These five test questions may explain why American students score lower than their counterparts in most other advanced nations. The first is a sample problem offered by the University of Wisconsin/Oshkosh  to high school math teachers. It was designed with the stated goal of ‘Closing the Math Achievement Gap’:
Jack shot a deer that weighted (sic) 321 pounds. Tom shot a deer that weighed 289 pounds. How much more did Jack’s deer weigh then (sic) Tom’s deer?
Basic subtraction in high school? The second comes 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?
While the second problem does not contain language errors, its 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?
And I found this 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?
Remember that these are math problems for high school students! They require simple numeracy at most, and “Snakes” can be solved by counting on one’s fingers.
Next is an example of what lies ahead for 8th graders–not high school students–under the new Common Core National Standards, which are supposed to introduce much needed ‘rigor’ to the curriculum. This question (without illustrations!) is from New York State’s sample tests.
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.
Did you go ‘Huh?’ I did.
The fifth and final question was given recently 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?
For simplicity, let’s call these problems ‘Deer/Canoe/Snakes,’ ‘Triangles’ and ‘Fuji.’ Those high school problems are far too easy. With enough practice, just about anyone can solve undemanding problems like that and, consequently, feel confident of their ability.
Note that ‘Fuji’ is not a multiple-choice question. To get the correct answer to this engaging question, students had to perform a number of calculations. The correct answer (11 AM) was provided by 55% of the Shanghai 15-year-olds but just 9% of the US students.
Speaking of confidence, the PISA results reveal that American kids score highest in ‘confidence in mathematical ability’ despite underperforming their peers in most other countries. Is their misplaced confidence the result of problems like ‘Snakes’ and others of that ilk?
School is supposed to be preparation for life, but spending time on problems like ‘Deer/Canoe/Snakes’ 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.
Now to ‘Triangles,’ which represents education’s brave new world of the Common Core, adopted by 45 states and the District of Columbia. In this new approach, students will be exposed to higher and more ‘rigorous’ standards. The hope is that the curriculum, locally developed to reflect the standards, will challenge and engage students. I suggest you read ‘Triangles’ aloud.
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?
Are you feeling ‘engaged’? Imagine how 8th graders might feel. If ‘Deer/Canoe/Snakes’ are the educational equivalent of practicing free throws, then solving problems like ‘Triangles’ is akin to spending basketball practice taking trick shots like hook shots from midcourt—another way not to become good at the sport. I worry that questions like ‘Triangles’ will impede the understanding and appreciation of math for the 99% who are not destined to become mathematicians.
If our schools persist with boring, undemanding curricula, our kids will be stuck at the free throw line, practicing something they will rarely be called upon to do in real life. If, however, in the name of the Common Core’s ‘rigor’ we give our kids lifeless questions like ‘Triangles,’ schools may end up turning off the very kids they are trying to reach.
- 1. Wisconsin source: http://www.uwosh.edu/coehs/cmagproject/many_word/documents/1_Dear_Hunting_Problems.pdf The web page notes that ‘slightly more difficult problems are coded with a shamrock/diamond.’ Here’s one of those: “In the first half of a recent game, the Packers scored 14 points on touchdowns and 9 points on field goals. In the second half, they continued scoring, and they ended the game with 43 points. How many points did they score in the second half?” ↵
- Pearson source: https://www.teachervision.com/tv/printables/botr/botr_140_3-3.pdf↵