For U.S. students, math is too hard to master

Perhaps we just acknowledge that math isn’t really our thing.

U.S. teenagers bombed on an international test for 15 years olds, with scores declining in math compared to 60 other countries.

Reading and writing results weren’t anything to write home about, either, assuming people could write.

On a scale of 0 to 1,000, U.S. students scored a 470 on the tests, the Associated Press reports, dropping the nation to 35th on the list of nations.

In other words, most students wouldn’t be able to figure out what percentile the nation is in now.

“The U.S. would be well served to take a hard look at the strategies used by the top-performing education systems and adapt lessons learned from them to fit the U.S. context and needs.” said Marc Tucker, president of the National Center on Education and the Economy.

“It has always been the most difficult subject for Americans,” said Andreas Schleicher, the Organization for Economic Cooperation and Development’s director for education and skills.

Students were allowed to use calculators to figure out the math problems, although the test was designed so that the need to use them was unlikely.

Like this one, for example:

math_1

The correct answer is it’s not a reasonable conclusion because the graphic focuses on a very small part of the graph. Another correct answer is “I don’t know” because one would need more data to determine if an increase is huge or not.

The testing agency also pointed out that “no, it’s not correct because reporters always exaggerate” is not a correct answer. That clarification was for you, America.

This one was particularly geared toward a good guess if nothing else.

math_2

The answer is 10 o’ clock for the first question. For the second, the correct answer is:

Sydney: 4:30 PM – 6:00 PM; Berlin: 7:30 AM – 9:00 AM
OR
Sydney: 7:00 AM – 8:00 AM; Berlin: 10:00 PM – 11:00 PM

Some of the questions require real math chops.

math_3

The answer is 144 and 6.

Here’s the whole sample test.

In the past, by the way, its been easy to see how Minnesota students fared against the international competition. But in the latest test, Massachusetts and North Carolina were the only states to participate as their own entities.

“We’re losing ground – a troubling prospect when, in today’s knowledge-based economy, the best jobs can go anywhere in the world. Students in Massachusetts, Maryland, and Minnesota aren’t just vying for great jobs along with their neighbors or across state lines, they must be competitive with peers in Finland, Germany, and Japan,” U.S. Education Secretary John King said.

Related: What do international tests really show about U.S. student performance? (Economic Policy Institute)

PISA Day 2016

  • MrE85

    I would crack wise about kids today, but my math skills have always been terrible.

  • ec99

    I get a kick out of going to restaurants and watching 40-somethings pull a calculator out because they can’t figure out a tip in their head. But that is just consistent with when school became about fun and self-esteem, academic rigor and rote learning got tossed.

    • You might want to read the test organization’s assessment of high-functioning China’s education system, which specifically mentions minimizing rote learning.

      http://www.oecd.org/pisa/PISA-2015-china.pdf

      • ec99

        When it comes to math and science, you can’t get a way from rote. Times tables, periodic table, formulas. But that’s so boring. Where the Asians are criticized is not their learning of the basic material, but their inability to apply it creatively. Which is why the Chinese are so adept at pirating, but not inventing.

        • Alex

          You mention learning formulas as an example of rote learning. That’s true in some sense, but the school system I went through (a public system in the suburbs of Chicago) placed emphasis on not only learning the formulas, but learning how to rederive them. We weren’t allowed to use formulas until we could (with guidance) come up with them again (and, similarly, weren’t allowed to use a calculator for a function that we hadn’t demonstrated ability to do on paper).

          This could be as simple as everyone’s favorite Pythagorean theorem diagram (http://www.myastrologybook.com/PythagoreanTheorem16c.gif) or it could be as complex as working out geometric relationships through proofs that draw on previously-learned theorems (and then the relationship we just demonstrated would get added to our vocabulary of theorems which we could then use on future assignments). Same with trigonometric identities; we’d start with some simple ones, then work out more complex ones before we were told that they were actually held to be common mathematical truths.

          The other thing that we were taught was how to read a word problem. The roof problem up there is full of unnecessary information. The first question is really asking you, “What’s the area of a 12×12 square?” and the second just wants to see that you understand that TEF is an equilateral triangle half the size of TAB (of which it’s a section). This is really the essence of what’s important out in the world. Learning the formulas is part of it, but those formulas and theorems are useless if you can’t work out what the question is really asking.

          In short: rote learning is definitely a problem, but there’s an easy solution, and that’s to back up the rote learning of ‘what’ with an understanding of ‘why’ or ‘how.’

          • ec99

            My son teaches AP Biology. The tests are no longer geared simply for information, but to take that and apply it to a specific scenario.

          • Dan

            Oh really he’s not just teaching fun and self esteem

          • ec99

            It’s AP…he gets the best students who actually arrive having learned, not just crammed for tests and promptly forgot.

          • Dan

            Cramming for tests, like for rote learning? Anyway don’t worry, even though I’m 40 and *of course* our generation did learn the times tables and the periodic table, we also produced some malcontents to whine about millennials and carry on your legacy.

          • ec99

            Interesting how criticism is always reduced by some to whining. Cramming involved short term memory, not learning. Which is why someone coming into an 11th-grade history course is a blank slate, even though he had it in 8th.

          • Dan

            “Whining” was the self-censored version, as was “malcontent”.

          • Alex

            That’s good. What we need is for that same philosophy to extend below the AP/honors/accelerated level and become the standard method of learning and instruction in all levels of education. “Let me show you a thing working so you can see what happens, then I can tell you about how we model it, then let me show it to you in a variety of contexts so you can learn to recognize it in a mess of other information.”

          • ec99

            He does this with cell morphology. Students derive analogies with each part and its functions: football teams, families, cars,etc

    • Anna

      My mother taught me an easy way to figure out a proper tip.

      A 15% tip is a dollar for every seven in the bill. 20% which is more common nowadays is a dollar for every five in the bill.

      No calculator necessary.

      However, many upscale restaurants save you the trouble by automatically adding 15% to the bill. 🙁

      • jon

        shift the decimal one place and multiple by 2 to get 20%
        i.e. 15.60 becomes 1.56 then times two comes out to 3.12. Though I usually round to the nearest dollar…

      • Kassie

        20% is much easier to do by taking the most left number (or two if it is over $100) and doubling. So if the bill is $70, the tip is $14. If there is change, add another dollar to be safe, so $73, make the tip $15. Also, never tip below $5 unless you just order a drink.

        • crystals

          Ooh – I’ve never heard the last sentence before. Say more. (I’m thinking about alllllll the times I’ve gone to lunch and ordered a $8 sandwich. I should leave $5 instead of my typical $3 something? Do servers hate me?)

          • Kassie

            I don’t think it is a hard and fast rule, just something I stand by. If they bring you food, a drink, check on you, do the things they do, they deserve $5. Places, like Perkins or diners, where check don’t ever come to more than $20, those servers end up screwed. They work just as hard, maybe harder if they are refilling sodas or coffee, than servers in the nicer places and also deserve a living wage.

            But, if you are eating with say three others and you are splitting the check, as long as everyone tips 20% and the total tip comes to more than $5, that’s ok. But again, this is all my personal opinion.

          • ec99

            What happened to the days of tipping for the quality of service?

          • Kassie

            Yes. Start at 20%, if it is terrible, go down to 18%, great service gets 30%. $5 is the cost of sitting down to eat at a full service restaurant. If you don’t want to tip that, go to Chipotle.

          • crystals

            It’s helpful to hear! I always give at least $3 even if 20% would be $1.60, so I think we have the same general philosophy around minimums but you go with $5 and I have been going with $3. I’ll definitely think twice next time.

      • Dan

        I have an easier strategy, I just take the total amount and multiply by zero.

        Just kidding!

  • Anna

    When you start introducing calculators in kindergarten like one elementary school where I’ve taught, is it any wonder we are not competitive with the educational systems in countries across the pond?

    Some rote learning is necessary—grammar rules, math facts and scientific formulas but it doesn’t always have to be a dirge.

    Smart Boards and Promethean Boards are common in many classrooms across the country including colleges and universities and they allow teachers to make learning as fun as it is necessary.

    • Alex

      “Some rote learning is necessary—grammar rules, math facts and scientific formulas but it doesn’t always have to be a dirge.”

      It also needs to be backed up with understanding. It’s one thing for me to memorize a formula or theorem, but it’s another for me to be able to demonstrate how I can derive it from other formulas and theorems I already know.

      Calculators aren’t the problem. Calculators before learning to do something by hand or brain is the problem. That’s the difference between showing and teaching.

      • Anna

        I won’t disagree with you there. As a fourth grader, I had real difficulty with doing long division which is basically made easier by memorizing multiplication facts.

        I couldn’t do division well until I had learned my multiplication tables.

        “Calculators before learning to do something by hand or brain is the problem.”

        That reinforces my comment about calculators in kindergarten. How about doing some basic addition and subtraction by hand with them first!

  • Dan

    The pyramid one got me wondering, how many would answer a question “what is the area of a square with sides 12 feet long” vs. the one preceded with the diagram and all the extra information (and the metric system 😉

    • Alex

      That really is the core of what actually needs to be fixed in most American schools. We spend a lot of time on “memorize the formulas” but not enough on demonstrating how those formulas came to be and certainly not enough time on how to read the problem statement. The bit up there about the roof is two simple questions:

      1. What’s the area of a 12×12 square?
      2. Do you understand that because TEF is a portion of equilateral triangle TAB with two sides half the length of the sides of TAB, the third side of TEF is the same length as half the length of a side of TAB?

      • Dan

        Yeah I understand that’s the point, it just got me wondering what the delta in correct answers would be.

        • Alex

          Oh, yeah. Probably quite a bit.

  • RBHolb

    The reason for poor math skills could be more than just kids today and their calculators. We seem to have a cultural aversion to anyone being adept at math. After all, who are the risible nerds on any sitcom? Yes, the guys who are good at math! Is it any wonder no real American would want to learn how to calculate volume?

  • BReynolds33

    Anyone else ever wish they had an apathy metric to the test? Like a political poll is within a certain % +/-. So, in this case it would be, “US students scored 470 / 1000, with an apathy factor of 200.”

    While I am fully willing to admit children may actually be bad at math, it seems to me they are also tired of taking tests, and simply do not apply themselves on something that does not change their grade.

  • jon

    Took me a bit on 1.2. Equilateral triangles, overlooked that at first.
    But the question didn’t go the way I thought it would either… I kind of figured it was going to be about roofing and how many sq meters of singles he’d need (which is a trick, you need to overlap singles so an exact number would be wrong any how.)

    9.1 is a pretty standard occurrence nowadays.

    and I’ve had to deal with time zones most of my working life… usually a few hours difference, but tonight I’m going to be working at 7-8pm in order to talk to some folks in Asia… (as an early bird I much prefer working with Europe.)

    • Someday we’ll all operate on Zulu time. (UTC)

      • jon

        That be great for documenting when and event is happening… but unless everyone is going to be awake at the same time it won’t help me much.

      • Will

        Not on Mars…

  • Leroy

    We’re number 1!

    • jon

      Number 1?
      Is that good?

      • Leroy

        My poor attempt at humor. (Numbers are hard)

  • Kassie

    I guess I have a number of thoughts on this. First, what were kids told about the test before they took it? Were they told they needed to do well to graduate or pass a grade, or were they told it was to see how they ranked against students across the world and results meant nothing? Because if I was told it was only for pride, I wouldn’t put much time or effort into ti.

    Second, I was very good at math. I have a full year of college level math and a full year of graduate level statistics. And you know what, I don’t use any advanced math in my life. I don’t use anything past what I need for cooking, home improvement, and maybe some very simple algebra for my job. Almost no adult I know does. Why do we put such high value on something that isn’t needed by most?

    • Leroy

      I work in an office full of programmers. While we may not be solving complex formulas, we do use the critical thinking and problem solving skills that were developed in Math classes.

      • Kassie

        I think we should teach critical thinking and problem solving and those things can be taught without learning how to do advanced math. I took calculus in high school because I thought I had to. I though I’d not get into college or get a good job if I didn’t take advanced math. But that’s crap. It really isn’t needed for most people, and those that do choose to become engineers or programmers or physics professors or radiologists or whatever can pick those skills up in college.

        • Will

          The issue arises if you want to understand everything around you then you will need a basic understanding of high level math (i.e. calculus). Cruise control, self-driving cars, aircraft, most programming, using your cellphone, any electronics all use some form of calculus.

        • RBHolb

          I took a great deal of math in college (four years). I don’t use much beyond simple arithmetic (what happens as I approach the speed of light is something that seldom comes up), but math did teach me problem solving in an orderly, reasoned fashion. It also helped sharpen my mind to think critically. Teaching only the things we can demonstrate using on an everyday basis shortchanges us in so many ways.

          • Will

            Well if you use GPS the theory of relativity is something that comes up quite often.

          • But you wouldn’t need to know the theory of relativity to use a GPS.

          • Will

            No, because smart people who understand it did the math for you…sure you can play the game that someone else can do this stuff for you because you don’t want to take the time to learn it but that kind of attitude is why people like Bernie Madoff got away with his fraud for so long. Very few took the time to understand what was going on, and that was with THEIR own money!

          • Really, that’s why Bernie Madoff got away with it?

            Huh. I ‘ve never created fire by rubbing two sticks together but I probably should before I turn the stove on tonight. Wouldn’t want someone to lose their life savings.

            I’m not arguing against the value of teaching physics and the theory of relativity. But if the best reason you can come up with when kids ask “why do I need to know this stuff” is “because you own a GPS” or “because Bernie Madoff might steal your money”, I think you need to go back to the drawing board.

            The GPS is a great EXAMPLE of the theory of relativity. But it’s not the reason to know it.

            BTW, i’ll bet you $100 some of the people who lost their fortunes to Madoff understood the theory of relativity.

          • Personally, I’m a fan of just asking people if they want to go back in time. And when they say “yeah”, I got em.

          • Will

            Sure but you understand the concept of fire and how it works…you should understand the basics so can determine when something does or doesn’t make sense… which is why we learn math from the ground up.

          • I hate to admit it publicly, but I can’t tell you what the flash point is of a stick. So I use a match.

            Do I think people should learn math. Sure. I also think they shouldn’t split infinitives and end their sentences with prepositions or have subjects and verbs that disagree.

          • Rob

            Madoff got away with it for so long because of investors that engaged in magical thinking.

        • Jerry

          To have a reasonable chance of success in the sciences, most students need to enter college taking some flavor of calculus. At least that group of individuals should definitely be taking the math that has become standard in most good high schools.

    • jon

      I don’t think people often realize that advanced math can solve problems much faster and easier than not using it.

      I’ve drawn out karnaugh map at work to solve issues co-workers spent days working on and had a solution in minutes, they didn’t even realize they had a math problem… they also would have gotten to a solution eventually, but math was so much faster and so much more reliable than their guess work.

      This has played out over and over again for me… I think people are dismissive of math because people are dismissive of math, it’s just a recurring cycle…

      • BJ

        >karnaugh map

        Never heard of such a thing…. Google here I come

        • jon

          You are in for a treat… they are great, If you’ve got a basic understanding of the application of boolean algebra (if/then, and, or, etc.)

          In my example I used them to simplify process workflows (think flow chart).
          Though I learned about them for simplifying logic circuits… same principle.

  • Will

    These were very basic math and critical thinking skills, subjective terms like “huge” should be a major red flag in a math class… students should be taught to understand that. The others are basic conversion and spacial relationships, which should be easy enough to teach or learn with repetition. Why can’t every student be expected to understand these basic concepts?

  • Jerry

    Food for thought: as far as mathematics *research* is concerned, the United States is one of a few global centers. Our universities seem to do an excellent job of preparing scientists, too. Yet our high schools, on the whole, are crap. Why the disparity?

    • Will

      The college level is much more rigorous, I think half the engineering majors dropped out or transferred at the U of M before graduation.

    • 42% of grad students at M.I.T. are from somewhere else.

      • Jerry

        Yes, and they all came to the United States to attend one of the world’s best schools for mathematics. Interesting, no?

      • Will

        That’s called a brain drain, the rest of the world is missing out because the smartest people in the world want to learn in the USA and many stay and contribute to America. That’s a great thing.

    • jon

      I don’t think it’s fair to say that high schools are crap on the whole.

      They are on average, average.

      I’ve seen more than one round of testing that breaks US states out separately from each other and places like MA and MN and CT are consistently at the top of the list with Japan, Singapore and South Korea.

      There are some very low performing schools in the US also, the deep south usually holds that title in AL and MS.

      On whole our schools are average. Individually our schools range from excellent to terrible.

      But then it’s just a matter of numbers…
      Some 60-70% of students who graduate high school attend college, these are usually the higher performing students… the 6 year graduation rate from college is only ~60%
      From those number we can roughly say ~1/3rd of high school graduates go on to graduate college.

      Asking why our college graduates are so amazing, and our high school students aren’t when we filter out more then 2/3rds of them (more when you consider highschool drop out rate) it shouldn’t be a surprise that the top 30-40% of students perform better than the bottom 60-70%.

      That’s why the disparity, it’s a big filter to weed out the bottom half of the percentile… and give a piece of paper (and a big bill) to the top half.

    • Daniel Phu

      High school algebra is fragmented. Students can not bridge between math subjects by themselves. As a result, few students can solve random algebraic equations. Thus, schools try to teach critical thinking can go too far without basic skills.

  • Hugh Shakeshaft

    Was there an achievement gap?