With AeSI exams nearing. I thought of searching the web for some ways in which the web can help us! Guess what ! People who say Internet is a great tool are right. I landed on a particular article that can improve your marks in the maths exams !!
The article, by a maths professor Eric Schechter, mainly discusses the common errors made by students. Its an experience of a math's professor.
The page is very long and i think, like myself, no one of you like reading on a computer when the clock is ticking in the cyber cafe. So i have copied part of the page that i liked the most and presenting it here in a simple structured form.
This particular section discuss about the importance of revision and re-checking. So guys and gals read this article and profit by it.
Going over your work. Unfortunately, most textbooks do not devote a
lot of attention to checking your work, and some teachers also skip
this topic. Perhaps the reason is that there is no well-organized
body of theory on how to check your work. Unfortunately, some
students end up with the impression that it is not necessary to check
your work -- just write it up once, and hope that it's correct. But
that's nonsense. All of us make mistakes sometimes. In any subject,
if you want to do good work, you have to work carefully, and then you
have to check your work. In English, this is called "proofreading";
in computer science, this is called "debugging."
Moreover, in mathematics, checking your work is an important part of
the learning process. Sure, you'll learn what you did wrong when you
get your homework paper back from the grader; but you'll learn the
subject much better if you try very hard to make sure that your
answers are right before you turn in your homework.
It's important to check your work after you do it; but "going over
your work" is not the best way of checking math -- in fact, it's the
worst way (except for not checking your work at all).
I have twisted some words here, in order to make a point. By "going
over your work" I mean reading through the steps that you've just
done, to see if they look right. The drawback of that method is
you're quite likely to make the same mistake again when you read
through your steps! Here is a typical example: After an irreversible
computation, if you forget to check for extraneous roots, then you'll
probably forget again when you "go over your work."
You would be much more likely to catch your error if, instead, you
checked your work by some method that is different from your original
computation. Indeed, with that approach, the only way your error can
go undetected is if you make two different errors that somehow, just
by a remarkable coincidence, manage to cancel each other out -- e.g.,
if you arrive at the same wrong answer by two different incorrect
methods. That happens occasionally, but very seldom.
In many cases, your second method can be easier, because it can make
use of the fact that you already have an answer. This type of
checking is not 100% reliable, but it is very highly reliable, and it
may take very little time and effort.
Here is a simple example. Suppose that we want to solve 3(x–2)+7x=2
(x+1) for x. Here is a correct solution:
3(x–2)+7x=2(x+1)
3x–6+7x=2x+2
3x+7x–2x=2+6
8x=8
x=1
Now, one way to check this work is to plug x=1 into each side of the
original equation, and see if the results come out the same. On the
left side, we have 3(x–2)+7x=3(1–2)+7(1)=3(–1)+7(1)=(–3)+7=4. On the
right side, we have 2(x+1)=2(1+1)=2(2)=4. Those are the same, so the
check works. This computation was by a different method than our
original computation, so it's probably right.
Different kinds of problems require different kinds of checking. For
a few kinds of problems, no other method of checking besides "going
over your work" will suggest itself to you. But for most problems,
some second method of checking will be evident if you think about it
for a moment.
If you absolutely can't think of any other method, here is a last-
resort technique: Put the paper away somewhere. Several hours later
(if you can afford to wait that long), do the same problems over --
by the same method, if need be -- but on a new sheet of paper,
without looking at the first sheet. Then compare the answers. There
is still some chance of making the same error twice, but this method
reduces that chance at least a little. Unfortunately, this technique
doubles the amount of work you have to do, and so you may be
reluctant to employ this technique. Well, that's up to you; it's your
decision. But how badly do you want to master the material and get
the higher grade? How much importance do you attach to the integrity
of your work?
One method that many students use to check their homework is this:
before turning in your paper, compare it with a classmate's paper;
see if the two of you got the same answers. I'll admit that this does
satisfy my criterion: If you got the same answer for a problem, then
that answer is probably right. This approach has both advantages and
disadvantages. One disadvantage is that it may violate your teacher's
rules about homework being an individual effort; perhaps you should
ask your teacher what his or her rules are. Another concern is: how
much do you learn from the comparison of the two answers? If you
discuss the problem with your classmate, you may learn something.
With or without a classmate's involvement, if you think some more
about the different solutions to the problem, you may learn
something.
When you do find that your two answers differ, work very carefully to
determine which one (if either) is correct. Don't hurry through this
crucial last part of the process. You've already demonstrated your
fallibility on this type of problem, so there is extra reason to
doubt the accuracy of any further work on this problem; check your
results several times.
Perhaps the error occurred through mere carelessness, because you
weren't really interested in the work and you were in a hurry to
finish it and put it aside. If so, don't compound that error. You now
must pay for your neglect -- you now must put in even more time to
master the material properly! The problem won't just go away or lose
importance if you ignore it. Mathematics, more than any other
subject, is vertically structured: each concept builds on many
concepts that preceded it. Once you leave a topic unmastered, it will
haunt you repeatedly throughout many of the topics that follow it, in
all of the math courses that follow it.
Also, if discover that you've made an error, try to discover what the
error was. It may be a type of error that you are making with some
frequency. Once you identify it, you may be better able to watch out
for it in the future.
If you are not worn out with this, check out lots of tips offered by this professor here.
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Visit www.aesi.org or http://www.csirwebistad.org/aesi/ for the examination results.
