Wednesday, January 21, 2009

Wednesday Math, Vol. 57: Second thoughts on math education

Last week, I started my series of posts on what math skills I would like to see taught to all high school students, the kinds of things I think should be on a reasonable exit exam. Last week, I wrote about differently stated problems and seeing the similarities. This is an important part of mathematical literacy, also known as numeracy. This week, I'd like to discuss the kind of real life word problems people should be able to handle as a result of a math education rooted in basic skills and applications.

Scenario: There is a driver who fills the tank on every visit to the gas station and then restarts the trip odometer. On this particular day, the trip odometer reads 273.4 miles before the gas is pumped and it takes 9.233 gallons to fill the tank.

1. How many miles per gallon did the car travel on average during this trip? Give the answer rounded to the nearest mile, and rounded to the nearest tenth of a mile.

2. Given these numbers, how many gallons of gas does it take to travel 100 miles on average? Give the answer to the nearest gallon and the nearest tenth of a gallon.

3. If the driver buys gas costing $1.959 per gallon, how much did the gas cost to the nearest penny? If the driver opted for the gas costing $2.099 instead, what is the total cost to the nearest penny? What is the difference between the two totals? What is the percentage difference?

4. The driver has a round trip mileage from home to work of 41.2 miles per day, and works five days a week. What is the cost of gas for these trips each week to the nearest penny, assuming the gas mileage stays the same as the numbers given in the original scenario and the cost of gas is steady at $1.959 per gallon. What was the cost last year when gas was $3.499 per gallon?

5. The driver works 50 weeks a year, and on average in those weeks worked, there are ten holidays. How many miles does the driver drive the car to work in an average month?

6. Trip from home to work took 25 minutes on Monday, and the trip from work back home took 33 minutes. What was the average speed on the trip in? What was the average speed on the trip home? What is the average speed for both trips combined? If these times are typical, how much time does the driver spend going to and coming from work in an average month, written as x hours and y minutes?

Being a math person, I don't think of these problems as particularly difficult. I am not interested in setting a super high standard for graduating from high school. From what I can see, this just adds to the dropout rate. I do expect universities to set higher standards than this for admission, but the overall question I am trying to get a handle on here is what mathematical skill set should we expect from people who will be workers, consumers and citizens in a modern industrialized society.

In Matty Boy's dream world, I wouldn't just ask these questions of a bunch of nervous 18 year olds, but showing literacy and numeracy would be a requirement for citizenship. I know that literacy tests have a bad and racist history, so I wouldn't make the prize for passing a test like this every five or ten years the continued right to vote. Maybe proof of numeracy and literacy could be worth a tax credit.

Just an idea. Since a lot of people already understand that lotteries are a tax on people who are bad at math, maybe the government could give some small bonus to people who keep their math skills sharp.


Wormwood's Doxy said...

In the short-term, I'd be happy with cashiers who could count your change back to you...


Karlacita! said...

Yeah Doxy, I love it when you hand over a fiver for the $3.43 bill, and then you find three pennies in your wallet.

You hand the .03 to most cashiers, and you can watch a complete brain freeze in super slo-mo.

I'd say we need to get serious about math and stop teaching it (and all sciences) as if there is a right answer. We've erased the natural mathematicians and scientists - those who love to ask the questions, make mistakes, and keep working - we've trained that natural ability right out of our students.

Instead, we have a citizenry that can follow directions and and take tests, always looking for the "right" answer instead of understanding that math and science are a lifelong process of discovery. This is a terrible thing for a titular democracy to have done to its people.

dguzman said...

Karlacita for Sec of Education! Over-reliance on standardized testing (which is nothing more than a huge money-making scam industry) has completely ruined education. People need to be allowed and taught to think critically, not just fill in bubbles. And whether someone can do well on the white man's tests doesn't determine whether that someone is "college material" or not.

jolie said...

and here in texas, the esteemed state board of education is roiled in debate over teaching evolution.
a majority of the SBOE supports creationism, and they want to continue to frame evolution as having "strengths & weaknesses." this is their devious way of inserting creationism's bastard offspring, intelligent design, into science classrooms across the state.

this isn't a new effort. the strengths & weaknesses language has been included in science textbooks for two decades.

jolie said...

here's a good blog entry on how the religious right elected to the texas state board of education intends to continue to subvert science curricula, and specifically teaching evolution: Half-Empty.

hal writes a terrific blog, btw.

Matty Boy said...

I'm going to respectfully disagree with my sister about our educational system. I agree that reliance on standardized tests is a serious problem, but it's not like this is brand new.

I think the more telling problem is how the "natural scientists" can make their talents manifest these days. There's a famous story about Newton building his own toys when he was a kid, little toy wagons with working axles and such. The world is so complex nowadays, about the only thing the clever kid can do along these lines is taking apart some simple toys and putting them back together. If a child never shows an interest in anything but video games and electronics, he or she doesn't have a similar path to become a "hands on" person with technology.

Mathman6293 said...

At open house I had parent jump my ass about his daughter's inability to multiply. But at some point parents need to take some responsibility, too. That kid should have learned to multiply in 3rd or 4th grade. He did not like my solution - Mr. TI 30 so I can teach rate of change. Where was he when she should have learned it?

Numeracy, I think is very important but when parents have a tough time with it the problem often follows the kids. Compound that problem with elementary teachers who are expected to teach everything.