What do these four questions have in common?You know what makes math more fun? Being able to do it. After you've mastered decimals, fractions, percentages, multiplication tables, and positive and negative numbers, math becomes much more interesting. A little number sense goes a long way.
1. Can all the children of Lake Wobegon be above average?They are all math questions for high school students. They differ from typical school math problems in that they are phenomenon-based and stated as real-world problems, not as math exercises. More and more educators these days are pushing for such phenomenon-based problems to engage the students, to get them excited about STEM, to advance their critical thinking skills, and to make math and science more fun.
2. On average, do your friends on Facebook have more friends than you do?
3. Do credit cards make you gain weight?
4. How do I estimate distances to nearby stars?
I'll grant that the questions above can be interesting to pursue. They're also time-consuming--and the people who pay the bills, the taxpayers, tell us through their elected representatives that we need to teach a rather wide body of information (just check out the high school common core standards).
Let's quickly go through the questions above.
#1: It depends on what your population is. Easily discussed and resolved in a couple minutes. Next!
#2: Isn't that rather easy to determine? And we're talking about averages, certainly not anything high-level.
#3: Silly. More a sociology question than a math question.
#4: K-12 students don't really have the background knowledge necessary even to start that one.
There, that didn't take long.
Certainly math can be put to uses more interesting to students, but a math class isn't the place to do that. If you want to put math to social science uses, do that in social science class. If you want to graph the lengths of words in Shakespeare's plays and relate that to either the vernacular of his day or that of ours, do that in English class. Those might be fun explorations in math class, but they certainly can't drive the curriculum. Neither can they be the primary form of pedagogy. In a math class we need to teach math. That doesn't mean that math must be the memorization of formulas and algorithms; on the contrary, that does as much a disservice to math education as does building a math class around the silly questions asked above.
Do you want to show math's utility? Then do it outside of a math class! Sure, good math teachers often show the applicability of what they teach, but the purpose of doing so is to show why we teach what we do. It does inspire some interest in the topic. But utility isn't why we teach what we do in high school. For the vast majority of Americans, utility comes in elementary school math--in decimals, fractions, percentages, multiplication tables, and positive and negative numbers, and in number sense. High school should be about going beyond that, about a little abstraction, about learning what the future can hold. Heck, freshman algebra doesn't teach too much that's new; rather, it takes all those elementary school math concepts and combines them all into one problem! Introductory Algebra is most students' first capstone course.
But I'll be honest, I'm tired of being told how to teach math by people who weren't (or aren't) good at math. The author of the above post is on the other extreme of the spectrum--he's already mastered math, and he thinks people learn math the same way he understands its applications. It's people like him who gave us the "new math" of the 60's and 70's, the creators of which seemed to believe that "if students could just learn about calculating in different bases and understand sets, everyone would see and understand the beauty of math and students would flourish". Why was I calculating in base-7 in 5th grade??? Anyway, today, instead of set theory and different bases, the silver bullet to math education seems to be matrices--boy, if students could just understand those, they'd see and understand the beauty of math and.... Throw in a dash of so-called discovery learning, as the author at the above link did later in his article, and you've reached math education Shangri-La for many people.
The problem isn't that math is boring. It can be taught in a boring way--so can any other subject. What makes math problematic is that it's difficult and requires constant effort. It's easier to look for excuses than to insist on effort.
No one suggests teaching music like this. No one says that learning scales is too boring, that young musicians should dig into concertos. No one suggests coaching football like this. No one says that drills are too boring, that players should go straight to touchdown-making plays. No one suggests that a student's first time behind the wheel should be during rush hour traffic. In fact, I'm hard-pressed to come up with examples of areas outside of math where such recommendations are expected to be taken seriously. Why do you think that is?