by Dr. Mark H. Shapiro
"Do not worry about your difficulties in Mathematics. I can assure you mine are still greater."... ....Albert Einstein.
Commentary of the Day - February 19, 2004: Real Math - What if they gave a test, and nobody passed? Guest commentary by Felice Prager.
I am standing in the fruit department at Safeway. I have narrowed my choices to three cantaloupes. They are all pretty much the same: same size, same firmness, same coloring. I pick each one up and give it the "squeeze and sniff" test. I wonder to myself, "How many other people have sniffed the end of this cantaloupe? How many fingers have squeezed this melon rind?" I also try to recall where I learned how to do this. Did I watch my mother at the supermarket squeezing melons? It definitely isn't something that was inborn, except I'm sure there are men out there who will swear they have a sixth sense, the melon sense. For me, I'm sure it's something that took practice. I'm sure I didn't always do it right. With experience I've become quite adept at the art of choosing my melons. Regardless, I put the cantaloupes back on the stand; I can't eat melon while I'm on the Atkins Diet.
I like supermarkets. I spend a lot of time there. I find comfort in being near things I can't eat. Plus, the people at the supermarket know me by name. "Thank you," says the clerk, (glancing at my credit card receipt,) "Mrs. Prager. You've saved $11.56 by shopping at Safeway today."
"If I've saved $11.56," I reply, "where is it?"
My response leaves the clerk dumbfounded. "Can we help you to your car with your bags, Mrs. Prager?"
I don't even correct his use of "can" instead of "may" --- I am on my best behavior at the supermarket. I need Safeway more than Safeway needs me. "Thank you, but I can load my own groceries," I say with my polite supermarket smile.
Back in my Jeep, I examine my receipt. How could this meager amount of low carbohydrate food I just moved from the shopping cart be worth $100? (And how much fat did I burn moving it?) This gets me thinking about math. I start multiplying and dividing in my head:
If Felice works five hours, how much per hour does Felice have to earn to cover the $100 she just spent at Safeway on foods that definitely need some fiber in them to make them seem worthwhile?
I always find satisfaction in knowing I am able to solve for unknown variables.
Felice has Q pounds to lose. Given her highly resistant metabolism, she is only losing 1.5 pounds per week during her extended Induction Phase of the Atkins Diet. If she sticks to her diet, how many pounds will she have lost in six months, and will she fit into that expensive bathing suit she bought in 1993 and never wore. Will the bathing suit still be in style? And will her husband ever find out?
I've been thinking about math a lot lately. A day doesn't go by when I don't think about math. Maybe it's that it is almost income tax time. Or maybe it's the fact that I'm paying out-of-state tuition for my son to attend a state college in another state so that he can be with his girlfriend. Or maybe it's what I read in the newspaper.
This was in the Arizona Republic (Jan. 25, 2004):"On Monday, the State Board of Education will consider making it easier for this year's eighth-graders to pass the AIMS (Arizona's Instrument to Measure Standards) math test they'll face in April. "This is the correction of an error," Arizona schools chief Tom Horne said. "The problem is the way the test is scored." In the past four years, no more than 21 percent of Arizona's eighth-graders have passed the AIMS math test, well below the passing rate of students who take the test in other grades. To pass, eighth-graders must get 78 percent of the 50 math questions correct. State officials want to change that passing score to about 72 percent, allowing students to miss three more questions. Had the change been in place in 2003, Horne said, 32 percent, instead of 21 percent, of Arizona's eighth-graders would have passed the test."Two years ago, when my kid was in eighth grade, he passed the Aims test. He didn't need a three questions gift to get over the bar. He did his homework, went for extra help when he didn't understand, and worked hard.
"It's 2 AM on a Tuesday morning, and Felice can't sleep. She's not hungry, but she just needs something to eat. She goes to the refrigerator and finds the half can of Diet Rite® Cola she didn't finish. She chugs it down. "Nope," she says to herself, "I need something to chew." She goes to the cabinet and finds the bag of pecans halves she bought at Safeway earlier in the day. According to Dr. Atkins' New Diet Revolution (page 174) one ounce of pecans equals approximately five grams of carbohydrates. If one ounce, according to Dr. Atkins, is equal to thirty-one nuts, and Felice eats fifteen and a half pieces, does Felice count these carbohydrates for Tuesday or for Wednesday? And did Dr. Atkins count a pecan half as one nut or do two halves equal one nut? Did Felice eat two and a half grams or one and a quarter grams of carbohydrates?
This was in the Arizona Republic (Jan. 14, 2004) a few weeks ago:"Students who excel at math say a love for the subject and their parents' support are among the reasons they do so well…Parents can help by letting children gravitate toward the areas of math they like best, math experts say. Some children like variables while others are good at geometric shapes. 'Let them go with their interests,' said Bill Butterworth, associate professor of mathematics at Barat College of DePaul University in Lake Forest, Ill. Butterworth, who judged the high school math competition in Phoenix, said game shows such as "The Price Is Right" help children develop math skills of strategy and probability. He recommends parents work with their child's teachers and check out what math resources are available through the school. Many schools hold family math nights. Sophomore Jake Gottlieb of Scottsdale looks for math's real-life applications. When he was a child, he would play "McDonald's restaurant" with his mother, making 'purchases.' At age 3, he could count to 100. When he was seven, his parents bought him $100 in stocks so he could practice percentages. He sold the stocks about a year ago for $3,000."Maybe I was doing the right thing when I used to let my kid, with my supervision, make transactions at the store. When I owned my own business, I'd show my sons how invoicing worked. My sons knew what the "bottom line" was before they could ride two-wheeled bikes.
When hiring employees for my business, I used to ask two questions. They helped me decide who could think enough not to make a stupid math error when making a sale.
These were the questions:
1. If an item that costs $9.99 is on sale for 50% off, about how much will it cost?
2. You have to give a customer $26.25 in change. From the list below, what is the way you will use the least amount of bills in giving the customer change:
a. two ten-dollar bills, one five-dollar bill, one one-dollar bill, and a quarter.
b. One twenty-dollar bill, one five-dollar bill, one one-dollar bill, and a quarter.
c. One twenty-five dollar bill, one one-dollar bill, and a quarter.
Job seekers answered "c" for the second question more times than I want to admit, and figuring out "about how much" for the first question took a pencil, paper, and time, and many times, their answers were far from five dollars. I would watch in amazement as they added or subtracted or multiplied or divided; then I'd show them the right way to estimate it in their heads and tell them I'd call if an opening became available.
My kid got both questions correct without my help. He was eight at the time.
So, what does this say? Nothing.
The proof was in the Arizona Republic (January 21, 2004) again:"Scottsdale's newest reality TV star apparently has chosen fame and possible fortune over a career as a Catholic schoolteacher.
Randi Coy quit her job Wednesday as a first-grade teacher at Pope John XXIII Catholic School Community in northeast Phoenix.
Coy, 23, appears on the Fox show, "My Big Fat Obnoxious Fiancé", which debuted Monday night with 19.6 million viewers nationwide.
Coy had been on unpaid administrative leave from the school since Thanksgiving…
On Friday, Coy told The Arizona Republic that she was unsure about her future.
"I'm young and I did this for the experience, and who knows what's going to happen?" Coy said. "But right now, I'm just taking it day by day. And hopefully, yes, definitely I'd like to go back to teaching. I'm just going to see what happens."
But on the first episode of the six-episode series, Coy mentioned the difference between her teacher's salary and her potential $500,000 prize."
I've been thinking about math a lot lately.
My older son called the other night. This is the son who is going to an out-of-state college for which we're paying out-of-state tuition. Apparently, he and his girlfriend are planning to go to Florida for spring break. They have it all figured out. They'll get a cheap fare on plane flights and they'll stay with her relatives. My son did not mention sending us any money to cover the cost of his car payments or auto insurance. Nor did he mention any other expenses they'd have in Florida beyond getting there.
Maybe it's me. Maybe I've been spending too much time thinking about math.
© 2004 Felice Prager
Felice Prager is a former English teacher and freelance writer from Arizona. She publishes the Write Funny pages.
The IP comments: Whether it's 32% or 21% of Arizona eighth grade students who pass the AIMS test, the sad fact is that the majority of students don't pass. What does that say about mathematics education in the Arizona elementary schools?
© 2004 Dr. Mark H. Shapiro - All rights reserved.