Comment: no right or wrong answers

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no right or wrong answers

Is there such a thing as right and wrong in our society these days? I personally believe this is at the heart of this discussion. If I don't believe in absolutes, how would I view something as rigid as mathematics? I think I'd want to change it to my way of thinking, wouldn't I? Shades of gray? Or maybe grey?

In the bad old days, there were about equal numbers of numbers problems and word problems. In today's math textbooks there are almost all words, pretty pictures, and few numbers. Instead of the word problems with all the setup given in the problem (aka "ready to solve" word problems), students are asked to estimate what these numbers might be. Sometimes they might be asked to invent the problem itself.

An example might be to ask a student to estimate the cost of building a house. First they'd have to think of permits, materials, labor, and so forth then put a number to each of these things. They are, in effect, forming their own problem. Each student would then do whatever math they might invent and each student would come up with a different answer. The teacher could say, "See, there's no such thing as a single right answer to the problem!" I suppose she'd feel pretty smug about that.

The issue is that the students set up their own problem and guessed their own initial conditions to the problem they created. If they did the math correctly, the algorithm used would probably have been exactly the same. This is how to devise a math program that embraces the relativism in our society, moral or otherwise. It's also a way to create a math program where there's more to grade than the correctness of the answers.