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.

But if you play Scrabble, you already knew...

TEACHER anagrams to CHEATER. According to an article in yesterday's Atlanta Journal-Constitution, one hundred nine employees in the Atlanta school system, including 40 principals or other administrators, have been flagged for possible sanctions due to the widespread cheating scandal based on the 2009 CRCT (Georgia's acronym for the state-mandated testing I regularly refer to).  Of note, "many" of the schools involved performed dramatically worse on the 2010 CRCT, with failure rates of 2 - 4 times that of 2009.  Of the 109 employees flagged in Atlanta, 78 are from 12 schools.  All 12 of those principals have been reassigned, pending final state review and a decision on their certification.


One final note on the specifics of this story: the investigators presumably wanted to find out if teachers cheated.  There are several ways to cheat, including erasing wrong answers and filling in correct ones after the student has turned in the exam.  Another is to give correct answers to students during the test, or provide other assistance during the actual exam.  So of course, you'd want to interview a lot of kids to see if this kind of thing happened.  How many kids were interviewed? 12.  Of 292 total interviews, 12 were with kids. Hmmm....

"The commission's report cited no evidence that either Hall (the Atlanta schools Superintendent), who created an aggressive accountability system tied to test scores, or other top officials orchestrated or condoned cheating."


I have two issues here... first, I am deeply troubled by the fact that nearly 70 teachers in one school district are highly likely to have cheated.  I don't know how many teachers there are in total in Atlanta's elementary and middle schools, but 70 has to be a non-trivial percentage of them.  And that's just the ones who cheated blatantly enough to get caught.  And of course it doesn't include the ones who would have cheated but didn't get the opportunity or didn't need to because the kids they proctored were good enough on their own.  I thought teachers were the ones who abhorred cheaters...


Second, I find it laughable to suggest, as the quote above does, that the Superintendent has no culpability in this affair.  I don't think she encouraged cheating; I think, if asked directly, she would have forcefully discouraged cheating.  But I also think she set up a game in which CRCT scores were the only measure of how well you played, and she set the stakes on the outcome at an incredibly high level.  You have to be a fool to imagine, in that environment, there won't be widespread cheating.  Maybe she simultaneously "created an aggressive accountability system" tied to abiding by the rules, but I tend to doubt it.  (By the way, if the Journal-Constitution hadn't run several articles about the statistical near-impossibility of the test gains from 2008 to 2009, there'd be no scandal. The demise of newspapers will have costs.)


Bottom line: she, like most administrators I've encountered so far, cared about higher test scores, not better education.  The reason for that is simple:  she gets compensated for higher test scores.  When will we learn that to get better teaching, we need to incentivize teachers to teach better, and administrators to create an environment that fosters it?  Instead, we incentivize everyone to have students who get better scores, just because scores are easier to measure.


Final rant (of this message):  The school grade, the most important factor in the principal's bonus compensation, is based in part on graduation rate.  Suppose a senior is failing your Biology class, a subject he needs to graduate.  You're called into the principal's office to discuss this student.  Which of the following is the most likely to occur:
a) the principal praises you for maintaining high standards and insisting students master the content the state says they must in order to graduate,
b) the principal encourages you to work harder with this student to enable him to master the content he needs to pass your course, and offers support to enable you to do that,
c) the principal informs you that the failure rate in your classes is unacceptably high, and that you are not only not eligible for a bonus based on teaching excellence, but your job is potentially in jeopardy if that rate doesn't come down.
d) option (c), plus the student is withdrawn from your class and put into an on-line Biology course he miraculously manages to pass within 2 weeks despite being unable to spell "biology," or speak in full sentences.

Hey Mister Can You Spare a Dime?

I've sent a request for donations to support my AP Statistics course to many of my more, um, salary-enhanced friends, and have been very pleasantly surprised at the positive response. In addition, my brilliant daughter one of my brilliant daughters recommended I request that recent graduates who no longer had a use for their graphic display calculators (GDCs) send them to me, who has an urgent need for them.

I've gotten $550 and 4 GDCs so far, and pledges for another $100 and 3 GDCs. I've given one of the executives where I used to work a proposal to have my class run an analysis for him; I've asked for about  $3,000 in equipment. For various reasons, I think it's extremely likely he'd agree to do the project.

There's a part of me that doesn't want to beg my friends for money, but there's a bigger part that really wants my kids to have a chance to do well on the AP exam. Without money for calculators, stats programs and teacher training, there's not much hope. Moreover, I've been really impressed with the generosity of many people. I know that this is the definition of charity, but there's really nothing in it for them to give this money to the school -- they're doing it because I asked. I'm humbled, and grateful.

8 More Miles

School starts for the students in 2 weeks, but the math, English and science teachers return early next week for a program called "Early Return" (who thinks of these names?), and the week after that is Pre-Planning. I've been going to my classroom just about every day the last couple of weeks to try to sort out what to do and how to do it.  I feel like I have a pretty good handle on it, but of course, the proof of the pudding is in the tasting.

Looks like my schedule will be:  Honors Algebra II, Honors Geometry, AP Statistics and the two IB courses, which are essentially just Honors Algebra II and Honors Geometry, but with a British accent.  "Presume your boot measures 1 metre by 50 centimetres by 30 centimetres.  If each brolly cost 40 quid and is packed in a cylindrical tube 35 centimetres long and 5 centimetres in diameter, what would it cost to fill the boot with brollies?"  (Of note, "diameter" is the British spelling of "diameter," despite the fact that "metre" is the British spelling of "meter," the unit of distance.  However, "meter" is the British spelling of "meter," the measuring device.)

The school grades for the state were released yesterday (a couple of months late) and our school grade has gone from a D to a ... well, we don't know yet.  High schools are graded this year based on several other factors, which for some reason the state couldn't have been calculating while waiting for the test results.  So the high school grades will not come out until November.  The rumor is that we went from a D, 7 points above an F to a D, 2 points below a C.  I don't think the actual answer has any impact on me whatsoever, with one exception -- if we are a D school, I get a (small but not insignificant relative to my salary) bonus if any of students pass the AP exam, plus another, much smaller, bonus for each kid who passes.  I'm pretty sure I don't get the bigger bonus if we're a C school.  Whatever.

If It's Summer, Shouldn't I Be Somewhere Else?

I signed up to "teach" the incoming pre-IB Summer Bridge program, which was developed to assist these kids in their transition to high school.  An amazing number showed up -- 36 of the total of 45 or so who are enrolled in the program -- and I enjoyed the week of talking about stuff I find interesting in mathematics to a group of kids who are clearly interested in learning, even if math isn't their favorite subject.  I mention this only because it explains why I was wandering around on campus last week...

So Mrs. D (who is teaching summer school because her youngest child needs braces) and I were coming back from lunch when we noticed that a bunch of textbooks had been delivered to the school, and were sitting outside the book room, in the open air hallway.  (Note:  The school is surrounded by an 8 ft chain link fence, with perhaps 6 gates which are locked (but easily scalable - a fact I know because I've been locked in twice) during the evening but open during the day.  The books were in an area that is not far from the gate in front of the student parking lot.)  Mrs. D wondered aloud if those were the new math texts, and I said we should go find out.  So we went over to the pile and found several boxes clearly labeled as Algebra II texts.  We also noticed that a box of history books was open, so we opened a box of math texts.  As we perused the book, the book lady walked through another hallway, and shouted to us from about 40 feet away, asking what we were doing.  When we told her, she began heatedly saying we're not supposed to "take" books, and that she often ends up short of books because several of them have "walked away."  We left, and that was, I believed, the end of it.

Mrs. D, however, was offended, feeling we had been accused of stealing.  So she wrote an email to the book lady apologizing for opening the books, while also trying to justify the action (the open history book box, weren't going to take them, etc.)  Apparently Book Lady emailed back, and basically reiterated her contention that we were a threat to walk off with "her" books.  Mrs. D wrote her back; the note was nice, and the thrust of it was just that she would never take a textbook without asking, and that wasn't what she was doing.  All very middle-schoolish, but hey, what else is there to do in the summer?

So that would probably have been the end of it, but apparently, Book Lady was irritated enough to send a note to the new Vice Principal, whom I shall forever more refer to as "Tempest" (as in "... in a Teapot").  My guess is that Book Lady sent the email to Ms. Tempest prior to the exchange of emails with Mrs. D, but don't really know.  Anyway, Ms. Tempest sends a very snotty note to Mrs. D and copies me (why wouldn't I be a co-addressee?) essentially reiterating the "we can't trust you" theme.  Mrs. D and Ms. Tempest exchange a couple of additional emails, with Ms. Tempest getting snottier by the moment.  To this point, I had stayed out of it, figuring I couldn't do any good.  But the Tempest notes to Mrs. D were incredibly annoying, particularly given that Mrs. D has been teaching at MHS longer than Ms. Tempest has been alive.

So I finally waded in, and sent her an email (copying the principal) noting that the "crime" she's berating us for was the desire to see the textbooks we'll be using in August -- something I'd think she'd want us to want to do -- and that if she or Book Lady are concerned about pilferage then they should probably try to find a way not to leave the books out in the unprotected hallway for 3 days.  In response, I got a note about how we'll get the books in plenty of time to prepare (not my point), that the Book Lady didn't have a choice about leaving the books outside (not my point, but now that you mention it, why not?) and that it is never appropriate for anyone to open mail that isn't addressed specifically to them.  Riiiiiiiight.  That's what we were doing -- snooping through the mail.  Then she talked about the need for professionalism, something she clearly implied I lacked, by virtue of being willing to open someone else's mail.  (She hammered this point about 3 times).  I have a tremendous desire to fire back a really scalding response.  I'm going to suppress it.  Not because she is, in some ways, my boss, or even because I'm afraid it will get me in trouble with someone I actually respect, but mainly because I'm pretty sure she's not bright enough to recognize a cogent argument if she hears one.

It could be a long year.

That said, I can't wait to get it started... I think the classes could be really good.