Wednesday, March 28, 2018

Nice Try, But No

Here we go again, yet another article bemoaning how "boring" math is.
What do these four questions have in common?
1. Can all the children of Lake Wobegon be above average?
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?
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.
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.

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?


Anonymous said...

Back in the dinosaur era (50s), we did real-world math problems in ES on a regular basis: how much paint for a room of specified dimensions and the total cost, at x price/gallon; double, halve or triple a specific recipe; calculate mpg on a vehicle; calculate interest rates, mortgage payments etc; calculate profit from a summer job, calculate cost of sewing a dress, curtains etc from a pattern or measurements at a specified price per yard, calculate, how much fertilizer for a lawn or vegetable garden of given dimensions ... without a calculator. Plus, we really did those kinds of things.

I agree that the the goal, for some people, is to make math (STEM in general) less mathy - to try and force equal outcomes, masking the fact that both ability and effort is necessary for success, and that neither is distributed equally among students. The same goes for the current effort to make STEM more girl-friendly.

Ellen K said...

All of us are tired of being told how to do our jobs by people who have never entered a classroom.
The assumption seems to be that we are a bunch of dimwits in spite of our experience and need to change things up Every Single Year to keep the distracted darlings engaged. There is nothing wrong with basic education that have grades and advancement based on merit rather than insisting that all students must succeed at the same rate. Face it America, sometimes kids are just dumb.

lgm said...

As a parent, my when my kid came home bored out of his skull bc of the insistence that everyone be taught at the speed and depth needed for the lowest IQ not in special ed, I reached for homeschool resources. There I found more than the 'nines finger trick'. Darn, I put a neighbor out of work by not making sure my kid was only up to Algebra 2 in twelfth grade. Put another one out of work by not going to CC for two years before starting a four year U program that req'd calc as the first course. In return, I put a few college kids to work for the middle school years by giving my kid appropriate depth, speed, and level. School is dead for math unless on is in a rich district.