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Re: Showing work
Posted:
Sep 13, 2001 3:16 AM
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>>It seems that the mathematicians do not always show >>their work either.
When they write "it's obvious", it will >>usually take quite a while for a
lot of people to >>figure out why it's obvious.
I am a high school student currently studying Yr 12 mathematics. First of
all, let me say that I agree with a lot of the comments made here about
showing one's work. However...
Mathematicians actually do show their work. It is all to do with the
audience that one is writing for. To give an example, in our exams we are
expected for a proof by induction to write out every single step along the
way (possibly 20 lines of work). Early- to mid-university students will use
dramatically fewer steps (maybe 5 or 6 lines maximum), while postgraduates
and professionals may even simply skip the proof by induction altogether,
assuming that the intended reader (i.e. other professional mathematicians)
can see the proof easily.
The other point I want to make is that it is not only dangerous not to show
your work, it is also dangerous to show too much work. I have two or three
classmates who have had teachers who insist on every single line of work,
right down to going from (2+3)*(6+1) to 5*7 before getting a final result of
35. These students have trouble finishing exams simply because they put too
much unnecessary working in.
My advice is to adjust the amount of working required to the grade and the
problem. Understandably, if the problem says (6+7)+(6-5)*(8+5) in Yr 7,
each pair of parantheses should be simplified first before getting a final
result. On the other hand, if the same expression came up in, for example,
a real-world problem, or an integration, I would have no problem with simply
writing down the final answer on the next line.
One final point is: when using a calculator, always note that a calculator
has been used, write down everything that's shown on the calculator, before
rounding on the next line. To assist in this, try not to use the
calculator's rounding functions, but manually round it off. Use the full
result, or better still, the original expression, in any further working
needed. For example...
=*expression*
=63/17
=3.70588235294117647058823529411765
=3.7059 to 4 decimal places (dp) or 5 significant figures (sig figs)
Take care all.
Sebastian.
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