Is There Always One Right Answer?
Let's see. Try selecting a figure from the five shown on the right that is different from all the others at least in one respect. Do select a shape before you proceed further.
If you chose figure b), congratulations! You've picked the right answer. Figure b) is the only one that has all straight lines. Give yourself a pat on the back!
Some of you, however, may have chosen figure c), thinking that c) is unique because it's the only one that is asymmetrical. And you are also right! c) is the right answer. A case can also be made for figure a): it's the only smooth one. Therefore, a) is the right answer. What about d)? It is the only one that has both a straight line and a curved line. So, d) is the right answer too. And e)? Among other things, e) is the only one that looks like a projection of a non-Euclidean triangle into Euclidean space. It is also the right answer. In other words, they are all right depending on your point of view.
The problem with having the one and only right answer crops up in math education in two ways. First, through the perceived dichotomy that anything, especially in mathematics, is either true or false. Channeled via the bureaucratic and administrative framework, this perception engenders the desire to teach and learn what is right. That tendency is fostered by the universal acceptance of and the importance bestowed on, standardized tests.
In addition, the acrimony that exists between different streams of math education philosophies is indicative of the widespread adherence to the principle of the one and only right answer. My pedagogy is right so yours is necessarily wrong - is the common background for the discourse in math education.
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