A Math Paradox: The Widening Gap Between High School and College Math

My sixth-grader has scored very well on standardized tests for math, but he finds a blank page of math problems intimidating and boring. He spends hours — literally hours — wasting time at the kitchen table, not doing his long division or word problems. Yet for pleasure, he reads Death by Black Hole: And Other Cosmic Quandaries
and the last two bedtime stories we’ve finished have been kid-friendly biographies of Archimedes and Galen.

My son wants to be a scientist, but finds math boring. Clearly we have to do something about this!

Age-appropriate development and understanding of mathematical concepts does not advance at a rate fast enough to please test-obsessed lawmakers. But adults using test scores to reward or punish other adults are doing a disservice to the children they claim to be helping.

It does not matter the exact age that you learned to walk. What matters is that you learned to walk at a developmentally appropriate time. To do my job as a physicist I need to know matrix inversion. It didn’t hurt my career that I learned that technique in college rather than in eighth grade. What mattered was that I understood enough about math when I got to college that I could take calculus. —Joseph Ganem, American Physical Society

One day, my wife put the book 10 Things All Future Mathematicians And Scientists Must Know: But Are Rarely Taught into the stack of books at my son’s bedside. I glanced through the table of contents and got very excited.  The book mentions the Challenger disaster (managers ignored the engineers who warned that a low-temperature launch was risky), Dr. Snow’s study of a cholera outbreak (he plotted deaths on a map and realized one water pump in the neighborhood was infected), and the principle of Occam’s razor (which, in the absence of compelling evidence either way, favors the simple explanation over the complex).

Each chapter features a series of anecdotes that explain a big-picture concept (causation and correlation; bias; mistakes as an integral part of scientific inquiry; ethical experimentation), a cartoon mouse and cartoon Einstein comment on the stories, and the chapter ends with discussion questions that first require you to solve a word problem before you can weigh in with an opinion. This chapter is training young minds not to jump to conclusions, especially when all the information they need is right in front of them.

While I won’t pretend this one book has solved all our math woes, I will say that at bedtime the other night, Peter was happily pondering this question:

A hot-air balloon can safely hold 1055 pounds. It currently has 6 people in it whose average weight is 128 pounds. In addition, it has a 4-foot by 6-foot metal floor that weights 8 pounds per square foot. How many 25-pound bags of sand can be safely placed in the balloon?

This question came at the end of a chapter that described the 2001 death of the up-and-coming singer Aaliyah. (A pilot initially said it was unsafe for her entourage and all their baggage to fly in a small plane; but the group refused to leave any people or any baggage behind. The pilot relented, the plane crashed soon after takeoff, and all nine people aboard were killed.) My son has a well-developed sense of morality, so he was pretty much furious at that pilot.  The emotion motivated him to answer the word problem number story.

I guided him through the process, of course, asking questions to make sure he remembered the various subtotals.

When my wife came past the door and saw that we were still up reading (and calculating), she ordered us to stop for the night.

6 thoughts on “A Math Paradox: The Widening Gap Between High School and College Math”

1. jack hooper says:

The problem is that we are not giving maths in interested formats to our kids. Once they enjoy in doing maths they can easily involve in the subject.

2. Maxon, thanks for that detail. That was one of the first examples in the book, so I think maybe the author might have simplified so that it turned into a simple addition problem, rather than one of gemometry and physics. But for a book that emphasizes scientific and mathematical accuracy, that sounds like an oversight!

3. steven says:

i think i may buy that book for my little brother. he’s twelve, but he’s flying through algebra.
a lack of explicit interest isn’t the only thing stopping kids from learning math. there’s also the fact that bright students don’t learn appropriate concepts soon enough in their lives. i wish i would’ve learned algebra as a fourth grader…but i learned it in the eighth grade. i wish i would’ve learned calculus in the eighth grade….but i learned it in college. while nobody taught me math, i admit that i also didn’t teach myself math. however, it would’ve been nice to have been pointed in the right direction.

4. Maxon Crumb says:

Not to be pedantic (no pun intended), but the cause for Aaliyah’s plane crash was not that it was overloaded – airplanes are flown beyond their gross weight all the time. Stall speed increases as the square root of the load, so even overloading a plane by several hundred pounds only affects the stall speed by 15 knots. It’s common for ferry pilots to overload airplanes with hundreds of pounds of extra fuel in order to make trans-atlantic and trans-pacific deliveries of small aircraft.
Aaliyah’s problem was that the pilot loaded the aircraft such that the center of gravity (CG) was beyond
the allowable rearmost limit, causing the plane to be unstable and overly sensitive to pitch changes.