we are in…like…so much in trouble… episode two.


In my grouchier moments (one of which I am having right now), I am considering a public relations campaign to make fun of people who can't do simple math and shame them into either acquiring some fundamental skills or staying quiet and not bothering the rest of us with their ignorance.

I've devoted a significant part of my career to education: working with K-12 teachers, teaching at a university, developing programs for the public.  I'm beginning to wonder whether we are not all just wasting our time and we would do much better to focus on developing an elite cadre of high-powered science literate researchers who will discover wondrous things and save us all from ourselves.  Of course, that won't work because the people who know the science will be prevented from fulfilling this task by the science-ignorant who comprise the public, as well as the executive and legislative branches of the government.

I'm tired of hearing from people how hard math is.  Do you ever hear people saying things like "oh, yeah, reading.  I was just never good at that."  Admitting that you are illiterate is harder than admitting that you are an alcoholic or a drug addict at this point.  But admitting that you can't do math – well pfftt, I could never do math either, so that's just OK.

The truth is that most people don't want to be bothered, just like most people would rather state their opinion about things without wasting time looking up the facts.   The NASCAR race I'm watching features the AT&T ‘Fastest Pit Crew of the Year Award’.  Fans VOTE for the fastest pit crew.  The last I looked, time is not subject to human opinion.  Sure AT&T donates $20,000 at the end of the program to a deserving charity.  But how silly do you have to be to think that 'fastest' has anything to do with your opinion?  How about sponsoring something mathematically meaningful, like showing us a histogram of all the pit stop times, showing who was exceptionally fast or slow.

ADDITION:  Anonymous Coward noted in the comments below that there could be different definitions of fastest.  I should have given more information.  The contest is per race and the voters are given no information about either what 'fastest' means or numerical information as to the pit times.  I'd have no problem if they just switched it to "most valuable" because — as you point out — people can make their own interpretation of what is most valuable.  Perhaps it is because I am a physicist:  In my mind, "fastest" is a pretty precise term. Thanks for the comment!

A Dallas Morning News article on September 15th about dove hunting contained the following in an article by one Ray Sasser.

Remember your old geometry lesson about the long side of a triangle being equal to the two shorter sides. That means a dove 40 yards out and 10 yards high is 50 yards from the gun and clearly out of range.  — Dallas Morning News

Umm… No.  Even if you don't remember the formula, just draw the picture.  Or, GoCPP_DoveHuntingd forbid, use some common sense.  The shortest distance between two points is a straight line, right?  If you had to walk 40 feet East and 10 feet North, but you had the option to walk directly th ere, wouldn't you just intuitively know that it was shorter to take the direct route?  (Yeah, those ought to be 'yds' not 'ft' in the drawing, but I am in the middle of moving and trying to do this in a big ol' hurry.)

Apparently not if you work at the Dallas Morning News.  The point of the DMN article was that people shouldn't try to kill things that are out of their accurate shooting range.  Shooting something incompletely is worse than shooting it dead, as the injured animal generally dies an agonizing death a few hours or days later. 

I realize this is the state that thinks that history textbooks have a pro-Islamic slant, and that  creationism should be taught in science class; however, I am confident that there is nothing in the Bible that casts doubt on the validity of the Pythagorean theorem.  That's it on the right, where d is the distance to the shooting target.  The distance to the target is 41.2 yards, not 50 yarCPP_Pythagorasds. (Thanks to Brian for pointing out my error in units.)


I don't think I'm being too demanding.  This is pretty simple math.  Squares and square roots are not beyond the ken of ANYONE who wants to understand them. 

And that, unfortunately, seems to be the crux of the problem.  I know plenty of people who can calculate how much the 40% off sweater on sale at Neiman Marcus will cost, but claim that things like mortgages or interest on their bank account are just too hard to understand.  If you don't understand percentages (and compounding), perhaps you shouldn't be allowed to take out a mortgage.  (I know, not feasible because it would lead to another financial crisis.)

Maybe we need to start applying intense social pressure to science and math illiterates. What we really need is branding.  Let's recruit personalities from the fields of music, acting and sports who are willing to stand up for math and science.  Great advertising opportunity:  "If Paris Hilton can understand it, certainly YOU can."

Or maybe I've just been watching too much television lately.

34 thoughts on “we are in…like…so much in trouble… episode two.”

  1. Diandra,
    I am a native Texan who is graduating with a BSc in Mathematics at the end of this year from the University of Houston. I agree that the Texas Board of Education appears to be filled with people that want to rewrite history and teach creationism alongside evolution (or perhaps instead of) and I find it appalling. If I had my way they would have already been replaced with a board that supports proper science and accurate history. I also agree that innumeracy is a real problem in this country, in this state, and even in my school. I hope that this will no longer be an issue by the time I have children, and I will work towards that goal in whatever ways are available to me.
    However, I am also licensed by the state of Texas to carry a concealed handgun, which I do solely for the purpose of self defense. I would never willingly shoot or harm anyone or anything that was not threatening me or a loved one with deadly force. As such, I take offense to the statement that “people in Texas will shoot just about anything that won’t shoot back.” Your point could have easily been made without that little snipe. In the future, please don’t lump all Texas gun owners together as crazy people that have a burning desire to kill things. When you do that, you end up looking just as bad as the other side.

  2. I followed your link to Ray Sasser’s article in the Dallas Morning News – I think as disappointing as his error in describing the Pythagorean Theorem is, it’s equally disappointing to see that there was only a single comment correcting his mistake (the second and only other commenter didn’t seem too concerned about the mistake).
    I guess that 1) the other readers didn’t catch the error, 2) they didn’t care to clear up the mistake, or 3) there weren’t actually that many readers at all.

  3. diandra@trivalent-productions.com

    You’re right, Brian – I shouldn’t have painted everyone with the same brush and I didn’t even think that someone would interpret my comment to include people as targets. Texans do disproportionately shoot doves. Last year, Texas had about 235,000 mourning dove hunters. California is second with about 70,000. Shooting the universal symbol of peace is ironic in a very discomfiting way.

  4. I certainly can’t argue with your statistics. I, too, dislike the idea that so many of my fellow Texans hunt “game” animals, and I agree with the irony of shooting the symbol of peace. However, not all Texans are like that! For example, my wife and I helped a pair of mourning doves out as best we could when they decided to make a nest on our front porch! http://www.facebook.com/album.php?aid=417728&id=562895401 (Please forgive me if the link doesn’t work!)

  5. “Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house.” — Robert A. Heinlein, Time Enough for Love :-)>

  6. Regarding this subject, I am always reminded of this David Mumford quote:
    “I am accustomed, as a professional mathematician, to living in a sort of vacuum, surrounded by people who declare with an odd sort of pride that they are mathematically illiterate.”
    This sums up my feelings exactly. It truly is a very “odd sort of pride.”
    And you are absolutely right. We have an urgent need to make mathematics “cool” to the public, and we need all the help we can. Science in general is needing it too, you know. While these are deep issues in the field of education, I do believe a big deal of PR is essential here in order to start making any progress. And I think the little things are a great place to start, as they can have a big impact. Make the scientist and the mathematician the heroes in movies and TV series. Make the smart gun kiss the girl. The Science and Entertainment Exchange is in a great place to do this, but it needs to be more active on nudging these projects in the right direction.

  7. >An Dallas Morning News article on September 15th about dove hunting (yes, SOME people in Texas will shoot just about anything that won’t shoot back – see comment #1 below)
    You know, it’d be nice to read reasonable criticism of mathematics without unwarranted sniping at gun owners.

  8. diandra@trivalent-productions.com

    Eric, I removed your comment because I already distracted people from the main point. Let’s not go any further in that direction.

  9. Right on about people who are comfortable in their mathematical illiteracy. I try to call that out whenever I hear it.
    I’m studying to be a researcher in mathematics education; we’re applying science not only to how people learn mathematics, but what their relationship is with mathematics, including attitudes toward mathematical literacy. I agree with a lot of what you say here, but we do need better mathematics education. A motivated individual is a powerful part of that equation.
    I hope your frustration passes soon. I’ll try to do my part for science and math. Cheers.

  10. most often the rot sets in very early, as open mind, curiosity and idiosyncrasy is killed by school as i know it. so some work might be aimed at the way early school is organized ?
    many kids are set back by their home situation. i have good experience with family groups within a primary prevention setup. there was no selection of members by me. mother, father and kid(s) were all included. the groups had to meet outside of work hours.
    there was a marked decrease in mistreatment at home, and better function over some time. the unfortunate learnt from the fortunate, and the fortunate learnt respect for the background of others.

  11. The equation was in yards, not feet. Whether you did the math right or not, you still got the answer wrong. 😉

  12. Hello,
    I’ll suggest that you, and anyone else who hasn’t yet, read “What’s Math Got To Do With It?” by Jo Boaler. Boaler not only describes the problem but has suggestions and recommendations about how to work to solve it.

  13. Well-written. I think that part of the problem lies with the approach to numeracy. Maths ability requires skills, which take practice. Unfortunately curricula are often written with mind-numbingly boring amounts of repetition. I did not finish high school and am mostly self-educated, and people find it hard to believe that I never “did well” in mathematics. Why? Oh, maybe because I make my living as a software engineer who specializes in mathematically challenging applications. Why didn’t I do well? I just didn’t have the patience to work through all the exercises. I don’t always think things through sequentially and sometimes take a different path to the problem, then check my results using conventional methods.
    So I agree with you wholeheartedly, but I think the solution requires more of a creative approach in teaching. My wife went to school in India and got ranked based on scores, and the whole pressure was to score well. When people get that kind of pressure they learn to pass tests, but the maths skills often don’t stick in the real world. But given questions like this classic train and bird problem: http://mathforum.org/dr.math/faq/faq.fly.trains.html I take the engineering approach.
    Some people have the potential for numeracy, but the assumption that all minds must work alike leaves many of us by the wayside.

  14. I like your example from the Dallas Morning News as a good example of innumeracy. (Although if – to hit the dove – the bullet did have to take a 90-degree turn after traveling 40 yards, I’d certainly agree that the shot is “out of range”).
    But I’m not so sure about the example:
    > But how silly do you have to be to think that ‘fastest’ has anything to do with your opinion?
    For something like a pit crew, I do think ‘fastest’ may be a matter of opinion. Different people could reasonably define ‘fastest’ in a variety of meaningful ways: lowest average time over a season, lowest time for the best single change over a season, lowest time for the worst single change, etc. In addition, due to different drivers, cars, and technology employed by different teams, one could imagine a definition by which the “fastest crew” wasn’t reflected in times at all.
    We should combat innumeracy wherever it appears, but I think it’s a mistake to try to force everything (especially entertainment, which is the example you’ve picked here) to numbers.

  15. Like Diandra I think the voting for the fastest pit crew is stupid. Looking at the “top” pit crews in the voting, it seems mostly another favorite driver award.

  16. Note that by getting yards vs. feet wrong, you are off by a factor of 3, while getting the Pythagorean Theorem wrong only made the author wrong by a factor of 5/4.

  17. I don’t think people are lazy, I think people are intimidated. Most people are given the idea that math is difficult and once they are done with their requirements for it in school they are happy to move on. I don’t think it’s so much them disliking math or disliking “intellectualism” just that people don’t have confidence. Everyone can read history or non-fiction, but there had been such a fence around Science and Mathematics that people are afraid to go there. Math is in many ways like advanced reading/comprehension, something most Americans aren’t good at either. It’d be nice if we could expose them to science through some soft and non-intimidating math. But then a lot of what I see on the sciencey blogs I read is pretty far up there. I don’t talk about anything I consider enormously complex on my blog and my mom made a comment it was “far above” her. And there’s no way! So honestly I think it just comes down to confidence. I at one time in my life thought I wasn’t “good at math” either. But now I know it’s like anything. It just takes some effort, some perseverence, and a drive to get through it. I try to encourage everyone I know that math is not in itself difficult just something that takes some effort like being good at photography or drawing or any other skillset.

  18. Things are much the same over this side of the pond…in England there is a strange pride and a feeling of superiority in NOT being able to do things…”Oh, I don’t know anything about THAT!” they say, in a manner that shows such things are beneath them. They are also the people with the money and the status…thus the engineers,scientists, mathematicians and technologists are perpetually beneath the bankers, accountants and stockbrokers. It is interesting that when one looks at the people travelling first or club class on the airlines, they tend to be the “money men” whereas the engineers etc. are back in “cattle class”.
    As for educational standards..I had to interview young lads for apprenticeships in a motor vehicle workshop; they weren’t going to be brilliant, but needed basic abilities. Some of our sample questions and answers: “What is 10% of 100?” “Oh…we did do percentages but I never quite understood it…can I use a pencil and paper?” or “How many tenths are there in an inch?” “I don’t know…we only did the metric system.”

  19. I hate to say it, but it is true – I’m not great at math. I grew up at the end of the “girls don’t need math” era, and as I didn’t show any natural talent for math, there was no real effort to help me learn it. Not so for my daughter, who I expect to learn not only the basics, but advanced math as well. She can and she will.
    I love Danica McKellar for her insistance that “Math Doesn’t Suck.” I have purchased her books for my daughter, my friend’s daughter, and our local school district.

  20. Eight years ago I was arranging the purchase of an espresso machine from an espresso machine manufacturer in France. The company didn’t do business in the USA, but would sell me the machine, sending it air freight to my location. The company required payment wired in euros to their bank. At that time, the dollar was worth slightly more than the euro.
    My bank would accomplish the currency transfer. Living in the USA, I of course, would pay the bank in dollars (USD).
    The local banking representative arrived at the initial currency conversion (less bank fees) using her computer and informed me of the dollar amount. I then immediately informed her this was incorrect because her calculation had the USD > Euros.
    I started with the basics. How many euros is a USD? Okay, then if 1 USD = 1.16 euros, how did the my dollar amount become larger than the euro amount for multiple USD. She answered, that’s what the computer said.
    I attempted to show her the math on a piece of paper, creating a proportion and solving for ‘x’. The fractions and cross-multiplying resulted in a look of panic and she again made reference to her computer.
    Next attempt was to create a little matrix. We will call one column dollars and another euros. We created the following.
    1.00 USD = 1.16 Euro
    10.00 USD = 11.60 Euro
    100.00 USD = 116.00 Euro
    1,000.00 USD = 1,160.00 Euro
    10,000.00 USD = 11,600.00 Euro
    We agreed the above amounts true. She even calculated the last three rows. Then I pointed out all the dollar amounts were always less than the euros amounts. Then I asked how her calculated dollar amount was greater than the euro amount. – “You’re confusing me. I need to get my supervisor.”
    And so it it went again with her supervisor and then the bank manager. Amazing. I somewhat reluctently told them to transfer the money using their calculations and asked for a contact within this commercial banking organization whom I could discuss the transaction.
    The following day, I called the banking main office in another state. The first person spoken to again worked the transaction incorrectly. “How can you say our computers are wrong? We’re a major financial institution.” I replied that I had great faith in their computers, trying to be polite. However, apparently the input method was most likely incorrect. It’s 7th grade elementary algebra, I said, and we really don’t require a computer. We again created the two column example and again they couldn’t explain the irregularity and I was confusing them. I was tranfered up the food chain to their VP of currency exchanges.
    Same conversation again, with the same outcome – Unbeleivable! When I asked how the dollar amount in the dollar column was greater the euro amount in the euro column, she said, “Maybe they do math differently in France.” – I kid you not. She was serious. That comment was absurd. Algebra is not different by where one resides on the planet and we just happened to be doing it (okay, attempting to do it) in the USA.
    She then provided me with the telephone number of one of the bank’s currency traders who could better explain the math to me. Our parting comments where somewhat as follows.
    Me: Yes, remeber how we struggled with alegbra in school? It was horrible.
    VP: Oh yes. I hated it.
    Me: Remeber how our teachers said that one day we would find a practical use for algebra?
    VP: Yes, he always said that.
    Me: Well, today is that day! I have no idea how you reached the position you hold.
    When I called the currency trader and explained my tale of woe, he nearly laughed his head off and then corrected my account for the transaction.
    Yes, it was sort of funny. Then again, it was and is extremely sad.

  21. I sympathize with your observations and conclusions after 40 years of working in the aerospace industry and struggling with employees who couldn’t perform simple math or logical calculations. And I too thought that the best we could do was educate those that showed interest and aptitude in math and let them carry the rest of the world on their brainy shoulders. But, as one of the previous commenters notes, people will always be faced with tasks as simple as converting currency, so just having an elite mathematical intelligencia, while a highly desirable goal, is not enough, we need to get everybody up to some mathematical speed or other.
    To do this the student must be convinced that math is important; the parents must believe knowing math means success; the teachers must have a missionary zeal to tell the story of mathematics; and society has to recognize the fundamental usefulness of mathematics and give respect for those who teach and know math. This is a lot of things to set right in our society; maybe the recent realization that STEM education needs upgrading and support will help accomplish these goals.
    Recently I have encountered several blog sites that seem to offer pieces of the puzzle of how to meaningfully augment the presentation of mathematics such that the student gets a better foundation. At the moment I have no plan on how these resources may be used, but I would like to tell you about them and receive any other comments or critiques.
    First, a blog called “Fun With Numbers”
    presents many articles with clear and rational explanations motivating the need to know math.
    Second, WolframAlpha
    provides access to a computerized system for calculating almost anything.
    The third blog, “Gowers’s Weblog–Mathematics related discussions”
    is a professional review of modern mathematics, not suitable for the undergraduate student. But, the article “Is the Tricki dead?” from September 24, 2010, suggests the development and usefulness of a Wikipedia-like resource that could answer student “How do I do…” questions that lead to suggestions of appropriate mathematics. At the moment Dr. Gowers seems to be trying to figure out if this is a useful thing to have or not. I believe it is. I would recommend anyone involved in mathematics education visit Gowers web site and offer an opinion (besides, who would not want to have their opinion in the same comments section as Fields medalist Terry Tao?).
    Unfortunately I am at the end of my ideas other than to ask isn’t there some way we in the mathematics education community can make use of incredible online resources like these to somehow accelerate all students perception and knowledge of mathematics?

  22. The problem is much greater than just math. We tolerate an ignorance of all technical fields much more than we do the traditional liberal arts. I think this is because, on some level, many people consider the liberal arts kinder and more empathic than technical fields. This is foolish, of course, but I have seen it again and again. I blame movies and television. I mean, when was the last time you saw a movie about an evil linguist who attempts to take over the world?

  23. “Learning something, no matter how complex, isn’t hard when you have a reason to know it” Homer Hickman, Jr. (from the book Rocket Boys).
    We have to give these children a reason to want to learn it. Show them it is fun, exciting, and interesting. Most importantly, make them believe they are capable.
    I agree we are in so much trouble right now and it is our children who will suffer the most. But it is our fault and we need to fix it fast.

  24. Well this might have been an interesting blog but apparently the contributors are more interested in making bigoted comments about against the state of Texas than actually clarifying a math or science issue. Texas is a leading state with regard to engineers – from petroleum engineers to civil engineers to electrical engineers. Of course, there is a substantial number of scientists and engineers in Clear Lake that work with NASA. In addition, there is something called The Medical Center in Houston, that is a huge medical complex if you haven’t heard of it that has some of the most advanced medical research in the world. And of course Austin is filled with people that have advanced degrees in every field. So there is actually a huge complex of engineers, scientists, physicists, and medical doctors in Texas, as well as the academic system necessary to support it.
    As far as the article you quoted, I bet if you took the time to investigate it instead of making snarky comments, you would find it was most likely written by a liberal with a journalism degree, who finds logic and math to be too logocentric or even phalocentric (if he/she had the right liberal or feminist professors). In fact, I wouldn’t be surprised if the journalist wasn’t even from Dallas or Texas.
    Now I don’t know if you go around proofing the New York Times or the LA Times, but if you do I hope you don’t generalize from the idiocy of the journalistic class as evidenced in many newspapers to the cities that happen to endure them. To do so would be irrational and a misapplication of simple logic. And you wouldn’t want to be guilt of that would you?

  25. The wrath of Pythagoras

    Okay, hes dead, and even if he wasnt dead he probably wouldnt read Sportsday in the Dallas Morning News. But I cant imagine him being pleased with this: Remember your old geometry lesson about the long side of a triangle bei…

  26. Maybe it would help if, when a child in school gets a problem wrong, teachers didn’t just put a big X next to it and then move on to the next thing.
    How about just putting a question mark next to the bits that are wrong and handing it back to the student? That combined with a more collaborative learning environment might work wonders.
    Practice in figuring out how to get from incorrect to correct is at the core of maths.

  27. justanothermathteacher

    I made the comment to my Pre-Calculus students that there should be a requirement to understand rates before being able to get one’s driver’s license. This came after a couple of the students could not understand how someone who drives for 30 minutes at 60 mph will have traveled 30 miles. With this additional part of the licensing process we would either have a more “math literate” society or a much greener society with a lot of people having to walk.

  28. You might have mentioned the fact that a two year old who can toss a ball into a trash can has the capability to calculate extremely complex ballistics on the fly that would take you days to scratch out on a pad. Now there’s the irony… Get off your high-horse. There are plenty of people with talents you do not have and will never, ever possess, like walking and chewing gum simultaneously. And lay off Texans. There are idiots in every state of the union and in every country on the planet. You are smarter than this.

  29. I have a friend who is a writer. She was working on a history curriculum for fifth grade students and, because of the squirrely educational requirements these days, her history class needed to include a math lesson. So she wrote one, although she professes to be “hopeless at math.” Then she sent the math lesson to me and asked me to double-check her answers to be sure they were correct!
    This is an intelligent woman with a Masters degree! (I have a BA in English, btw.) She’s not a best-selling author, but she’s been published. Somehow she has avoided bankruptcy and IRS audits. But designing a few simple questions for fifth graders that used numbers seemed to flummox her! I was near despair. Thankfully she did get the right answers, else I might have given up hope.
    I’m inclined to agree with FrauTech’s comment: people have allowed themselves to be intimidated by mathematics, even simple arithmetic. Looking back, I am grateful that my Dad introduced me to baseball when I was nine years old, and taught me to calculate batting averages and even earned run averages soon after. By the time somebody told me that I was supposed to be afraid of math because I’m a girl, I’d gotten pretty good at it.

  30. Agreed that people allow themselves to be overly intimidated by math. But like your friend, I would have asked someone to double check too, especially if it was for a class. Strikes me more as being careful.

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