Is it true that we suck at math?

“If everyone knows a thing it’s almost for sure it aint so.”

“It’s not so much the things you don’t know that hurt you as the things you know for sure that aint so.”

I don’t take anyone’s word for anything. Take those quotes, for example, which I’ve both heard attributed to Mark Twain, Will Rogers and several others, ironically by people who were just certain they were correct.

One thing everyone knows is that Americans suck in math. We are so far behind Asia, we are continually told, that we are soon all going to be learning how to say, “Would you like fries with that?” in Chinese.

There was an article in the Los Angeles Times today that profiled a mother who had an Excel spreadsheet with a schedule for her child from 8:00 a.m. to 11 p.m. seven days a week. She said she started in kindergarten, because life is hard and students need to learn to deal with it. Her son, as a tenth grader, scored a perfect 800 on the SAT. Rather than convincing me further that we suck at math, it made me question the goal of propelling a child  to perfect scores.

One thing writing a dissertation on intelligence testing taught me is that test scores are very, very far from absolute and objective. Two critical points to keep in mind:

1. Some group of people decide what is tested, inevitably the group of people that has the most power. If we insisted that being fluent in more than one language is a factor in achievement scores, Hispanic children would be getting admitted to elite institutions in droves. Before you discard this as a silly notion, think about the arguments made for including high math scores – these are relevant to courses students take, to careers. An argument could be made for functioning in a global market place, for the ability to read texts in the original Spanish (or whatever second language a student reads).   I could write a whole dissertation on this – oh wait, I did ! – the point is we make decisions about what goes into the tests and those decisions favor some people and not others.

2. The scores we use to evaluate both at an individual and larger (school, country) level are almost never how many questions were answered correctly, which you might logically think is your test score. There you go with the logic again. Cut it out. In fact, scores depart several steps from the number of correct answers. First, there is the issue of partial credit, yes or no and if yes, for what. Second, there is the step of standardizing scores. Usually this means setting the average at some arbitrary value, say 100.  If the average student gets 17 questions right, then that is set as a score of 100.  The standard deviation, the average amount by which people differ from the average, is also set at an arbitrary value, say 10.  (If you’re not familiar with these ideas, think of your family. We’re kind of short in my family, and if you went to a family re-union you’d probably find that the average woman is around 5’3″ give or take two inches. So, you can think of five feet three inches as being the average and two inches as being the standard deviation. If you are reading this and from a country on the metric system, 5’3″ is equal to a furlong plus a bushel, a peck and a hug around the neck.) To return to my long-forgotten point – if 84% of the people score 22 points or lower, than answering 22 questions correctly is given a score of 110. (The mean of 100 +  one standard deviation of 10).  The scores you see reported aren’t that closely related to the number of questions answered correctly and they tell you almost NOTHING about what precisely people do or do not know.

I think most statisticians know this. I am certain that nearly everyone who does analyses of educational tests knows this. But I am equally certain that the average person reading the newspaper does not. This is important because it has to do with our sucking or not.

My assumption, based on what I read in the papers and hear on TV is that American kids just don’t know basic math. So, I downloaded the TIMSS (Trends in International Mathematics and Science Study ) data and I also downloaded the items that had been released, to see what it is that American kids do and do not know. Here are a few examples:

Students were shown a  rectangle divided into twelve squares. Five of those twelve squares were shaded. Then, they were given five choices of circles that were partly shaded and asked:

“Which circle has approximately the same area shaded as the rectangle above?”

To solve this problem you need to figure that the rectangle has 5/12 shaded and understand that 5/12 is a little less than one-half. (The figures show a circle that is 7/8 shaded, 3/4, exactly one-half, a little more than one-half and a little less than one-half.)

This question was answered correctly by 80.2% of American eighth-graders.

The next question asked :

A gardener mixes 4.45 kilograms of rye grass with 2.735 kilograms of clover seed to make a mix for sowing a lawn area. How many kilograms of the lawn mix does he now have?

This question was answered correctly by 71.9% of American eighth-graders.

I must admit that I was surprised the figure was that low, although not extremely surprised, since I know many, many adults and some young kids who never do math like this. Every phone, every computer has a calculator on it and they just think this is a useless skill, like cursive. I happen to disagree and the world’s most spoiled thirteen-year-old is not allowed to use a calculator to do or check her math homework.

Another question dealt with inequalities:

X/3 > 8 is equivalent to….

To get this answer correct, you need to understand the idea of inequality and how to solve an equation with one unknown. Essentially, you need to reason something like 24/3 = 8 so X > 24 . This, of course, presupposes you also know that 24/3 = 8.

This question was answered correctly by 42.8% of American eighth-graders.

A question that was answered by even fewer was:

What is the perimeter of a square whose area is 100 meters?

To answer this you need to know:

  • The formula for finding the area of a square
  • The concept of a square root
  • That the square root of 100 is 10
  • The area for finding the perimeter of a square (or rectangle, either would work).

This question was answered correctly by 26.5% of American eighth-graders.

One last question,

A bowl contains 36 colored beads all of the same size, some blue, some green, some red and the rest yellow. A bead is drawn from the bowl without looking. The probability that it is blue is 4/9. How many blue beads are in the bowl?

This question was answered correctly by 49.4% of American eighth-graders.

Are these percentages bad or good? Honestly, I thought the questions were pretty easy and I was surprised by the low percentages on some of them – but I do math for a living and I was in 8th grade almost forty years ago. So, I have known this stuff a very, very long time. I THINK some of the questions were actually what was taught in ninth or tenth grade when I was riding a brontosaurus to school, so the fact that eighth graders today don’t know this information doesn’t convince me we’re all a bunch of drooling idiots.

Here is a blasphemous question for you –  Does it matter if you know the answers in eighth grade? I’m serious. Is it worth having your child study from 8 a.m. to 11 p.m. so that he or she knows all of this in the eighth grade instead of the ninth grade?

A few weeks ago, I was looking for data for a proposal I was writing and came across a state Department of Education website that had a note on its pages on test scores that said proficiency meant something different according to the federal government definition and that many people could function perfectly fine will being scored below proficient in math.

At the time I dismissed this as an excuse for poor performance. Today, when I looked at the questions and the results, I was not so sure. My two older daughters are a journalist and a history teacher. Both have degrees from good institutions (NYU and USC).  I believe neither of them could answer the question about finding the perimeter of a square with an area of 100. Perhaps they could have answered it when they took their SATs or while they were taking the one mathematics course they took as undergraduates. I’m not sure. I’m fairly certain if they ever knew this information, they’ve totally forgotten it. The truth is, as much as I hate to admit it, that neither of them at any point in their lives will feel the lack of this knowledge.

On the other hand, my daughter who knocks people down for a living (she competes professionally in mixed martial arts) could almost certainly answer these questions off the top of her head, just because she likes math and has always been good at it.

What percentage of Americans (eighth-graders or not) SHOULD be able to answer these questions?

I have no idea what the answer to that is.

Some people would say 100%,  because they need to know this information to do well on the tests to get into a good college.  I’m not sure that is true. More and more, people are asking WHY you need to do well on the tests. If I want to be a sportswriter or a history teacher or a doctor, what good does it do me to be able to calculate the perimeter of a square given the area?

I think the mother in San Marino may be part of an education bubble that will burst just like the housing bubble has. I am far from the only person to be suggesting this. Not only has the cost of higher education reached astronomical levels where it exceeds the cost of a home in most parts of the country, but it also, for selective institutions, is costing more of your life. Not only are fewer people going to be able to pay it, but, perhaps like the housing bubble, more people are going to say, “This isn’t worth it.”

I did not work from 8 a.m. to 11 p.m. I spent several hours today reviewing grants. Then I went running down to the beach, because it was a beautiful day. I had a Corona while reading the LA Times. I analyzed the TIMSS data and I watched The Daily Show. I also checked my daughter’s math homework and pointed out the one answer she had incorrect. She figured it out and fixed it on her own.

Life is not hard. Life is good.

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  1. “Some group of people decide what is tested, inevitably the group of people that…”

    .. will score highest.

    Then some government agency will mandate that the test be given to all students and that X% shall pass. So school departments will adjust curricula to teach what’s on the test, and teachers will be rated on how their students perform on the standardized test. And more kids will answer questions like these correctly, and still not know how to think.

  2. What would be interesting would be to give this test to a large selection of people in the workforce. Then you could figure out which questions were “important” to know for each profession (or knowledge in general).

    I remember a publicity stunt a few years ago where some Fortune-500 execs took the CA middle-school exam. Most failed miserably. I wonder if the data is out there anywhere.

  3. “came across a state Department of Education website that had a note on its pages on test scores that said proficiency meant something different according to the federal government definition and that many people could function perfectly fine will being scored below proficient in math.”

    This is true. The definition of proficient in common english usage is very different from the one set out in NCLB, which requires mastery of “challenging” subject matter. The definition of Proficient for NAEP was set using approximately the 75th percentile. Take a look at the two items referenced in the last paragraph of this post: http://blogs.edweek.org/edweek/NCLB-ActII/2008/01/nclb_and_the_meaning_of_profic_1.html

    The more important is this. I work with statistics all day long, as do you. I teach statistics in a community college in the evening. I now have a PhD. In my day job recently I was looking at mathematics placement testing for our students, and took a practice algebra placement test. (Not a college algebra test; a placement test to determine whether you get to start college algebra.) I took it cold, no prep, and got a 52. I would have been placed in remedial mathematics. Why? I don’t know when the last time I factored a polynomial was, and frankly had forgotten how. So I got those questions wrong.

    We are judging “suck at math” against a standard that is only necessary for certain fields – engineering, computer science (not information technology; hard-core programming) and other fields may require regular use of some of these techniques, but most jobs don’t.

    I agree that the above questions are pretty easy, and that by the end of high school most students should be able to do those things. But I don’t know that they need to master them all in 8th grade, nor do I believe that most students need to go much beyond that point. I would rather most people know those things WELL than try to go on to something the will never again use.

  4. I actually think I would do extremely well on an algebra placement test, but a good part of that has to do with having a daughter in 7th grade who is doing algebra and geometry. As I help her with her homework, I’ve had a refresher.

    Of course, some parts of mathematics I use daily and others I haven’t thought about in years. When was the last time I needed to be able to define an ‘arc’ versus a ‘ray’.

  5. To be completely frank, our kids in Hong Kong where I’m from do math at that level in grade 4.

  6. And Leo, what good does that do them? I mean that very seriously because we have people who are re-arranging their lives and their children’s lives to do well on these tests. So assuming (and I am skeptical) that the average child in Hongkong is doing as well in 4th grade as the average 8th grader in the U.S, what benefit can you point to either to those individuals or the society as a whole? Why do you think (and I am asking because I really want to know) given you have an entire nation of math prodigies that Hongkong isn’t in some way much better off than other countries? I’ve been to Hongkong. It’s fine. But so is the U.S. So are a lot of places.

  7. These problems are quite easy and as an 8th grader, I know that the people worst at math in our school can solve these problems. In fact, We were being taught this in 3rd or 4th grade

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