THERE are math teachers who like to teach only one method of solving problems and who will mark students wrong if they use another method but arrive at the correct answer anyway. This is all the more unfortunate if these are elementary or high school teachers, because they are giving kids very wrong foundational ideas about math.
Math is already a complicated and stressful subject for most kids. The least any teacher can do is to aid them in understanding it in any way they can, instead of insisting on their way as the only way. (I am, of course, referring to the subject as traditionally taught in schools. Those of you who have been following my recent articles would be aware that I am advocating a wholly different method of education altogether but that is a topic for another day.)
If you look at how brilliant mathematicians solved “unsolvable” problems, it was because they were able to see things in a different way that other people did not see before. They were able to break conventional methods by introducing something others did not see before. Teachers ought to encourage that instead of quashing it. Egotistic teachers, however, see a different method as a bruise on their ego, especially if it was one they had never thought of before.
I remember, with much appreciation, my grade 6 teacher, Mrs. Lilia Peralta. During her lecture of a certain method, my classmate Anthony Montecillo’s hand shot up and he suggested a better, simpler way to solve the problem on the board. Mrs. Peralta invited him up to show and explain his solution. After he was done, she smiled and commended him saying, “We should name this the Montecillo method.” That cemented in my mind what a great math teacher should be.
At the heart of it, math is simply about solving problems. The particular solution doesn’t really matter (as long as it is logically correct and doesn’t break any rules). There is a famous story about a physics teacher who asked a student to measure the height of a building with a barometer. The supposedly correct answer was to use the pressure measured by the barometer, then plug it into a formula and solve for the height. But the student said he would simply tie the barometer with a string and lower it down from the roof of the building. The length of the string would be the height of the building.
The teacher complained that the solution didn’t demonstrate any physics principles. So the student rattled off several other ways like a) dropping the barometer from the roof and measuring the time it takes to hit the ground, from which he could compute the height; b) using the sun and measuring the barometer’s and building’s shadows then using simple ratio and proportion to compute the height; c) making a pendulum and measuring the periods from the top and bottom of the building and so on.
To top it all, the student added more wacky (but still correct) solutions like using the barometer as a ruler and slowly marking the height of the building while climbing the stairs to the top; or giving the building contractor the barometer as a bribe for telling him its exact height.
The point is, that problems have many solutions and the teacher who is fixated on only one is doing his or her students a great disservice.