Five Test Questions for YOU

These test questions will help you understand why American students score lower in mathematics than their counterparts in most advanced nations.  I found these examples a few years ago while surfing the web.   The first sample problem was offered by the University of Wisconsin/Oshkosh to high school math teachers and was designed to help ‘Close the Math Achievement Gap.’

Jack shot a deer that weighed 321 pounds. Tom shot a deer that weighed 289 pounds.   How much more did Jack’s deer weigh than Tom’s deer?

Basic subtraction for high school students?   

My second example came from TeacherVision, part of Pearson, the giant testing company:

Linda is paddling upstream in a canoe. She can travel 2 miles upstream in 45 minutes. After this strenuous exercise she must rest for 15 minutes. While she is resting, the canoe floats downstream ½ mile. How long will it take Linda to travel 8 miles upstream in this manner?

This question’s premise is questionable.  Will some students be distracted by Linda’s cluelessness?  Won’t they ask themselves how long it will take her to figure out that she should grab hold of a branch while she’s resting in order to keep from floating back down the river?  What’s the not-so-subtle subtext? That girls don’t belong in canoes?  That girls are dumb?

I found my third sample question (I’m calling it “Snakes”) on a high school math test in Oregon:

There are 6 snakes in a certain valley.  The population doubles every year. In how many years will there be 96 snakes?

  1. 2
  2. 3
  3. 4
  4. 8

These three high school math problems require simple numeracy at most.  With enough practice, just about anyone can solve undemanding problems like that–and consequently feel confident of their ability.

School is supposed to be preparation for life, but spending time on problems like those three is like trying to become an excellent basketball player by shooting free throws all day long.  To be good at basketball, players must work on all aspects of the game: jump shots, dribbling, throwing chest and bounce passes, positioning for rebounds, running the pick-and-roll and—occasionally–practicing free throws.

Come to think of it, basketball and life are similar. Both are about rhythm and motion, teamwork and individual play, offense and defense.  Like life, it can slow down or become frenetic. Basketball requires thinking fast, shifting roles and having your teammates’ backs.  Successful players know when to shoot and when to pass. As in life, failure is part of the game.  Even the greatest players miss over half of their shots, and some (Michael Jordan!) are cut from their high school teams.  And life doesn’t give us many free throw opportunities.

But if school is supposed to be preparation for life, why are American high school students being asked to count on their fingers?  That mind-numbing and trivial work is the educational equivalent of shooting free throws.

My fourth example is a Common Core National Standards question for 8th graders in New York State. (Keep in mind that the Common Core is supposed to introduce much needed ‘rigor’ to the curriculum.)  

Triangle ABC was rotated 90° clockwise. Then it underwent a dilation centered at the origin with a scale factor of 4. Triangle A’B’C’ is the resulting image.  What parts of A’B’C’ are congruent to the corresponding parts of the original triangle?  Explain your reasoning.

This problem represents the brave new world of education’s Common Core, national standards adopted at one point by 45 states and the District of Columbia. This new approach exposes students to higher and more ‘rigorous’ standards. The hope is that the curriculum will challenge and engage students.   Reading that prose, are you feeling ‘engaged’?  Now imagine how 8th graders might feel.

If the first three problems are the educational equivalent of practicing free throws, then solving problems like this one is akin to spending basketball practice taking trick shots like hook shots from midcourt—another way not to become good at the sport.  

If schools stick with undemanding curricula and boring questions, our kids will be stuck at the free throw line, practicing something they will rarely be called upon to do in real life.  If (under the flag of ‘greater rigor’) we ditch those boring questions in favor of ‘Triangles’ and other lifeless questions, schools will turn off the very kids they are trying to reach, the 99% who are not destined to become mathematicians.

My fifth example is a question was given to 15-year-olds around the world on a test known as PISA (for Programme in International Student Assessment):

Mount Fuji is a famous dormant volcano in Japan.  The Gotemba walking trail up Mount Fuji is about 9 kilometres (km) long. Walkers need to return from the 18 km walk by 8 pm.  Toshi estimates that he can walk up the mountain at 1.5 kilometres per hour on average, and down at twice that speed. These speeds take into account meal breaks and rest times.  Using Toshi’s estimated speeds, what is the latest time he can begin his walk so that he can return by 8 pm?

Note that ‘Fuji’ is not a multiple-choice question.  To get the correct answer, students had to perform a number of calculations.  The correct answer was provided by 55% of the Shanghai 15-year-olds but just 9% of the US students.

Ironically, the PISA results revealed that American kids score high in ‘confidence in mathematical ability,’ despite underperforming their peers in most other countries.  Is their misplaced confidence the result of too many problems like ‘Snakes’?

(PS: A prize to the first reader who posts the correct answer!)

8 thoughts on “Five Test Questions for YOU

  1. Let’s also remember that about one third of American graduating seniors have taken and “passed” one or more Advanced Placement exams in one or more subjects.
    If any adults reading this would not mind feeling dumb, I suggest they look up an AP exam in any subject they like and try to pass it. No fair if you are a teacher of that AP course, naturally.
    Back 50 years ago, when I took my only AP exam in calculus, I was one of about 42,000 others.
    Now there are over TWO MLION AP exams being taken and passed every year.
    So, all is not lost.


    • And, logically, as we worry and complain about overall lowering AP and SAT scores, we are simply missing the point that we should instead be celebrating the fact that it is no longer a very small and elite group of test-takers playing our nation’s meritocracy game.


  2. Yes, we should offer students more rigorous (I prefer “genuine”) content — that PISA question is a good example, is that what you’re saying? — and less “boilerplate” work.


  3. Are the PISA results any worse for Americans than they have been for 5 decades? Isn’t it the case that the countries who test the best are not taking a real cross section of 15 year olds in their countries? And the kids in the US who take it are a cross section of ALL students?

    There are two issues that I see:
    1. The notion that we must rush kids through the curriculum and the teacher/school has “failed” if 15 year olds aren’t learning Algebra. In fact, the most successful charter schools fail huge cohorts of kids — I find it a sign of their true disinclination to REALLY improve public education that they never mention this. If they have all the bells and whistles and still are finding that 25%(or more) of their at-risk kids are taking 1 or 2 or even 3 extra years to get through elementary school math, why is that being ignored? Instead, we have “reformers” perpetuating the myth that it is “low expectations” when they should be saying “slow down the curriculum” for many kids.

    2. The forcing public schools to teach to a terrible, terrible test while private school students get to study more esoteric subjects and are never tested directly against public school students. Until private school students opt in to the SAME tests as public school students do, I will continue to believe that billionaires are lying when they say they are valid. If they were valid, they would be demanding their own kids take them. Instead, only a few private schools opt in — despite ALL of them being allowed to do so — and they don’t get particularly good results. With standardized tests, it is astonishing that as soon as public high school students start taking the same tests that private high school kids take, the private high schools start pretending the tests aren’t worthy. AP Exams used to be nearly all private school kids taking them — now private schools are trying to pretend they don’t show anything. Could it be that only their top students were doing well, with the bottom half performing at a mediocre standard that many public school kids surpass? You betcha. Same thing with the SAT! So many more private school kids opting out (or taking the ACT instead, which they never did in the past) and private colleges that cater to the richest students saying “score optional!”.

    I find it funny that the PISA results aren’t used to show that private schools are just as bad compared to schools in Shanghai. If that started being publicized, I guarantee you that the billionaires who tell the DOE what to do will start demanding that we all acknowledge that PISA scores aren’t useful anymore.

    In the education reform movement, it is important that specially designed tests ONLY for public school students be designed to the billionaire reformers’ specifications so they can “prove” how bad public schools are. But private schools get to opt out their entire school because what would happen if 20% of the kids were shown to be below standards at some fancy private school? Oops!!


  4. Nice article! But do you think that students in other countries get better questions in their curriculum content? Maybe they do…

    It makes me think of the relatively recent book and documentary, “Most Likely To Succeed” by Tony Wagner and Ted Dintersmith, which provides examples and research indicating that kids are unable to apply what they’ve learned to real world scenarios. The book by the way also has a damning critique of the AP tests which another commentator mentioned. Apparently students who passed with great scores were unable to even pass it 3 months later, as they studied for the test and then forgot – so unfortunately little deeper learning is happening thanks to AP exams. AP exams are about getting into college, not long term learning, in my opinion – maybe you’re proving you have a good memory and worth ethic?


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