The Problem with Math: Problems

I am a math teacher, and it quite frankly amazes me that my life insurance rates are not prohibitively high because of it.

Periodically, I tutor young men and women in my neighborhood. Often they are having some trouble because they missed a few days of math clas, or maybe they just don’t quite understand their teacher as well as they’d like. So they come to me, and we do some problems together at my kitchen table.

I get angry. Not at the kids; they are generally doing the best they can with whatever they have been given. But I get angry at the problems they are assigned. And I figure if I, as a math teacher – as someone who is not afraid of sentences that begin, “Let H be a compact Hausdorff space. . . .,” as someone who periodically integrates secant cubed just to see if I still “got it” – if I get angry, what chance do the kids possibly have?

See, it isn’t ever enough to teach a concept, then see if kids can apply that concept. No. We have to teach several concepts, then make horrible examples in which they all apply at once. And throw in some ugly fractions at the same time. I’ll give you an example of what I mean:

Problem: Graph y = 7 + sin x.
Student: “No problem; that 7 just moves the graph up 7 units.” (Hums happily while sketching graph)



Problem: Graph y = 3sin x.
Student: “Easy. That 3 just stretches the graph 3 up and 3 down. I can do that.” (More happy humming)

Problem: Graph y = cos 4x.
Student: “OK, I know that 4 makes the period – uh, longer? Shorter? Let’s see. Oh, yeah, I divide the period 2 pi by that 4, and the new period is pi over 2, and so I just scruntch it all into pi over 2 instead of 2 pi.” (Proceeds to sketch graph. No humming this time.)

Problem: Graph y+7/3 = 5/2 tan (3x + 7/4).
Student: “Mr. Math Teacher, sir? Please come over here so I can beat you up.”

See? Anger. Anger is a perfectly rational reaction to that. Admit it. You wouldn’t take that kind of abuse from anyone, let alone some old guy who talks through his nose and is half covered with chalk dust. So why do we expect kids to take it?



Sigh. Good thing nobody reads this blog, or I’d have a lot of angry math teachers to deal with.

Channeling Carnac the Magnificent

I take the hermetically sealed envelope out of the mayonnaise jar, and holding it to my ornately turbaned head, I say:

"A camel with one too many straws, a movie with two gay cowboys, and me."

Tearing open the envelope, I reveal the question:

"Name three things with a broke back."

Yeah, apparently I have a stress fracture in one of my vertebrae. Which would explain some of the back pain. Maybe not all, but some.

Why do I have a stress fracture? I don't know. Honestly, I have no idea how it happened. No recollection of anything that could have done it. I'd like to think that it came from my performing some superhuman feat of strength, like lifting a bus off of an orphan. But no. More likely it was because I have the bones of a 70-year-0ld woman. I was going to sell them on Ebay, but they wouldn't let me (rimshot).

So it looks like maybe there will be less Diet Coke, more weight-bearing exercise, and more calcium-rich foods in my future. It figures. My doctor visits have this nasty habit of returning to the theme of exercising more, eating better, and getting more sleep. Perhaps I'll try it this time.

The Williams Way

I saw my cousin at the hardware store today. He lives about two hours away, and we see each other maybe once a year, at the family reunion. And of course, because we are roughly the same age and on good terms, we always exchange a few words -- maybe twelve. Let me count: "Hi, Tom, how you doin'?" "Fine. How are you guys doin'?" "Fine."

Yup, twelve.

Actually, our conversation at the hardware store was rather involved, by comparison, ranging over such topics as what project I was doing that brought me to the hardware store ("Oh, just fixing some stuff") and how Tom's parents, my aunt and uncle, were doing ("Real good."). I didn't ask him what brought him to the hardware store two hours from his home. If he wanted me to know, he'd have told me. But overall, it was really pretty chatty by our usual standards.

I think both of us are kind of relieved that we've pretty much taken care of our social obligations for the year. I figure this June, at the family reunion, we'll probably just nod at each other as we pass by. Don't want to overdo it. Besides, we both know how we'll be doin': Fine. We'll be doin' just fine.

And that's all a Williams really needs to know.

Erynn and the Terrible, Horrible, No-Good, Very Bad Day(s)

Just over a week ago, Erynn had a very very good day. She has been taking ballroom dance as an after-school class this year, and has therefore been dancing with the Dixon Middle School ballroom dancers at various concerts this year. Last week, the two Dixon teams went to a competition involving several local middle schools. Long story short, Dixon walked away with two gold ribbons and the trophy for overall best dancers. Erynn was justifiably happy and proud. I was originally planning to write a blog complaining about how everything needs to be made into a competition in our society. But I figured since my daughter's team won, I'd let it slide.

HA! In your face, Other Local Middle Schools!

Anyway, she's had a good week. And then, yesterday, the Dixon team had one dance at a Provo High School dance concert. As I found out later, Erynn (as she says), "biffed it" as she was walking into the school just before the concert. Scraped and bruised both knees and both elbows. Must have been quite a biff. It included a face plant, so that her upper lip came between her braces and the sidewalk, resulting in blood and puffiness.

Trooper that she is, she bandaged up and got ready to dance. And dance she did. We didn't know any of this, sitting in the audience, videotaping our daughter's one performance, which as near as we could tell went well. However, if you examined closely the videotape, you would be able to find, as we did later, the exact moment when her dress fell off, and she was scooting to the back of the stage in her black undies, there in front of God and everybody.



As spectators, we honestly didn't notice it at the time. I'm not sure if anyone did, really. Except, of course, Erynn and her fellow sufferers up on stage. But it's there, on tape. It brought a smile to our faces last night as we watched it. In fact, it brought loud guffaws and snorts of laughter. Erynn wasn't convinced it was that funny.

She managed to get her dress fixed in the intervening 15 seconds or so, while the dancers were in two lines (her in the back, thankfully enough), doing hand jives. And the rest of the dance went off without any major wardrobe malfunctions.

As if that wasn't bad enough, the luck continued to today, which, of course, is Mother's Day. Erynn spent her last package of -- well, it's some kind of crafty plaster-like substance -- in making a pretty heart-shaped present for her Mom. And when she was working on it, she picked it up to move it and it broke. Likely beyond redemption.

Sad indeed. But the saddest thing is what she said to me last night, as we contemplated the dance debacle. She said, "Well, I guess it was just getting back at me for being so happy last week." If you're not quite sure what "it" was, then you probably haven't spent your life convinced that "it" was keeping score, and trying not to be too obviously happy or worry-free, because you knew beyond doubt that "it" would pay you back if you were. I have spent my life that way, so I recognized the symptoms immediately. It's part of my family heritage. I got it from my dad, who gotit from his mom, and on back, somewhere into Denmark, which gave us, after all, Hamlet, and goodness knows he knew better than to get too happy. I'm not sure, but I think "it" lives somewhere near Copenhagen.


Anyway, I have a few words of advice to give my daughter: You don't have to be another dismal Dane. First, you have every right to be happy when good things happen. Second, nobody is keeping score but you. Third, if you don't believe what I just told you, then start right now to fight that feeling. Fight it for all you're worth. It might be too late for me, but you can still save yourself.

Of Hatana and Gach

We had an interesting guest this week, and with him came some interesting food. A nice mixture of Cardassian, Klingon, and Taresian.

The cook, who hails from the planet Madison

Gagh (Klingon Worms) with (Cardassian) Yamok Sauce

Rokeg Blood Pie
(Plenty of iron for growing Klingon boys!)

Hatana

Jimbalian Fudge Cake

All washed down with Klingon Blood Wine, of course.


And finally,

The cook again, this time sizing up a small furry life form for a possible Klingon Stew, I think.

Good Grief, Starshine!

Let us consider as Exhibit A the following list of some of the silliest songs ever written:

1. Good Morning Starshine by Oliver
2. Gimme Dat Ding by The Pipkins
3. I Wanna Dance Wit Choo by Disco Tex and the Sex-O-Lettes
4. How Do You Do by Mouth & MacNeal
5. Chick-A-Boom by Daddy Dewdrop
6. Jam Up and Jelly Tight by Tommy Roe
7. Yummy Yummy Yummy (I've Got Love in My Tummy) by Ohio Express

If it did not violate numerous international copyright laws I would love to give you a link to these songs so those of you not of my particular generation could listen to them and see exactly how silly they are. These are songs that would make my children roll on the floor, howling with laughter.

Example:

Dad's Stereo: "Glibby-gloob-glooby, nibby nobby nooby, la-la-la lo-lo"
Children: (rolling on the floor) "Har! Har! Har! Hoooo! *Snort*, *Choke*, Har!"

Anyway, the thing you need to understand is that these songs have almost no artistic merit, make very little sense, and are extremely un-hip, if I can be so un-hip as to use that term. They would make many people's ears bleed spontaneously. They could kill Simon Cowell at 300 yards.

The other thing you need to understand is that I personally own all of these songs. Worse, I just paid 99 cents for one of them this very week. If I didn't already own them, and many others only marginally less abhorrent, I would be actively looking through iTunes and Rhapsody and Amazon.com, seeing if I could snap them up. Such is the pathetic nature of my taste in music.

Next, as Exhibit B, let us consider the following list of . . . Well, let's have you make your own. Go ahead: make a list of the most maligned musical acts of the 60's and 70's. No, really, go ahead and jot a few down. I'll wait.

*Hums the Pina Colada Song while waiting. . . .*

OK. Now I know your list contained at least the following three:

1. Barry Manilow
2. Neil Diamond
3. The Carpenters
4. Barry Manilow

(Yes, I know, but some of you really hate Barry Manilow.)

As you have already guessed, I own the complete collected works of all three of these artists -- well, the complete works up until 1985 or so when they quit recording the really good stuff. But the point is I really like them, despite what you and your sophisticated musical taste might think of me.

Finally, as Exhibit C, we have: The Entire Genre of Bubblegum Music. I like it. Quite a lot. This is how bad I am: I recently worked hard and long to procure the song "You Are The One" by the Sugar Bears. It was actually an MP3 taken from vinyl, and you can hear the pops of the needle hitting the dust and scratches.

The Sugar Bears are not real. They are animated characters. They are actually designed to sell cereal. But they cut an album in the early 70's. In the words of Frank Larosa:

Of course there is Sugar Bear himself, kingpin of the Post Super Sugar Crisp franchise back in the wild days when you could say "sugar" on national television. The marketing folks at Post cereals must have realized that Sugar would need a few companions to fill out his band. After consulting the top 40 charts of the day, they decided that what he needed was a tambourine-playing prostitute bear and a couple of drug-addled hippie bears to complete his musical ensemble.

According to Dr. Mark Hill, the vocals were actually performed by Kim Carnes (of Bette Davis Eyes fame) and Mike Settle, one of her partners from The New Christy Minstrels. They were backed by the same studio group and backup singers as The Partridge Family.

It is sick that I know that.

The point is, I actively sought out, and was delighted to find, a bad recording of a song ostensibly performed by a group that made The Archies look like The Rolling Stones (Archie would be Mick; Jughead would be Keith).

So there you have it: The ugly truth about my musical tastes. Perhaps in the future, I will blog more about some of the other music in my collection, not all of which is as lame as what you've seen here. In the mean time, if any of you have a song even worse than the ones I've talked about today, I'd like to hear about it. There's still some money left in one of my music store accounts.

Channeling Mr. Goodwrench

Prologue

As I have explained before, my relationship with mechanical devices, especially cars, is not always friendly. And honestly, it's not because I'm completely incompetent mechanically. At various times in my life, I have replaced stabilizer bolts, shocks, rotors, and thermostats. I can change my own oil, put on new brake shoes, and set the gap on spark plugs. Once or twice, I have even fixed other people's cars. So I'm not a complete idiot.

But apparently, in a previous life, I somehow set fire to an entire fleet of chariots or something. And now modes of transportation in general are out for revenge. Of course, my cars don't do anything too blatant -- no failing brakes or fiery tumbling down cliffs. No, they attack my blood pressure instead.

For example, my Sentra decided not too long ago that it would be really funny if the spring that opens the hood when I pull on the release lever would just quit opening the hood. So now it takes two people to open it, one to work the lever inside and one to pull up on the hood at the same time. Doubtless my car had visions of my pulling the lever, then trying to run out real quick to pull on the hood. As if. I knew that wouldn't work after the third time.

So I outsmart it by sticking a pry-bar under the hood, which gives just enough leverage and weight to pull up the hood when I pull the lever.



And then the pry bar falls to the ground, ready to pick up and use again.



Additionally, in the "blood pressure" department, the Sentra has a driver's side window that sometimes works and sometimes doesn't, so you don't dare open it in case the switch decides to short out and not close it. We also have a fan switch with two speeds: off, and high. Talk about two high-end "dealer only" repairs (I don't do electrical).

Chapter 1

Three weeks ago, on a Friday night about 11:30, my car decided not to start. It had been parked in my driveway for about 10 minutes, and it wouldn't start. After arranging rides for everyone who needed them in the next 8 hours, we made plans to tow it down to Firestone the next day.

Luckily enough, my family now has in it a Car Whisperer. There are those who call him. . . . Jake. And he came over the next morning just to take a look. Before he came, he called and said that if it was the starter, sometimes it helps to tap the starter with a hammer. So my brother and I tried to decide where the starter might be. I should point out that my brother is always willing to help with these matters, and in this case we took it in turns to frown, peer into the engine, poke at something, and walk around the car.

Now, I should point out that most of my good mechanical work has been on older cars, whose engines did not have to exist partly in hyperspace in order to fit into their allotted space. So it turns out finding the starter in a 99 Nissan is not as easy as it looks. Nevertheless I gave it the old college try. I found something near the front of the car that looked to me sort of like a canteen, which is vaguely reminiscent of a can, which is sort of what a starter ought to look like. It was underneath an aluminum shield, but you can see the side of it here:




In my defense, I want to point out that it did look like it had some electrical power going to it:



So I tapped on it, and wonder of wonders, the car started! Well, you can't imagine how happy I was. "Real Man, Armed with Claw Hammer (I don't own a ball peen), Repairs Own Car." All I was waiting for now was official validation from Jake the Car Whisperer.

Validation, in this particular case, came in the form of Jake telling me I had been tapping on the exhaust manifold.

Chapter 2

But, darn it, the car started, and that was worth something. To be on the safe side, I accepted Jake's offer to look it over, run some tests, etc. We took it up to AutoZone (AutoZone figures heavily in the story) and hooked it up to the meter. Turns out the battery was good, the starter behaved admirably under a load, and all seemed right with the world. Jake suggested that sometimes this (not starting) happens, and may never happen again. Goodness knows I was willing to believe that my car was capable of not starting just out of cussedness. So I chalked it up to sunspots and put it behind me.

Now, to understand the next part of this story, you need to know that about 16 months ago, in Red Oak, Iowa, the very same car decided not to start after I had driven it through a car wash. We let it sit for a while, hoping that whatever got wet would dry out and work again. And so it seemed to be. It started, and we rode merrily on to Nebraska. Where the "Check Engine" light came on. It seemed to run a little rough, so when we stopped for gas in -- Lincoln, maybe? -- we drove into town to an AutoZone to have them read the code. The code said we needed a new idle air control (IAC) valve, but they assured us that it wouldn't hurt us to keep driving and make it to Utah before we really replaced it. So we kept on westward, and eventually the "Check Engine" light went out, and we chalked it up to water or something.

But psychologically, the damage was done. In my subconscious, the IAC, the Check Engine light, and the car not starting were all tied together.

The Check Engine light had actually come on a couple of weeks before the "not starting' incident, and we had again taken it to AutoZone, and they told us that the code could mean any number of things, including the IAC, but maybe not, so there. And it started running better, so we made a mental note to have it checked out in March, when we needed to have it inspected anyway.

Until the car didn't start again.

Chapter 3

Well, I figured, if tapping on the manifold made it start, so might tapping other places. So I tapped away, and the car started, and I thought, "Well, my hammer and I can make it to payday, anyway. " Eventually, we started tapping it up by the IAC, and then eventually on the IAC, and lo! it suddenly became clear to me. For some reason, the faulty IAC was making the car not start. It was clear I needed to replace it. Back to AutoZone, and $160 later I had a brand new IAC to put in the next day, when it was light again.

That night, I made a run to Rite Aid with my son. The Divine Ms B, being sensible in most matters, warned us not to turn off the engine. But, as two males who had each tapped the car back to life numerous times, we were confident of what we could do with a claw hammer.

My brother came to our rescue in the Rite Aid parking lot when no amount of tapping would make the car start. I put the new IAC in by flashlight. The new IAC was clean and shiny. Hopes were high. My brother and I had given it our very best frowns.

The New IAC

The car wouldn't start. So of course we called the Car Whisperer. He came, he tapped (this time on the real starter, with his long pry-bar) and it started. So it was now clear that the starter was, in the words of The Princess Bride, "only mostly dead." And getting deader. Jake estimated it would start about 6 out of 10 times, until we replaced the starter. Still a few days left until payday, too.

Jake showed me the little gap in the manifold that was the only access to the starter from the top:



And I learned to use my pry bar to tap, tap, tap.




For a while, I seriously considered using a toilet plunger handle to tap the starter, under the not-as crazy-as-it-sounds belief that the Car Gods would be somewhat appeased if I just admitted that I had to carry a toilet plunger to start my car.



Chapter 4

In a couple of days, the Car Whisperer came over, and put a new starter in my car. We got it at AutoZone, of course. He had to do it from underneath, and bend a cross-beam to get at it, and probably had to use his tricorder to do a little work in hyperspace, but he got it done in less time than he thought (given my Car Karma, it's good to double the estimated time and go up one unit, e.g. 2 hours -> 4 days). But it all worked, and Jake has earned an assured place in heaven, if I have anything to say about it.

Postlogue

1. I claim I needed to replace the IAC anyway, and the check engine light hasn't come on again. So let me have that small bit of comfort, OK?

2. Last week, I dropped $2000 to rebuild the transmission.

Apparently the blood pressure route was taking too long.