The National Council of Teachers of Mathematics wants students to learn math by problem solving rather than by word problems. Why?

Answer 1

The National Council of Teachers of Mathematics (NCTM) is attempting to obtain a national standard for the teaching of mathematics. This will cut across all areas and through all grade levels in an attempt to better organize and present the essential ideas of mathematics to the math student, no matter the student's location or whether he's in first, sixth, eleventh, or any other grade. In its efforts, the NCTM has its eye on problem solving methods. This does not mean there will be no world problems. When we look at their guiding principles for mathematics, we see "Problem solving means engaging in a task for which the solution method is not known in advance." There is nothing in that suggesting there won't be word problems. How foolish it would be not to use some word problems; they're just super. Word problems give the student of mathematics an opportunity to "construct" a framework that will lead to the discovery of an approach to solving a problem. With the framework in place, plugging in values and turning the crank to get the answer should be almost routine. Given an equation with variables and some values invites the use of a calculator. But with some facts in hand and no equation, how does the student use what is know to discover what was asked for? This is the problem that the word problem presents to the student. No, the word problem will not be abandoned as a teaching/learning method. It's far too valuable. Having said that, let's try something. Here's an equation looking for a solution: t - 1 = 400/s If t = 6, what will s be? We'll plug the 6 into the equation in place of t there. And 6 minus 1 equals 5. As 5 equals 400 divided by s, if we multiply both sides of the equation by s, we'll get 5s equals 400. If we then divide both sides by 5, we'll get s equals 80 for the answer. Piece of cake. Now let's look at this problem: A fast commuter train covers a route 400 miles long. It spends a total of 1 hour dropping off and picking up passengers at stops, and the rest of the time rolling down the track. What is the average speed of the train when it is moving if it makes its run in 6 hours? Now what? How can you figure out what the answer is? What will the average speed of the train be while it is moving? How do you set this up? Let's work through it. The train covers 400 miles in 6 hours, but it is stopped at stations for an hour of that. That means it is only actually rolling for 5 hours. We need an equation. We'll say the time for the journey is t and the average speed of the train will be s. As the journey is 400 miles, to find average speed, we'll set up this "starter" equation: t = 400/s This would normally give us the average speed, but the problem here asked for the average speed when it was moving. And in our "starter" equation, we did not account for the time standing at stations to accommodate passengers, which was 1 hour. We'll need to subtract that 1 hour from the total time for the journey to account for the actual time the train spent rolling down the track. Here's the revised equation: t - 1 = 400/sDoes this equation look familiar? We just worked it for t = 6, and that's what you'll do to solve this word problem. A correct solution will yield that 80 miles per hour figure, just like before. The "level of difficulty" in getting to the equation makes the actual solving of the problem (solving of the equation) almost trivial, does it not? Why on earth would we drop "word problems" from a mathematics curriculum, and that's not a question. It would be foolish beyond measure to kick them to the curb. When we encounter problems in the real world, they come at us more in the way of the word problem. We don't get a "package" with an equation and have the boss ask us to solve it. The boss or even the boss' kids could solve an equation. Rather, the complex and difficult problems that have to be solved today demand higher orders of mathematics skill. A classic question comes to mind. "Would you get on an airplane and fly in it if the aircraft was not designed by engineers?" No sane person would say yes to that. Mathematics is not some mystical ritualistic mumbo jumbo that is included among school subjects to confound students. Rather, it is a tool. It begins as a hammer and turns into a wrecking ball that we use to smash the difficult problems associated with things like figuring the loads on the wings of aircraft, heat build up on the belly of a space shuttle, the diameter and wall thickness of piping for municipal water supplies, and the thickness of the concrete road bed for a multiple lane freeway overcrossing. We often don't think about the "math power" behind all the complex underpinnings of the society in which we live. The latest goings on with Hanna Montana or the Jonas brothers make mundane things like algebra a big drag. But that big drag is a gateway to higher orders of mathematics, and none go there but through that portal. 'Nuff said.