Category Archives: Math

Loaves and fishes

The Bureau of Labor Statistics released the latest round of unemployment numbers today. The current unemployment rate is sitting at 14.7%.

If you are not among that 14.7%, I see three ways to look at this problem:

  1. Erect a Somebody Else’s Problem field around it and keep going. Anyone who considers this a reasonable option probably isn’t reading this blog in the first place. (I hope not, anyway; I’d hate to think my writing appealed to that sort of person.)
  2. Drown in guilt and frustration over the unfairness of it all. I did that for a while this week. You may be shocked to learn that it benefited exactly no one.
  3. Let the math motivate you. When the world seems to be spinning out of control, I tend to close my eyes and trust-fall into the arms of Muhammad ibn Musa al-Khwarizmi, better known as the Father of Algebra. In the >30 years since I learned to solve for x, ol’ boy has never failed me.

With that in mind, let’s look at the numbers:

If 14.7% of us who normally have jobs are now unemployed, that means 85.3% of us are still working. (Note: The unemployment rate is different from the labor-force participation rate.)

If my scratch-paper scribbling is right, if every working person had the same income, the 85.3% of us who are still working could take care of the rest by sharing just 17.2% of our income.

We don’t all have the same income, and we can’t all afford to share that much. But honestly, I think 17.2% represents a worst-case scenario, because a lot of currently employed people are white-collar workers who can telecommute, and a lot of currently unemployed people are service-industry workers.

Because white-collar jobs tend to pay better than service jobs, we probably don’t need every currently employed person to give away $1.72 of every $10 s/he earns in order to pick up the slack; we just need all the current haves to take an honest look at our available resources and figure out how to leverage them to help as many of the current have-nots as possible.

If you identify as Christian, you already know a guy who did that at least twice and ensured that his initial investors got a pretty impressive ROI out of the deal.


Mathematical misconceptions

As an old math teacher, I was more than a little concerned by some of the comments I saw on a stats-driven story we ran in the paper today. Because the misconceptions I saw in the comments are fairly common — and because some of my former students read this blog — I thought it might be worthwhile to address a couple of the more egregious examples here, for the benefit of anyone who has slept since freshman algebra.

Misconception 1: If you don’t have data for the full year, any conclusions you draw based on that data are statistically invalid.

Reality: Full-year stats are nice to have, but as long as you’re comparing apples to apples, you can draw meaningful conclusions without them. If I compared an 11-month period in one year to full-year data for another year, my conclusions would be invalid. But if I compare an 11-month period in one year to the same 11-month period for several preceding years, I can make valid comparisons even if I don’t have that twelfth month.

Misconception 2: If numbers look bigger, they are.

Reality: Not necessarily. Remember fractions? Ratios? Decimals? Let’s look at some examples:

1/2 is bigger than 1/3, and 1/3 is bigger than 1/4.

If your odds of something happening are 1 in 14 (which can also be expressed as 1:14 or 1/14), then that thing is more likely to occur than if your odds of it happening are 1 in 18 (1:18 or 1/18).

At least one reader didn’t understand that. He was convinced that even though the number of crimes in a given jurisdiction had gone down from one year to the next, the crime rate — expressed in the article and accompanying chart as a ratio of crimes to population, reduced to lowest terms — had gone up. I assume he drew this conclusion by looking at the second number in each ratio. Since that second number got bigger, he thought that meant the crime rate was going up.

These folks aren’t alone in their confusion. A lot of people don’t understand how stats work — which makes them easy targets for unscrupulous people who do.

You shouldn’t trust stats blindly, because they can be manipulated, and people can make mathematical errors. But you don’t have to be afraid of them, either. Statistical data can be incredibly useful, but it’s hard to use a tool if you don’t know how it works.



So this evening, my best friend from college — who is obviously male — asked me an earnest question about the connection between weight gain and women’s bustlines.

I replied with a mathematical function. But I would like the record to show that I did not calculate the first derivative of that function based on my own measurements, because that would have been tacky.

Maybe I should just start having my paycheck direct-deposited in Thinkgeek’s account.


Chocolate pi

This is what happens when a math teacher accidentally melts too much chocolate and then remembers that she owns a silicone tray that makes pi-symbol ice cubes. Not quite as geeky as the cake my sister made the other day (she constructed a three-dimensional replica of the Starship Enterprise out of marshmallows and fondant for my nephew’s birthday), but nerdy enough for my purposes.

I’m thinking of using the Wilton candy book’s recipe for “sparkle jells” to make some pi-shaped candy for my Algebra I kids. We’ll see how that goes. It’s pretty hard to screw up Jell-O….


Chalking it up

My Algebra I kids are learning to graph inequalities on a number line. To teach them effectively, I needed a tool that would allow them to graph several problems in rapid succession, with answers big enough that I could see them from halfway across the room. After some thought, I came up with a number line written on a yardstick that had been coated on one side with chalkboard paint. I used the inch markings — which were stamped into the wood — as guides to keep the spacing even. They were cheap (less than $30 worth of materials for the whole project) and worked really well.

The picture above shows one of the number lines and another little tool I made for the classroom: I took cardboard cutouts of robots (available from Michael’s for $1.99 a dozen) and sprayed them with the chalkboard paint. The kids will use them to show me their answers to problems they work in class.

Here are some closeups of my handiwork:

I like the robots. They’re kind of like those dry-erase paddles you get at teachers’ stores, except they’re a lot cheaper ($5 for a class set instead of $105) and a lot cuter. I’m hoping they’ll overcome some of the kids’ shyness about sharing answers in class. Calling out an answer is scary, but holding up a cardboard robot with the answer written on it is just funny.

The other cool thing about using homemade items in class is that they make the kids feel loved. My kids always get really excited when they find out I made something for them myself: “You made that? Really? How long did that take? I can’t believe you spent all that time making that just for us!”

Handmade means something to them. My mentor/saboteur at my first teaching job understood that. She had her faults, but her classroom was a very warm, inviting space, with handmade valances at the windows and little craft-show decorations everywhere. It felt more like a friend’s kitchen than a gritty urban classroom, and that really resonated with the kids.

It occurs to me that I have spent 12 years hoarding my bad experiences with this woman and dismissing the good. Until this minute, I don’t think it ever occurred to me to acknowledge what she was doing right or to consider that she might have loved her kids as much as I love mine. There’s another blog entry in that, but I’ll save it for tomorrow, as it’s getting late tonight.

For now, I’ll just bask in the knowledge that I am healing, be it ever so slowly.


Folk Thursday: Sharon Clark

Ron found this a couple of weeks ago and suggested I post it. More jazz than folk, but an amazing treatment of a song I’ve always loved. Karen Carpenter never had it so good.

On a completely unrelated note, I got an 87 on my calculus test today. Not as good as I would have liked, but much better than I was expecting based on the amount of trouble I had with the homework.

Calculus is so weird … I struggle and struggle and struggle through the homework, and then the day of the test, it all just sort of clicks. Weird.


Hippie nerd

So a reporter from Channel 6 called me last week to schedule an interview about the Amazing Technicolor Dreamcar.

As it turned out, the 45 minutes or so that I spent doing the interview was the only break I got from a calculus homework marathon that started at 8:30 this morning and ended about 15 minutes ago. “Ended” isn’t really the right word. I still have three problems left to work, and I have the feeling they’re going to be nasty. I spent five and a half hours in the math lab at TCC, and I’m guessing at least two hours of that was actual tutoring. (The rest was me frantically trying to get my homework done and desperately trying to figure out how to do things myself, which didn’t work all that well.)

I came home to find my inbox full of nice messages and Facebook friend requests from people who had seen the segment about my car on the 5 o’clock news this evening.

Fortunately, the segment is online, so I got to watch it a minute ago. I think it turned out pretty well. You can see it here. (I’m not sure whether that’s a permanent link or something that will disappear later, but the reporter, Rick Wells, told me the segments that appear on the Web site are all archived, so you should be able to find it later.)

I’m not sure what it says about me that I missed the segment on my hippiemobile because I am such a nerd that I spent the better end of 12 hours doing math today.

In case you are wondering, the calculus textbook will be coming with me when I go to Illinois this weekend. Maybe Daddy can help me with my homework.

I’m giving serious thought to cutting my losses and going to bed now. The left side of my brain is now ticked off at me for making it work overtime, and the right side of my brain isn’t speaking to me because I’ve been ignoring it all day.

Meanwhile, the entire rest of my body is grumbling about the fact that I’ve been forcing it to survive on a can of Slim-Fast, a small bowl of ice cream, and half a piece of garlic bread.

Maybe a dinner break will mollify everybody….


She shoots, she scores!

My trig instructor told us at the beginning of the semester that he would drop our lowest test score. This meant that if we did well on all the regular tests, we could blow off the final — which is scheduled for next Tuesday night, at the same time as the KISS concert at the BOk center.

Thanks to a solid performance on tonight’s test, I do not have to take the final, so I am free to rock and roll all night instead of worrying about the law of cosines or the polar form of y=ax + bi. Not that I don’t enjoy math, but graphing the arctangent of the secant of theta would be more interesting if it involved pyrotechnics.

By the numbers:

Score on this evening’s trig test: 90 out of 100.
Score on this evening’s trig homework: 20 out of 20.
Average for the semester: 95.

I have now settled all my old scores. Algebra and trig both kicked my butt in high school. I have finally returned the favor and am ready to take on calculus either next semester or in the summer, depending on how my schedule looks.

I must say, I am rather enjoying my nerdiness….


Hard-won victory

Conic sections and quadratic equations kicked my butt in 1991. Eighteen years later, I have returned the favor: I got a 94 on my algebra final and a 97 for the semester.

I’m trying to decide what I want to do next. I think I’d like to take trig and calculus, but I’m kind of wavering, because I’m also thinking about grad school.

I was thinking about it much harder before I figured out that the cheapest option would set me back more than $8,000, and I’d have to settle for something other than English (my first — and most obvious — choice) or math (my second).

Why is it that so many colleges assume that if you are a teacher, and you are pursuing a master’s degree, it is because you want to be an administrator? What if I’m perfectly happy being in the classroom? What if I have no desire to be an administrator? What if I just want to get class credit for spending the next two years shooting the bull about Faulkner? Is that so wrong?