Why are We So Illiterate in Mathematics?

(Originally published January 11, 2016 and periodically updated)

And why does our common culture perpetuate the illiteracy?  As a math teacher, it makes me crazy to see our common culture supporting bizarre impressions of numbers and shapes and to see how students, made victims of these notions, can sometimes struggle with what used to be the most basic mathematical ideas.

Take, for example, the ice "cube." A cube is a regular hexahedron: a polyhedron that has six congruent faces, each of which is a square (think dice).  I don't know about you all, but the freezer of my youth held rectangular plastic pieces that froze water in the shape of roughly hexahedrons, with all edges that are line segments that are either parallel, perpendicular , or skew at right angles to each other.  Now, mind you, my own freezer mocks me in my passion for mathematics by producing a solid with two edges that are arcs and  two pairs of edges that are parallel line segments; these solids are definitely not cubes. Therefore it is no wonder that current students are confused by the word "cube."

Also take the coach, well meaning that she or he is, encouraging players to give 120% (or even a larger percentage) effort.  How does that happen?  When I fill my glass to the brim, it is 100% full. When I try to pour more water (or orange juice) into the glass, it overflows. I cannot add more than 100%.  Thus it is with athletics. How can you possibly give more than all you have?  No wonder students struggle with the concept of percentages in elementary school or middle school or in high school with the idea of probabilities summing to 1 or 100%.

Willy Wonka played with the idea of more than 100% in the following scene. It's worth a look -- at least one of the characters says, "Hey, that's more than 100%"

My son, as a young child, participated in many sports, but particularly loved basketball.  He played in a pee-wee kind of league in Colorado Springs that played wonderful games, but clearly someone in the program wasn't a math teacher.  The teams played 3 quarters in a game.  Yes, instead of playing 4 quarters to make a whole game, they played 3 twenty minute sessions that they called "quarters" and the game was meant to be over.   When I asked the ref when we'd finish the game as we had only finished 3/4 of the game, he looked at ME as if I was the crazy one.  If they played 5 twenty minute sessions, I don't think they would have liked to play fifths.  That word has other implications.

Now ok, I'm contemplating these kind of challenges I face each day in the classroom as I walk my dog, Karma (as in "good Karma") around my neighborhood in Albuquerque and I start noticing the numbers on mailboxes.  I live at 1198.  To our left as we face the street live our wonderful neighbors at 1196.  Across the street from them is 1197; order is maintained with the folks across the street from us: 1199.  But much to my consternation, the wonderful folks to our right live at not 1200; they live at 11100.  Is this a problem unique to Albuquerque? 

Seems no one in the US is immune to the "I can't do math," syndrome.  Check out this ad, then do the math.  Is $19.99 the value you'd get if you take 85% off of the original price of $169.99?

I enjoy a good math joke as well as any other football player; people recognize this as they link comics, cartoons, and what-not to me on facebook; I do delight in the humorous additions to my day.  But I squirm at the one that had one triangle talking to another triangle: "You are so obtuse, you wouldn't know an isosceles triangle if it bit you in the hypotenuse."  Now stop right there.  The cartoon has a cute one-liner and anthropomorphizes triangles, but only a right triangle (and not an obtuse triangle) has a hypotenuse.

 My hairs stand up when I see a joke that implies that there are no points contained in a circle:

And no wonder people have trouble telling the difference between an isosceles right triangle and an equilateral triangle when this image is used to help people, "Maintain social distancing": 

 

And of course, there's always arithmetic:



I'll let you do the correction.  I'm not sure that each person would even get enough for a Big Mac. How much would each person get?  And a serious question: why is this so difficult for people?

November 29, 2020, during a year that is going down in infamy, the front page of the Sunday New York Times covered the return to school (really the start of school) for a set of kindergarteners.  The article says, "Ms. Hellman, 26, dodged the triangular desks, spaced 6 feet apart..." The following photo accompanied the text.  The desks are clearly not triangular, as any kindergartener would know. I don't know of any classroom desks that are triangular. These are in the shape of isosceles trapezoids.

And while we are on the topic of the global pandemic and '6 feet apart,' let's return to the image about maintaining social distancing.

If it's been a while since you've been in 10th grade geometry: if you have a quadrilateral with sides of equal length 6 feet, the diagonals are 6 times root 2 feet, or approximately 8.5 feet.  

While we may find this funny, there's a bigger concern.  It gets expensive to not know or understand mathematics.  Staying alert and savvy can help in a variety of places, but specifically while calculating tip.  A restaurant, which shall remain nameless, provided the following inaccurate guide to calculating tips.  It seems they are vigorously and inaccurately encouraging you to be extra-generous to the servers (to the tune of 47% instead of 22%, for example). I do support encouragement of generous tipping, but I also support awareness of your personal tipping practices. I also support ethically providing accurate information. When called out for the error, the staff said, "It's up the the customer to make their own choices about tipping," failing to recognize responsibility for grossly inaccurate information. I'll leave it to the reader to calculate what the receipt should report as a "tip guide."

Here's something interesting.  In India, where many young people have arranged marriages and meet their betrothed on their wedding day, parents gather information about the partner they are choosing for their son/daughter.  Sometimes they receive erroneous information.  In Spring of 2015, one young woman was given information about her husband's education which made her skeptical. On her wedding day, she asked him a question about math:  What is 15+6?  When he couldn't answer it correctly, she walked out.   Math literacy is a predictor of future success; she knew it.

So perhaps I need more to do with my life so I'm not so concerned with such trivia, but I already fill 100% of my time between the triangle of 1198, math classes, and a tonic with ice cubes. Real ones, mind you.

             In this New York Times column, Nicholas Kristof quotes several eighth-grade math problems on which U.S. students did worse than those in other countries:

-    What is the sum of three consecutive whole numbers with 2n as the middle number?

Only 37 percent of American eighth-graders answered correctly, lagging behind South Korea, Iran, Indonesia, and Ghana.

-    How many degrees does a minute hand of a clock turn through from 6:20 a.m. to 8 a.m. on the same day?

Only 22 percent of American students answered correctly, behind Palestinians, Turks, and Armenians.

-    A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7, and x +6. What is the length of the longest piece?

Only 7 percent of Americans got it right, compared to 53 percent in Singapore.

“This is the generation that will be in the labor force for the next half-century,” says Kristof, “struggling to compete with citizens of other countries. It’s not just that American results are dragged down by poverty. Even American millennials with graduate degrees score near the bottom of international ranks in numeracy.”  Indeed, one of my high school friends serves on the "Common Council" political leadership board in Middletown, Connecticut.  Over dinner one evening, it became clear that she could not calculate 20% of 400. She laughed this off, as did everyone else present because it's a "geeky thing" to have that skill.  Keep in mind this board discusses tax rates in percentages that include not only far more difficult numbers in calculations (i.e, not multiples of 10) but calculations often in the abstract.  Without those skills, how could she make informed and intelligent decisions that would well serve my hometown? 

            What’s going on here? Kristof believes we have a societal attitude problem with numerical literacy – and we need to get over it. “Numeracy isn’t a sign of geekiness,” he says, “but a basic requirement for intelligent discussions of public policy. Without it, politicians routinely get away with using statistics, as Mark Twain supposedly observed, the way a drunk uses a lamppost: for support rather than illumination… Statistical literacy should be part of every citizen’s tool kit.” And maybe we should deemphasize calculus.

            Yes, some people are exceptionally gifted at math. “But let’s not use that as an excuse to hide from the rigor of numbers,” says Kristof. “Countries like Singapore manage to impart extraordinary math skills in ordinary children because they work at it.”

For your own blogs, dear students, you have a choice.  1. you write on your theory about why U.S. Citizens aren't very savvy mathematically or 2.  you find some mathy idea to write about that interests you. or 3. Find something in the paper, a publication, an ad, social media, anything, that includes a gross mathematical error.  Point out the error and explain how it's wrong or how it could be considered correctly. Remember to submit it appropriately. Remember to make this blog your own, yet cite sources.