One of the problems is that most people learn the procedures of mathematics without really understanding the philosophy behind it. I gave three examples above and no one picked up on them.
- The instructor wanted the student to divide 2.2x10^19 by 100,000, and that’s equivalent to 2.2X10^19 divided by 10^6. You can do the actual division or subtract the second exponent from the first. The student should have been shown at some point in her education that they are equivalent.
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Our College of Education, for example, has a GPA “average" of 3.8 out of 4. So all their graduates are excellent teachers!
is presented as an example of grade inflation, and it most probably is, however, we can't just say that without recognizing the mathematical possibility the the lower 95% of the students had dropped out so only the top 5% got the grades they deserved in relation to those who left. - Asking to simplify " 2/3 - 1 “ we would think of it equalling 2/3 -3/3 thus equalling -1/3. However, if the student has learned the basic math, but not how to deal with fractions, 2/3 - 1 equals in her/his mind 2/3 -1/1 which is correct. If the student hadn’t learned that you can’t mess around with fractions that have different denominators, it’s easy to subtract both the numerator and denominator of the second from the first to come out with (2-1)/(3-1) or 1/2. :lol:
Occam