Need Mathematics Taught in School Be Relevant?

Dan Mayer, a high school teacher, posted in his popular blog a story of a teacher development event where a coach posed the following problem:

A youth group with 26 members is going to the beach. There will also be 5 chaperones that will each drive a van or a car. Each van seats 7 persons, including the driver. Each car seats 5 persons, including the driver. How many vans and cars will be needed?

In the post, Dan descibed his dismay with the stupid problem and asked three questions:

"One, is the problem realistic? Would a real person need to solve this problem?
"Two, is the solution realistic? Would a real person solve the problem using a system of two equations?
"Three, in what ways does this problem help our students become better problem solvers?"

The discussion that followed makes an edifying and sobering reading. I took it to the heart and posted the following reply:

With all due respect, all three Dan's questions are utterly misplaced, which is not to detract from the fact that the problem is rather absurd.

What is a realistic problem? To whom should it be realistic? How many realistic problems can you compose? Do you need to? Must students be taught exclusively with realistic problems? Is the power and beauty of mathematics in solving realistic problems?

Mathematics is replete with problems that are not realistic in the context of the questions. So what? Let's tackle this one.

Can you reformulate the problem any how so that a modification has the same solution? Do that without solving the problem. Ask each student to come up with a different problem and then solve them all at once. This would give them a glimpse into the power of mathematics.

First, you can get away with the chaperones. 26 astronauts are to man 5 cruisers, some with 4 and some with 6 seats. There are 5 pizzas. the smaller ones cut into 4 pieces, while the big ones are cut into 6. There are 26 kids to feed. Ask the question. An art teacher brought 5 packs of 4 and 6 brushes to distribute between 26 students. If every student got a brush and none was left over, how many of each kind of packs were there? At an animal farm, 5 residents have ordered warm socks for the coming winter. Horses ordered 2 pairs of socks each, but pigs each ordered an extra pair. They received the total of 26 socks. How many pigs were there?

How many students do you have in your class? Will they all think of different scenarios? Regardless, what all scenarios are going to have in common? What if there were 25 students? (Just in case, at least one expected solution would result in a fractional amount of cars and vans. Could your students see that without solving the problem?)

You may teach numeracy or you may teach mathematics. But this is a bad idea to confuse the two. Students won't be paying electric or phone bills for years to come. Do you think they will remember, when the time comes, the lesson built around such calculations that are deemed so relevant?

The fact is that most of the populace have very little use for mathematics during their lifetime. The present system, from the kindergarten through college, that stipulates otherwise is built on a lie. The textbook publishers and writers benefit from that, the teachers are on the paying end of the myth. The system is unlikely to change any time soon. Any way, insistance on the need to feed students relevant problems cannot and will not change anything. The real question for the teachers to decide is whether they'll be teaching mathematics and if the answer is yes, then they may want to learn the art of making problems (even apparently stupid ones) relevant and not prowl for relevant problems.

MANIFESTO

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