Turns out, math isn't important.

An editorial, written by a professor emeritus of mathematics, statistics and computer science at the University of Illinois at Chicago is running in McClatchy-owned newspapers today, and states that math's importance to the daily lives of Americans is overrated.  In fact, he claims, the attempt to make math seem essential is a marketing ploy by colleges to create and sell mathematics education programs.

He asks exactly the question my students ask, namely "How much math do you really need in everyday life?" and goes on to say you should not only ask yourself that question, but "the next 10 people you meet, say, your plumber, your lawyer, your grocer, your mechanic, your physician or even a math teacher."

I'll leave the "math teacher" issue aside, and address physicians for a moment.  Consider the following scenario, a standard of every intro probability and statistics course:

You suspect you may have a brain cloud, for which there is only one cure - jumping into a live volcano.  If you do in fact have a brain cloud, you will survive the jump, become perfectly healthy and live happily ever after with someone who looks remarkably like Meg Ryan.  If you do not, you will die a gruesome death. However, if you have a brain cloud but do not leap into the volcano, you will die an equally gruesome death within days.  So it is imperative you make the right decision, which means you need to know, as surely as possible, whether you have the brain cloud or not.

Fortunately, brain clouds are very rare - affecting only 1 in 1,000,000 people worldwide.  Moreover, there is a test for tomhanksiplexy (the technical name for brain cloud) which is accurate 99.9% of the time.  There are no other symptoms or indications of any kind (up until the moment of gruesome death, of course).

You go to a physician and take the test.  He comes back from the lab, sadly shaking his head, and tells you that you have a 99.9% chance of having a brain cloud, and should go jump in a volcano immediately.  Your response is to...

a) jump in a volcano.

b) decry the state of mathematics education in America, and wonder how anyone could imagine it's unimportant.

If you chose (a), you're not alone, but you are, in all likelihood, gruesomely dead.  In fact, you're in a mathematical hell crowded not only with high school dropouts, but the vast majority of physicians as well.

Since the test is 99.9% accurate, if 999,999,000 healthy people take it, 999,999 will have false positive results. (one tenth of one percent of 999,999,000 is 999,999).  If 1,000 people who have brain clouds take the test, 999 will have correct positive results.  So if 1,000,000,000 random people take the test (and 1 of every 1,000,000 has a brain cloud), there will be 1,000,998 positive results, of which 999 will be correct.  That's approximately a 0.000998 chance of having a brain cloud, given you have a positive result.  Said another way, that means there's a 99.9002% chance you DO NOT have a brain cloud, even if you have a positive test, which is accurate 99.9% of the time.

Nobody expects "the average" person to get that problem right.  But people have a right to expect that their physician, when reporting on the results of their most recent battery of tests, will understand what those tests do or do not "prove."  Most physicians cannot do that, because math education in America doesn't do a good enough job equipping our future physicians and lawyers and plumbers and grocers with the math and cognition skills to think through a problem like that.

Okay, maybe doctors need math, but surely not lawyers, right?  Here's the same problem in a courtroom:  In a town with two taxi companies, a woman saw a man rob a liquor store and jump into a cab at 8:07 PM on Tuesday night.  The witness testifies that the robber got into a Yellow Cab, which has 10% of the cabs in town; the Ocher Cab company has the rest. You've checked her ability to recognize the difference between the two cabs, and concluded she's accurate 80% of the time.  Based on this information, and assuming the witness is telling the truth as she knows it, what are the odds that the perpetrator got into a Yellow Cab?

At this point, my students tell me that if they are confronted with situations like these, they'll just hire someone who's good at math to give them the answer (which, as it turns out, is 50/50).  The problem is, they're confronted with these questions every day without ever knowing it.  The paper tells us that the number of dropouts in Home County has doubled every year since the consolidation in 1990.  No one bats an eye.  Store A provides a coupon good for an additional 25% off on pants already on sale for 30% off, whereas Store B has the same pants on sale for 50% off.  People who buy at Store A think they've saved money.  A group in art class makes a scale model of a building using the same materials they'll use for the one 10 times as tall, note that the model weighs 3 pounds, then are befuddled when 4 of them together can't lift the final project.

In early Mesopotamia, unscrupulous individuals would offer parcels of land for trade that had the same perimeter as the land they wanted, but much smaller area.  A knowledge of geometry was vital if you wanted to avoid being swindled.  Anyone who plays poker without knowing how to calculate rudimentary odds is giving away his money to those of us who believe math IS important in everyday life.  Buying a house or renting an apartment, buying or leasing a car, investing in stocks or savings bonds, choosing a line at the supermarket and a thousand other daily chores are easier and more likely to lead to the outcome you want if you are comfortable with and know how to use some relatively simple mathematics.

We're not teaching kids the Pythagorean Theorem because we believe they'll be in a situation someday where they will need to know the straight line distance between Juan's house and Julie's, which is 4 blocks east and 9 blocks north of Juan's.  We're teaching them those things because in their job as District Sales Rep for BigCo., Inc., they'll be much better salespeople if they have been trained to examine problems analytically, and look for solutions using the tools they have in their arsenal.  High school isn't a trade school.  They may never again, after high school, ponder the morality of Jean Valjean or the empathy of Atticus Finch.  They'll certainly never be quizzed on them.  But they WILL be better equipped to make judgments about criminal punishment and racial inequities – things they will certainly face in the real world.  A similar reality exists for mathematics education, even if some math professors haven't figured it out.

The Law is an Ass

In researching the title phrase to ensure I remembered it correctly, I discovered things about it I didn't know.  In fact, nearly everything I discovered was stuff I didn't know, so rather than write about the things that put me in mind of the phrase, I'm going to write about the phrase I was put in mind of.

For example, I thought it had been uttered by a lawyer.  And I thought it was in reference to some bitter result having turned on the unintended consequences of an ill-considered law.  In fact, it's much more interesting than that.  It's from Oliver Twist, and is said in response to the statement "the law supposes that your wife acts under your direction." The person to whom this statement is directed is unmercifully browbeaten by his domineering wife, and rejoins "If the law supposes that... the law is an ass - an idiot.  If that's the eye of the law, the law is a bachelor."

I find that verbal exchange absurdly amusing.  I'm not sure why, but there it is.

Time is the fire in which we burn

I find myself, on an almost daily basis, choosing to take the time I have available to prepare what is required in order to satisfy administrative edicts, rather than prepare a better, more interesting, more involving lesson for my students.

This pisses me off.

First, let me be clear -- it isn't that I'm attempting to determine how to spend the 7.33 hours a day for which I am paid; that time and more is spent (a) teaching - 4.5 hours, (b) in mandatory meetings - 0.6 hours, (c) standing at my door between classes and walking my students to and from the lunchroom (both mandatory) - 0.25 hours, (d) maintaining the classroom (e.g., posting the mandatory agenda board, erasing the white boards in preparation for the next class, straightening desks) - 0.5 hours, (e) recording attendance and grades - 0.25 hours, (f) typing the three mandatory lesson plans per day (note: this isn't "preparing the lesson"... it's "typing the lesson plan") - 0.5 hours, (g) grading papers - 0.75 hours (note: I spend considerably more than 45 minutes grading papers; this is just my "planning period" time).

The time I'm talking about having to allocate to administrative edicts is (all or part of) the extra 3 to 4 hours a day I spend on school work during the week, or the 6 to 10 hours I spend each Saturday and Sunday on the weekends I'm not traveling to see my children.  I'm paid a little over $20 an hour for the time delineated in the previous paragraph; I'm unpaid for the time described in this one.

Don't get me wrong -- this isn't a request for pity.  I chose to take this job, knowing what it paid, and I choose to work the extra hours, knowing they're unpaid.  But I'm sitting here on a Sunday morning with 8 items on my agenda, in order of my estimate of their value to the education of the students in my class:

(1) designing an interesting, challenging, interactive game for my students to play in small groups that involves going to different stations in the room and solving problems like the ones they did so poorly on when taking their recent test. (I have the general concept, but I need to flesh it out.)

(2) using the "Jeopardy" PowerPoint shell to create an in-class review activity for the current module.

(3) planning the next two weeks of classes for each section, so that the students have an idea of what they'll be doing between now and the end of the quarter, and they'll be able to plan how they will bring their grades up prior to the first report card.

(4) writing and printing "scholarship warnings" for all of my students who currently have a D or F in my class.  This is somewhere between 50 and 70 students, because the most of them were taken by surprise by their first high school math test.  I guess middle school tests were absurdly easy.

(5) grading 5 classes' tests and putting them in the grade system.

(6) printing progress reports for all students so they know what grade they have and what they need to do to improve it.  Note:  they could go online for this information, but we're required to print the reports anyway.

(7) creating a "standards-based bulletin board" that shows students (who never look at it) how the project displayed on the board is graded, and what a good project would look like.

(8) creating "student-generated" charts.  There doesn't seem to be any other requirement for these charts, other than being student-generated.  I may have three students in first block tomorrow write "This is a chart generated by a student" on chart paper and hang those up.  But probably not.

Of course, it's extremely unlikely I'll get to all 8 things.  If I just got to the first 3, I'd feel pretty good.  Unfortunately, those 3 items are the three that my administration places no value on.  The other 5 are all items that will be checked on by my administration, and for which I will receive a poor evaluation should they be missing or incomplete.

I'm already tired, and it's only 10 AM.