Word problems. Remember them?
James has to ride his scooter uphill to school during a snowstorm one July. The school is 4.5 miles away, but first he has to stop at the shop to put snow tires on his scooter. To beat the cold, James holds two boiled eggs he just cooked for his lunch. The scooter tire shop is on the way, but opens two hours after school begins, and the radio announcer hasn’t said that the school is closed, so James has stalled long enough but now must leave. What color is his scooter? How does James manage to keep his hands warm on the ride back home later that afternoon since he will have consumed his hard boiled eggs for lunch, and why hasn’t the school superintendent called a “snow day” because of the bad road conditions?
Four of us sat around the table one night, working on the Super Quiz, a syndicated daily piece found in our local paper. Science, geography, literature, movie trivia, pop culture and music are usual topics, but this one night, it was word problems, requiring knowledge of basic arithmetic and algebra, and a bit of common sense.
The answer may be simple, but the question is ambiguous. It is not so much about solving the problem, but of secondary observation. Here’s the question: “Three pens cost $15.00. How much do five pens cost?” Are pens individually priced? Do they come in packages of three? One has to wonder if there is a discount when buying multiples, or if the pen manufacturer’s marketing department offers a “break” when a customer purchases the package that contains extra pens, even though two of these are in garish colors and the ink is purple. Maybe there’s a coupon somewhere, but if it’s online and a personal account has to be created, does the customer need to print out the coupon? This costs money to be sure. Printer ink comes in these ridiculously small packages and is quite expensive. Or perhaps the customer can electronically choose this item to be “moved” to their new online password protected account, and so the checkout scanner “reads” the lower, adjusted price and charges only that.
But wait, there’s more! Perhaps there is a discount if the customer uses cash instead of credit, because the banks charge a fee for each credit or debit transaction which then must, of course, be charged back to customers. And what if a large corporation buys pens? Do people use them anymore? Certainly there is the expectation that a handsome percentage will be deducted, and this is for a shipment that will be delivered and charged by invoice with payment due at the end of the billing cycle. Are pens more costly on certain days of the week, like airline prices? Who can answer this word problem until all these variables have been filled-in? And is the discussion for ball point, or click pens, and for gel cartridges, or traditional ink? Are there caps on these pens?
And forget the pens. What if the word problem offers a scenario where a boss needs to know how many more employee-hours are needed to complete a task in six fewer days than the projected four week timetable with 135 people already on the payroll working eight hour days? Sure, this can be calculated, but where does this scenario exist? People at a bank in January stuffing tax statements into envelopes work at different rates, right? More experienced envelope-stuffers can heap up a huge pile of the finished product long before most new-hires, unless the conversation is particularly good around the table and then nobody will finish in time. Or if there’s a paper cut, and then one has to factor in time to apply a bandage.
The problem assumes that each and every person works at the same speed and level of efficiency, and that each employee’s work has no bearing on the other employees’ work. What’s the point of doing the math if the obvious correct answer doesn’t correspond to reality?
Think about a construction site. There are only so many pieces of machinery that can be used at one time. Crane operators rely on workers to secure the item to be lifted. Other workers must untie the item once it has been hoisted to the correct position on the skyscraper being built. What manager will hire new people to tie and untie more bundles to get the building completed sooner when the site can only accommodate two cranes? What is wrong with these people?
Perhaps the manager of the building site needs to buy some pens (and paper, but that’s another word problem) to figure this stuff out. Or perhaps the manager needs to go back to managerial school because who would hire this lost soul? Or better yet, the manager should just hire James. After all, this kid had the wherewithal to get himself ready for school, make his own lunch, provide his own transportation and not rely on a school bus or parent to drive him, listen to the radio to determine the day’s schedule, take weather into account, and even figure out how to ride his scooter while holding onto eggs, one in each hand! Who wouldn’t want an employee like this?
And now I know why my dreaded teacher gave the entire second grade class a “D” for word problems. She must have known from the start that all these years later, we still can’t do them!