contains doctors, lawyers, teachers and other professionals who have managed to struggle by somehow, despite their severe math handicaps. Let us not write off Jenny entirely. She may have other redeeming qualities.

  24. Tony:
    The mathematicians comments in the article indicate that they see that far too many teachers responsible for teaching math and math related subjects have little understanding of math (as distinct from mathematics as understood by real mathematicians). For an NRC/NSF project on the Education and Utilization of Engineers, I recall looking at the SAT scores of most college majors and the scores for Education Majors were, and probably still are, abysmal – the lowest of all majors. I recall having a Boston HS Economics teacher in a grad class who could not (a) read a graph and (b) transpose an equation. Only Marxian Economsts have no need of these basic math skills. This was in the 80s!! 5 years ago, my wife had the Valedictorian of the local high school work in her store and the young lady, who was very pleasant and diligent, could do neither percentages nor simple division in her head, e.g., socks cost $27 per dozen pairs so one pair should cost?
    Subject matter mastery is a necessary but not sufficient condition for being a good HS teacher.

  25. The article suggests that math education began to degrade sometime in the ’80s. Leaders have been complaining about the quality of math education since Sputnik.

    At that time math education was heavy on multiplication tables and repetition. As a result of our perceived failings we got “the new math.” It jumped into new concepts such as set theory and “all that base 6 crap.” Every 20 years or so, we get a new new math. It might be a conspiracy to be sure that parents are incapable of helping children with their homework.

    I have spent some time tutoring kids in math. Kids today have very low confidence in their ability to do simple arithmetic. Many are fine with the advanced concepts, but ask them to multiply 7 x 8 and they freeze. Funny, when I was in high-school I didn’t trust my calculator. I would run my calculations twice to make sure I hadn’t miskeyed it. I still don’t trust calculators.

    I work with people who used to be good at math, but have forgotten 90% of it. The computer does it for them. It doesn’t get around the problem of knowing how to set up the problem and knowing which formula to use. These people know to use the harmonic mean to calculate an average P/E, but don’t know why, or even what the harmonic mean is. And, everyone I work with uses the population standard deviation when working with sample data.

  26. Doug:
    The problem is that without the simple math stuff, there is no way to evaluate the reasonableness of political discussions and assertions that are the basis of policy arguments. Take today’s Mammogram example. To my mind, if one does not understand percentages one is hostage to the scare talk that will likely accompany the change in policies with respect to Mammograms. One quickly descends into an all or nothing world that produces very, very inefficient and ineffective policy decisions and outcomes. For example, Matt used a % of accurate predictions for a positive test result. If he had only used actual raw numbers then the discussion gets slanted given the very large number of Mammograms. But for policy decisions that require an assessment of both costs and benefits, both absolute and % are needed plus a willingness to think critically about choices and consequences.

  27. Bernie,

    I don’t disagree with you. I am putting forth my observations. I do not suggest that this is the best of all possible worlds.

    90% of Americans will never do long division after they graduate. These people will rely on the advice of “experts” for many decisions in their lives. And, many of these experts will have different motivations to make their recommendations.

  28. I’m anxious to give this test to my 5th grader to see how he does.

    Also, my son’s fifth grade teacher told me that many parents have complained that the math homework is too hard because they (the parents) can’t do it, so how can their 10 and 11 year olds be expected to do it?

    In general, I’ve been shocked at the reluctance of the public schools to challenge elementary school kids in math. It’s especially depressing if you have a child who shows an affinity for math. Our school district has an acclaimed “gifted” program, and within that program, they have a “math component” for kids who score in the 99th percentile on the standardized math tests. The focus of the program is on “critical thinking”, which I welcome, but there is no effort to expand the academic content of the work.

    For example, the type of problem that they give to a group of students in the math compent is this: If you won a million dollars in the lottery, and went to pick up your winnings in $20 bills, how big of a suitcase would you need? It’s a fun problem for bright fourth and fifth graders, but it requires only basic arithmetic, a little simple geometry (area and volume calculation), but no algebra.

    As an aside, the problem used to be framed as a “bank robbery” problem with the calculation of duffle bag size required. But after “The Dark Knight” came out, the district forced the teacher to change the context. So now it focuses on state-sponsored gambling.

  29. OT comment/question: I had a math teacher in HS who taught us a pencil and paper algorithm for computing square roots. He called it “the Irish Method,” because you get it by Doublin’ –the algorithm involved doubling the remainder of a long division, or something like that.

    Is anyone familiar/recall such a method?

  30. I can tell you how I do it.

    X2= X1 – (X1^2 – A )/(2*X1)

    Suppose you want to get the square root of 12. Find a perfect square that is reasonably close. lets take 16. 16 = 4 * 4

    X2 = 4 – (16-12)/(2*4) = 3.5

    repeat

    X3 = 3.5 – 0.25/7 = 3.4643 which is close enough to 3.4641

    If you are trying to do this in your head, X2^2 – A = (X1-X2)^2

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