The average student in my experience loses between 3 and 15 percent of their exam marks
due to carelessness!
The average appears to be around 8% - at least, in the classes that I've taught.
Now, if you're losing marks due to making careless mistakes in tests,
this is especially frustrating because it's not that you don't know the work -
these are marks that you have studied for and earned and deserve!
Stay tuned, and I'll show you how to study to significantly reduce
the number of careless errors that you make.
G'day. Welcome to Crystal Clear Mathematics where it IS easier than you think.
I'm your host, Graeme Henderson.
If someone was to offer to increase your exam results by 5% or 10% for free,
would you be interested? Of course you would!
What I'm about to show you is how you can achieve that
by special techniques of study at home.
It doesn't require a great deal of time but unfortunately it's not taught well in school.
A great deal of money is invested around the world
in improving safety in factories and workshops and laboratories
for the personnel that work there.
Some of the money is spent on improving the equipment,
that is, adding sirens or warning lights or guard rails and things like that.
But, a lot of money is spent on training the personnel to work in safe ways.
For example, chemists are taught NEVER to look down the necks of test tubes
and ALWAYS to wear protective goggles.
Since these things have been instituted in training procedures,
the incidence of eye damage in chemical laboratories
has dropped incredibly.
You need to do the same kind of thing with your mathematics -
to train yourself in safe working methods.
When your mathematics exam paper is returned, don't throw it away like a lot of students do.
That very night, sit down with it and work your way through the exam paper
looking for questions that you got wrong because of carelessness -
and try to work out why it was that you made the mistake.
Was it that you misread the question, or perhaps you rounded a number off incorrectly,
or perhaps you did something wrong with a minus sign -
there are many, many possibilities.
Now try to think of habits that you could develop or improve
that would help you avoid those very errors.
Some of the more common and simple solutions are these:
One is to draw bigger diagrams, or to draw them in colour,
or to draw them somewhere else on the page.
One of my student's results improved dramatically simply because he started drawing diagrams
8 or 10 cm in size instead of 4 cm across.
It was just that simple!
Another simple thing might be completing one action before starting another.
For example, when dividing both sides of an equation by five,
some students divide one side by five and then try to resolve that before they go
to the other side of the equation.
It's a good habit to write 'divide by five' on both sides
and then resolve both sides later.
So, the simple order of operations can make a very, very big difference!
A very common problem is trying to do too much in your head
and especially under the stress of exam conditions.
Train yourself to write more steps than you think are necessary.
You'll be amazed how your accuracy improves.
And, quite frankly, in the time it takes to write the extra step or two,
some students will have spent a long time struggling to do the work mentally anyway.
It may be that you could benefit from simply writing headings
for each step of work that you do.
For example, as you prepare to graph a parabola, you might write four headings.
The first one would be the 'y-intercept,' the second one would be the 'roots,'
the third one would be the 'axis,' and the fourth one the 'vertex.'
And separating your work in this way makes it much more logically clear and consistent.
Many students have found that developing a habit of writing the formula first
BEFORE substituting numbers into it helps reduce their error rate.
Another habit that I like is a procedural one, and that is,
to re-read the question after you've finished answering it -
to check that the answer you wrote, in fact,
is in the form that's required and fully answers the question that was asked.
Another possibility is that you've been
solving problems in a lot of little parts, or steps,
that you may or may not remember to put together properly at the end.
A good habit to develop may be to try to solve the entire problem
in one big equation.
A good example of this would be in finding the area of composite shapes,
where it's possible to list the areas of all the shapes in one big line
and resolve them, line by line, down the page so your final answer is exactly what you want
and you don't have to remember to find other little bits to add in.
Now, there are other possibilities as well, but this is a good sample for you to start with.
What we're trying to do, of course, is to establish habits.
One lot of habits is concerned with how you set your work out on a page.
And I can't emphasise enough how important this is,
not only to think it out and do it properly, but to practise it until it is second nature.
Another group of habits relates to how you go about answering your questions.
It's good to establish a procedure or a routine that you follow faithfully
in your homework and your study and make such a habit
that it won't fail you in exam time.
For example, you might read a question, draw the diagram,
reread the question to check that your diagram has been constructed properly,
write your equation, reread the question or recheck the diagram
to make sure that you copied the equation correctly
or that you constructed it correctly based on the information given.
When you've finished solving the problem,
copy the entire answer from the calculator screen,
then reread the question to find how you should truncate your answer
and what kind of units are required.
This is a good habit to develop.
Now, you might refine it in various ways of your own,
and you need to find a system that works for you, reduces your error rate,
and one that you can live with and practise faithfully.
You need to practise that skill until it is so engrained, so deeply engrained,
that it won't fail you when you come to solve mathematical problems or to answer questions
in your mathematics exams.
In my next video I'll be explaining the last of the four study methods for mathematics,
that is, how to develop stamina and superior skill in solving mathematical problems.
This is Graeme Henderson, hoping that you can develop and practise good habits
that will significantly reduce your error rate during exams.
Please subscribe to this channel, or like or comment on this video.
Thank you.