Articles, Blog

Seven Study Attitudes Worth Cultivating

November 17, 2019

In the last three videos
I explained how your memory works. In this video I want to summarise this information
and to list seven of the most practical things that you can do to succeed with your study. G’day. And welcome to Crystal Clear Mathematics
where it IS easier than you think! I’m your host, Graeme Henderson. Here are seven simple and practical principles
to help you benefit from your study! Number one! START TO STUDY!
Actually do it! Even smart people need to practice
in order to achieve. And it’s an absolute myth
that they don’t. Olympic swimmers spend hours every day
swimming laps, concert pianists practise their scales
and other exercises diligently … it doesn’t matter how good you are
or what skill you want to develop, practice is essential
for excellence and success and it’s naïve to think otherwise. If you practise hard,
it’s almost impossible not to improve. If you do nothing,
it’s almost guaranteed that you won’t. So, make a firm decision that you WILL study. Number two! START NOW.
Don’t procrastinate. It’s better to start earlier
rather than later. I’ve observed that, quite often,
talented students who get their results based on ability,
but don’t develop a good study pattern, are significantly out-performed
during their last two years of school by ‘plodders’ —
that is, students with less natural ability
but who study methodically. The longer you procrastinate
and put it off, the less likely it will be
that you will ever get started. So, don’t just DECIDE
that it is a good idea to study — DO something about it
and START TODAY! Number three! FOCUS!
Focus on everything that you do — whether it’s homework or assignments
or study — try to do it all well. Be determined to produce QUALITY WORK. Remember that practice only makes permanent. Whether you practice sloppy
or excellent work, the practice itself
will begin to make it habitual. So, make a habit of producing quality work. This should lead also
to some measure of success for you and most people can enjoy success so that later work doesn’t seem
so much of an effort. Remember it’s
“perfect practice that makes perfect” and
“success is the sum of little things done well.” Number four!
Unless you’re doing oral drill work, always SHOW YOUR WORKING and always practice
SETTING YOUR WORK OUT neatly and clearly. When you’re first working in any new topic
you should be developing thorough understanding and developing a procedure
for setting your work out and answering questions
that improves your success rate and reduces the possibility
of your making careless errors. Determine to make this a habit
and it won’t fail you. Number five! DRILL WORK! Choose to do as many questions as you can
to build understanding and speed. Once you have
a well understood procedure in place for setting your work out clearly
and answering questions, try to do a lot of your mathematics study
using oral drill work, that is, ‘mentally.’ Having someone,
or a computer program, to check your answers
and give you immediate feedback allows you to concentrate on building speed
without having to practice all that writing. In this way you can often complete questions
at five and even ten times the rate that you would complete them
when writing them down. If you had a choice
between spending, say, four minutes of drill work
or twenty minutes of written work to achieve the same benefits,
which would you rather do? Of course, you’ll concentrate hard
for four minutes and then go and do something else
that you really enjoy doing for the other sixteen! So, after you are confident with your work,
make drill work a significant part of your study
to improve your time efficiency. You might also be surprised
at how rapidly you can solve some problems in your head,
with practice. Number six!
And this is a favourite of mine. If you want to become
a really first-rate mathematics student, NEVER LET A QUESTION OR A PROBLEM GO BY
THAT YOU CANNOT DO OR SOLVE. These questions actually provide you
with your best learning opportunities! Not only that, but questions like them
could appear in your examination papers. Be prepared to invest
significant amounts of time in the occasional difficult question. During my school days I sometimes spent
many hours on a question before managing to solve it. After they leave school,
mathematicians and others can spend years and decades
trying to solve questions or problems. This is what research is all about.
This is incredibly valuable time and most students never, ever,
get to benefit from it. Let’s think in terms of physical exercise
and physical fitness. If I asked you to push hard against a wall
for twenty minutes every day, would it be a waste of time?
Not at all! You would be exerting substantial effort
and using a large range of muscle groupings in a variety of ways
as you changed position. This is what is called ‘isometrics.’ You can get quite fit
pushing a wall that never moves. Of course, if you actually succeed
in pushing the wall over, you can also have a boost
to your confidence and motivation (not to mention your reputation,
if you want one). In the same way, when you spend a long period of time
on one question or problem, you’ll be trying out all kinds of approaches
and practicing all kinds of mathematical skills. If you manage to solve the problem
on your own, the sense of satisfaction and the huge boost in confidence
that you can receive are hard to describe to someone else,
but they are immensely valuable. Even if you eventually give up in defeat,
ask someone to show you the solution and you will still have benefited immensely. In short, this attitude makes a good student
into a really top student! And number seven!
EXPERIMENT, and learn about yourself! Experiment with a variety of ways
of immersing yourself in the learning experience and major on the ones that work for you. Now, these methods include things like
writing notes, reading out loud, listening to sound files, watching videos,
discussing with others, teaching others, practising a skill on paper,
reciting while walking, composing a poem or a song,
getting someone to check you orally, and the list goes on and on. Have fun thinking up, and trying out,
new and creative ways of learning. Search for “learning styles” on the Internet
and learn more about your personal strengths and weaknesses. Use your strengths to advantage! Be very wary of all those nice graphs that show that you only remember
10% or what you read, and things like that. The ‘research’ behind those figures
is bogus at best. The truth is that some people
learn better by reading and others learn better in other ways and that there are many factors
that influence your memory. Learn what works for you
and your study will be much more effective (and therefore will take less time)
and it should also be more enjoyable as well. Now, if you would like a record
or a printout of these seven points I’ve created a PDF summary
that you can download from a link in the description
below this video. This is Graeme Henderson
hoping that these seven principles will help you get started on developing
an effective study system that is tailor-made
for your learning style! Please subscribe to my channel,
or like or comment on this video. Thank you.


  • Reply Shanmukh Pathuri December 30, 2012 at 9:53 am

    thank you sir.. but it is not working for me because i get distracted to ant thing that comes to me please help me with this

  • Reply Crystal Clear Maths December 30, 2012 at 7:53 pm

    Thank you for your comment.
    There are many reasons why you may be distracted. It could be your working environment (see my video #9) or your motivation and goals (see my video #3) or you may have family or social or work issues that occupy your thoughts, or you may need to build discipline by starting with smaller goals, or it may be due to dietary allergies or medication. It is very hard to answer without knowing your situation.
    I feel very much for you and hope this answer helps a bit.

  • Reply Rajeev Kumar March 19, 2013 at 8:16 pm

    thank u sir ! last idea is realy helpful for me

  • Reply Crystal Clear Maths March 21, 2013 at 12:49 am

    I am very glad that you found the video useful. Receiving feedback like yours makes the effort very worth while. Thank YOU!

  • Reply Rough Skeleton May 22, 2013 at 9:55 pm

    I have my junior cert exams in exactly 2 weeks! I have to study like crazy if I'm going to change. My grades around!

  • Reply Crystal Clear Maths May 22, 2013 at 10:58 pm

    Mmmmm … hard to make massive changes in such a short time, but you can still achieve a lot. Make sure you get enough sleep so you can function (and remember) well. For the simpler skills, try to spend quality time with a "study buddy" doing oral drill work … i.e. check each other's mental calculations. For longer problems, practise setting your work out in stages/blocks with headings. See my video "Seven Hints for Sitting for a Mathematics Exam" for more ideas that may help. Best wishes.

  • Reply Rough Skeleton May 31, 2013 at 3:09 pm


  • Reply Crystal Clear Maths June 1, 2013 at 8:39 am

    It is wonderful to hear from you again, Patman. I have wondered how things went with for you your Junior Cert exams. I hope you received the results that you hoped for and that I was able to help a bit. Best wishes from Australia. Graeme

  • Reply thewikimaper23 June 20, 2013 at 12:39 am

    How do you study formulas?

  • Reply Crystal Clear Maths June 20, 2013 at 12:04 pm

    There are a variety of ways that appeal to different people. I like to practise deriving them. In this way I learn the principle and the formula and practise essential skills at the same time. Just once per day for a week or so seems to help my students. E.g. each afternoon, start with ax^2+bx+c=0 and derive the quadratic formula. You will learn the formula, and practise completing the square and other algebraic skills. This method takes just a few minutes per day. I hope this helps.

  • Reply Rough Skeleton June 22, 2013 at 8:34 am

    They went pretty well, except for french and science.
    I get my results in September.

  • Reply Crystal Clear Maths June 23, 2013 at 3:14 am

    I am glad that your results are generally good, Patman. Thank you for letting me know. In case it helps, my French improved rapidly when I started browsing French magazines (like Paris Match) … nowadays it would be visiting French websites and trying to read the articles. September seems a long time to wait but I hope you are very happy with your results and that my videos have helped you along the way! Best wishes. Graeme

  • Reply Crystal Clear Maths October 27, 2013 at 5:53 am

    Hi Toxel, it is wonderful that you recognise this! So many students think that writing notes out means that they are learning them but, as you realise, this is not true.
    People learn in different ways but you might try creating a brief summary and then try to write it from memory each afternoon (try to give it some structure with points etc.). You might also get a friend to quiz you. Some people record summaries and listen to the sound tracks. Some summarise their notes in song or verse.

  • Reply Crystal Clear Maths October 27, 2013 at 5:58 am

    (following from previous response) … some like physical structure (drawing patterns/webs, or moving around a room while reciting). The important thing is that, at regular intervals, you should try to recall the notes without looking. Either write them out or recite them to someone every day or every few days until you are confident that you can reproduce them.
    It is a difficult skill to develop but you do get better with practice!
    I hope this helps. Visit my website if you want to chat more.

  • Reply Crystal Clear Maths October 27, 2013 at 6:42 am

    hehehe … sorry for the extra comment, Toxel, but I realised that I forgot to mention a really important ingredient. It is vital that you UNDERSTAND what you are learning. That means that you must find MEANING in your notes/summary. This can come through experience and practice, through asking good questions, through discussing with and listening to others, videos on YouTube, good books, etc. Never give up until you understand.
    Best wishes to you from Australia.

  • Reply October Boi April 8, 2014 at 3:29 pm

    6th idea is the most original idea.. practise random question. ask question and solve them by ourselves

  • Reply salim elchoufi June 30, 2014 at 12:51 pm

    I'm soooooo glad I found this channel. I'm in yr 12 right now and I was struggling just to finish an assignment on time. But this is not the case anymore! Thank you so much for helping me out and I'll definitely tell my friends about your channel. 😀

  • Reply AmethystWinter October 28, 2014 at 2:42 pm

    Will be looking forward for more videos 😀

  • Reply enna jannet February 16, 2015 at 7:24 am

    Only subject in which I cannot concentrate is Maths , I just find it so boring because it takes a lot of time to solve . Help me to concentrate in Maths .

  • Reply Crystal Clear Maths February 16, 2015 at 8:48 am

    Hi Enna,

    YouTube won't allow me to reply to you directly but I will share this and send the message to you privately as well.

    I am sorry that you have such difficulty concentrating in mathematics … especially since you report that you can do so with other subjects.  There can be a variety of reasons for this.  Some difficulties can be more easily overcome than others.

    The short answer is that you either do not understand it sufficiently or you find it uninteresting (or both).  Also, your passions obviously lie elsewhere.  Some people love to be outdoors; some love the social life; some love hands-on activities and others love abstract thinking.  While mathematics can be experienced and used in all these ways, in its developed form it is primarily abstract.  That, alone, makes it a difficult subject for many people.  There is not a lot that I can suggest to change this, nor would I want to.  I don't want to live in a world where everyone is a mathematician!  Follow your passion and don't feel guilty about the mathematics.

    Having said that much, a lot can be done about your understanding and interest.  These are different matters.  Before making suggestions I would like you to think of something else that you think you may never like doing.  For me (I am ashamed to say it) it would be dancing.  I neither understand it well, nor do I find it interesting.  So, I ask myself, "What would I do if it was important to me to like and become good at dancing?"  I think I would search the local community for someone who is a good and passionate dancer who is also someone to whom I can relate well.  I would want someone who loved and thrived on dance and who may be able to enthuse me as well.  If I hated fishing, I would not buy gear and try to fish alone, but I would find a passionate fisherperson whi would be happy to take me with them and share their passion and experience.  I hope this makes sense.

    Therefore, I encourage you to do two things to build interest.  First, ask around your local community to discover passionate mathematicians.  They may be students at school, other teachers, people using mathematics in an interesting way at work or older people in the community for whom it remains a passion or hobby.  Arrange to meet with them and share your frustrations.  You may discover someone wonderful who can help, inspire, guide and encourage you.  Second, browse the mathematics section of your school and town libraries.  Just search for anything that grabs your interest and read it.  Go exploring.  You will encounter talented and passionate mathematicians (some of them hundreds or thousand of years old) who will pique your interest.  As you read these works or discuss and do mathematics with local people you will find that you will use the mathematics that you know in new and interesting ways.  Don't restrict yourself JUST to a diet of 'school text book' as these can be rather dry and uninspiring tomes.

    I also encourage you to do something else to build your understanding.  Try to find a 'study buddy,' someone with whom you can study for a short while each week (two or three times if possible).  When you meet, don't just concentrate on the really difficult questions that you have, but spend a good portion of your time doing 'drill work.'  This is mental calculation on shorter and simpler questions.  You could select a page of linear equations to solve (for example) and speak your answers 'out loud' while your friend checks your answers.  You can then reverse roles.  In my opinion, a 90 second or two minute burst of this is as useful as about 10-15 minutes of working on paper.  This is really efficient study!  It takes a lot less time.  It is fun because you can do it with a friend and race the clock (if you wish).  And it keeps you very focussed because the task is short and you have a friend monitoring you.  This kind of activity will help your concetration enormously.  In time, you will be amazed at how quickly you will be able to solve quite complicated questions in your head.

    Add these things to your normal study and I hope that they make a difference to your concentration and enjoyment of mathematics.  [I might add that concentrating on setting your work out neatly and clearly on a page can also help greatly.]

    I am sorry that my reply is so long, but your problem is one shared by many students and I wanted to provide you (and them … if they read your question and my reply)  with a fairly full answer!  I hope it helps and wish you well with your mathematical adventure.

  • Reply enna jannet February 25, 2015 at 1:05 pm

    Thanks a lot sir , though your reply was long but it's worth reading. You were right I don't understand its sufficiently and so I find it boring. I will try to have better understanding of this subject . Your suggestions are really helpful, I need to give more time to maths .
    Once again thanks for taking out time to reply with details.

  • Reply Crystal Clear Maths February 25, 2015 at 8:38 pm

    You are welcome, Enna.  I apologise that my reply was a very long one but I felt that it would be profitable for me to share what I did.  I hope my suggestions do help because it is awful being unable to concentrate well with anything that one does.
    Please let me know how things go for you.

  • Reply Edres Mn July 31, 2015 at 10:39 am

    This channel is just WOW.
    I am gonna bomb my exams next sem, I promise.

  • Reply Kamal Bhardwaj May 8, 2016 at 6:48 am

    I played this video in front of my kid in 9th grade and he appreciated the 7 methods a lot. I hope he will imbibe some of these in his studies and improve.

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