A large part of the rationale for study is to ensure that the things that you have learned
are transferred from your short term to your long term memory.
A wonderful tool to achieve this is a diary or a calendar.
Now, it really doesn'­t matter whether you make your own
or use your phone or your computer or purchase a cheap diary or a cheap calendar,
the main thing is that you are able to keep track of your study and revision.
G'­day, and welcome to Crystal Clear Mathematics where it IS easier than you think!
I'­m your host, Graeme Henderson.
So often I'­ve had students say to me that they understood the work when they studied it
but two or three weeks later, when they came to do the test,
they had forgotten it.
This doesn'­t mean that they were bad students!
What it does mean is that they had not learned how to transfer their understanding
from their short term to their long term memory.
Now, wouldn'­t it be lovely if your final mathematics exam for high school
consisted of questions like 2 + 3 and naming basic shapes?
You wouldn'­t study for this. You wouldn'­t need to cram the night before
to get all this information into your short term memory.
The reason being, that it'­s already in your long term memory
for you to recall at any time you wish.
What I'­m suggesting is that it would be lovely to have things like trigonometry, algebra,
statistics, calculus already in your long term memory
so that you could recall those things almost as easily as you can recall 2 + 3.
Now, there'­s no real secret about how to achieve this.
I am sure your teachers and parents have said it to you, over and over again,
the secret is practice ... repetition! Well, the problem is that
not all repetition is beneficial – and repetition can be quite boring.
Unfortunately, another typical scenario is that students will cram before an exam
only to forget that information within hours or days of completing the exam.
Of course, the next time an exam comes, they repeat the entire process again,
having to relearn and re-practice the same material and do it over and over
and over and over again throughout out their school career.
How much nicer it would be if they could learn that material
properly the first time!
Finally, I have an efficiency question for you.
If you had a choice between learning something in twenty minutes
and learning something to the same level in an hour, which would you choose?
Now, you'­re not stupid!
Of course, you'­re going to choose the twenty minutes - and so would I.
I'­d much rather learn something in twenty minutes
and spent forty minutes doing something else that I'­d rather like to do.
So, we need an efficient strategy to ensure that we learn something well
the very first time, that it will stay in our long term memory
so that we can use it whenever we wish.
We would also like our practice to take less time - that is, be more efficient -
and, if possible, be more interesting as well!
So, how do we achieve all this?
Well, what I'­m about to share with you is not the complete solution
(I will be sharing more about how to study in later videos),
but memory researchers consistently talk about two facets of good learning.
Doing a lot of work at one time is called massed practice.
It'­s a wonderful way of learning quickly but lessons can be forgotten quickly as well.
Spreading your work out over a long period of time is called distributed practice.
And this is a wonderful way for getting the things you need to know
to stay in your long term memory.
Good learning requires both massed practice and distributed practice.
I am sure you'­d like to benefit from all this research
and learn how to learn efficiently. And here's how!
Every time you finish some mathematics homework or study I want you to ask three questions.
The first two questions are designed to ensure that you'­ve done sufficient massed practice.
Question number one: "Do I understand this sufficiently well?"
Before information or skills can be stored in your long term memory,
you must understand them.
This sounds so obvious and so simple,
but so many students stop working before they'­ve achieved understanding -
or they do their homework with distractions
so they don'­t concentrate on developing understanding in the first place.
Remember, the aim of your homework is not just to get it done and satisfy the teacher.
The aim of your homework is to gain under- standing and speed and mastery of your work.
Your homework needs to be done with focus to achieve these goals.
The second question is, "Can I solve these problems quickly enough?"
It is also vital that you develop speed when solving problems.
Almost every test given in school is timed. That means that you race against the clock.
I'­ve watched students do very, very good work
but take 5 minutes to solve a 2 minute problem during their tests.
Now, if your answer to either of these two questions is "No"
then you need to do something about it within 24 hours.
You may spend some more time revising those questions on the night,
or you may choose to chat with your teacher or some tutor the following day
to get some further instruction, or plan to do some further questions
the following night.
For some particularly difficult topics you may have to do all three.
If your speed and understanding are good, however, then your homework has achieved
its purpose, and you have successfully engaged in massed practice.
Now, in order not to waste all this effort and have to relearn the material
all over again at some later date, you must ask the third question.
And that is,
"How long do I think I can go before I risk forgetting this work?"
This is a rather subjective question but you are the best judge
of how long you are likely to remember something.
You will remember some topics more easily than other students and, sometimes,
you'll struggle with topics that other students will appear to find easy.
So, while your textbook and your workbook are still open,
place a note in your diary or calendar on the appropriate date
to do a certain number of questions from that exercise.
Be careful to note the page number and exercise number
and even recommend to yourself how many questions you should do.
Now, when that date arrives, of course, and you check your diary,
it'­ll remind you to do those exercises.
When you come to do them, one of two things will happen.
You will remember how to do them - or you won'­t.
Now, if you don'­t, you'­ll have to go through the process
of relearning the skill all over again.
In itself, it'­s a good exercise, but it is time consuming
and we wish to avoid that.
If you'­ve timed your entry well,
you'­ll be able to do the questions quickly and efficiently.
And, after you'­ve completed that revision, you ask the same three questions over again:
Do I understand the work? Can I do it rapidly enough? and
How long before I'­m likely to forget it?
and make another note in your diary to revise it further down the track.
This is the process of getting information from your short term to your long term memory
and you should find that the time period between your revisions
will get longer and longer and longer.
Now, let'­s give an example.
Suppose, at school, you'­ve just learned to find the volumes of cones and cylinders
and your teacher has given you ten questions to do for homework.
You go home, and you complete the homework.
If you feel that your understanding is not good enough at that stage,
you really should try to find a few more questions to do.
Or, if you'­re really confused, chat with your teacher or a tutor the next day
and do some further questions the following night.
If you do understood the work and you'­re happy with your working speed,
then ask yourself how long you think you can go before you forget the work.
Now, let'­s say you'­re confident you'­ll remember it for a week,
but you'­re not quite so sure that, if you had to do a test in three weeks,
you would remember what to do.
Then, in your diary, you should put a note, perhaps two weeks from now,
to do a certain number of questions.
If you'­re quite confident, you might only want
to do two or three questions, or four.
If you'­re not so sure, you might want to do six or eight or ten of them.
But that'­s what you put in your diary.
Two weeks later, when you open your diary, you'­ll see the note and be reminded
to do this exercise.
Now, two possible things will happen.
Either you will remember how to do the work - or you won'­t.
If you do, of course, you'­ll be able to do the exercise
or the questions very, very quickly.
If you don'­t, then you have to go through a relearning process which is valuable
but it'­s time consuming and we'­d rather avoid that.
Either way, when you'­ve finished those exercises,
you ask the same three review questions: Do I understand it well enough?
Am I working rapidly enough? and How long before I think I'­m likely to forget?
Now, this time, you might feel that you can go a month before revising your work.
So, a month from now, in your diary, you write a note to revise the work again
with the same page number and exercise number and a suggested number of questions.
Each time you repeat this process, of course, this time period will lengthen.
My experience is that, within two to five of those cycles,
you'­ll be remembering the material for at least six months.
And this is a sure sign that that material, that understanding,
is now being stored in long term memory!
And it means, of course, that you no longer have to cram before exams.
So, now you have all four of those items in place for your sound study system –
you will have your goal sheet, your time table, your study graph
and your diary (or your calendar).
Learn to use those four things well and you should have a strong study system in place.
Now, there are other things for us to discuss, but those four things form the foundation
for anything else that I'­m going to share.
In the next video I'­ll explain how your memory works
and how to cooperate with your memory when studying.
This is Graeme Henderson looking forward to helping you study efficiently.
Please subscribe to this channel, or like or comment on this video.
I am particularly interested in receiving feedback from you
about how your four-part study system is working for you.
Thank you and best wishes.