I'm seeking opinions from math teachers, budding mathematicians ... anyone who has run into "issues" when writing solutions to problems involving decimal approximations.
I present a situation that has nagged me for years. I start by showing a sequence of equations "with a problem", and then offer three potential remedies. However, I conclude that that "the problem" is worth living with.
I would value and appreciate any comments from this great community. Thanks in advance. The link is below:
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I had a read of your page... for me the question is
1. do you want a student to give an exact answer.... which is what standard tests is able...
2. do you want a student to demonstrate understanding... which to me is the more important idea.
The reality of life beyond study is that you use the mathematics of your environment which needs simple approximations...
Beyond study, there are systems in place... companies, employers want quick and dirty solutions rather than solutions that use time to gain an precise value.
I always think of the errors in medicine... is it better to understand the units of measurement or measure a quantity...
Thanks for your response. Definitely---understanding is what we seek.
That's why I think it is preferable to "overlook" the "problems" of the first sequence. Of the four sequences presented there, do you have a favorite? Or, can you offer a presentation that you like better? (By the way, you're evidently a fast reader.) I'm less concerned here about one-on-one work with a student, where things can be (and should often be) quite casual; I'm more concerned about published math/science books, and published pages on the web. I think if something is going to be presented to a wide audience, the presenter has an obligation to try to get things right.