How can I implement the principles of deliberate practise in Mathematics?

[Maths Absorber]

I have been reading a lot of books on deliberate practise like Grit - Angela Duckworth, Talent is Overrated - Colvin and Peak - Ericsson and Pool and I'd like to implement the principles in my training to become a good mathematician.

There isn't much advice on how to apply these principles to become a mathematician, although interviews and case studies on mathematicians are cited.

I want a set of concrete steps I can follow to improve my mathematical skills. I should note, that by mathematical skill, I mean ability to solve problems (Like the Olympiad type, which will later help me in research). I'm not asking for advice to increase my grade or marks. I'm interested in improving my mathematical ability.

 

[jedishrfu]

Perhaps you can work through the Putnam Exam examples:

https://en.wikipedia.org/wiki/William_Lowell_Putnam_Mathematical_Competition

Another option would be to work through problems in Schaum's outlines for whichever math you're ready to study.

I think it takes doing problems mostly in some focused area and then branching out into other areas of math.

Here's an old WIRED article on gritty practice that may hold some clues:

http://www.wired.com/2011/03/what-is-success-true-grit/

 

[symbolipoint]

jedishrfu,
I wanted so much to keep reading that ..wired.. article but too many things keep popping into to view, and if Adblock Plus is used, the site also tells me I should disable the ad blocker, so I have not been able to finish reading the article., Nice from what I managed to read, but I wish the site or Adblocker Plus would let me finish it.

Hard Work is a trait, I guess. Still, I believe some people have a certain talent for something. Even so, those people cannot achieve much without long, dedicated effort.

 

[jedishrfu]

Sorry for the adblock issue. Its the bane of the internet. You could try another browser like firefox or opera. I do that sometimes to circumvent some site issue like this.

I had a friend who had a natural talent for math. He was basically four years ahead of kids his age finishing college math at a local college in twelfth grade. But then he lost interest while in college and eventually became a programmer like me.

So you must follow the mantra my dad taught me be persistent, consistent and insistent. It works for raising kids too until they liberate themselves from home-life.

 

[symbolipoint]

Reading the article using M.S. Edge browser was fine. (I should have thought of a browser change.)

The article is right in line with my guess. Effort more important (usually) than inborn talent. People on some occasions made comments saying how smart or of a genius a certain person is, all while not being aware how much extra time the person spent on the learning of the task or problem to reach his level of success. Think of this like a student in mid-level algebra class, who taking the course for the second time, solves seemingly complicated exercises well; as the other students who only recently came to this level of algebra course are so amazed how brilliant is this one student. The rest of the class have no idea that the student studied the course months earlier for more than 10 hours per week, and this was very hard work; and now the one such student is again studying the same course, also at 10 hours per week again as if it were as hard as the first time. Think now what will the rest of the class students do if they get a D or an F. Will they study this same course again? Will they study or review on their own before going to another class of the course? Maybe... and maybe not... some of them will become turned off and not do any more.

 

[Maths Absorber]

Can you guys please suggest some concrete steps to implement deliberate practise in my mathematical studies ?

As far as I understand, deliberate practise has two main principles :
1. It is focussed - For example, if you're a tennis player, it isn't just to play the most games or to hit the most number of balls as fast as you can. Rather, it would be to specifically practise the motion of the forehand and focus on the wrists, elbows and shoulder to ensure that the form is as correct as it can be. If you're a cricketer, it isn't to just hit the most number of balls, but to ensure that the bat lift is straight, the weight transfer is right, head is steady and that the elbows, wrists and feet move as accurately as possible for the best possible shot. It is to put deliberate focus into those things and correct the form, rather than just focus on hitting the ball the most number of times.

2. It has constant feedback - If you're a tennis player, you become conscious of which part of your swing is wrong exactly and decide if the ball doesn't have too much top spin. Having gotten that feedback, you specifically start tailoring that part of your swing consciously to increase the amount of top spin. If you're a writer, you don't just write more. You analyse your writing, and realize that your character psychology is fine but your description of events and settings isn't. So, you find some writings where those parts are excellent and specifically focus on improving that aspect of your writing.

My question is about how I can incorporate these principles into my studies ? Please advise me.

 

[symbolipoint]

Maths Absorber,
You have the right idea. Just use those same ideas for academic study. Students in junior high and high school are taught to do this. The same things need to continue in the rest of high school and into college or university. Not different really.

School subjects will have (usually) instructional textbooks and sometimes lab sessions. The books are often very well organized. Read. Think. Reread and continue thinking. Ask yourself questions about the written-book discussions. Look for answers or inferences in the discussions. Try to answer some of these questions yourself. Continue thinking. Do your answers or guesses make sense according to further discussions of the topic in your book? If not, you may WANT FEEDBACK from other students or/and your teacher.

--but more to do.
Attempt to solve any questions or examples within the discussion parts of the topic you are reading and studying. If you made an answer, find if it made sense, or is correct. If not, and there is a book's answer included, then use this to check your response.

Studying A Subject Which Is Not Too Neat:
Try to find some structure, or any basic concepts. This could help you to learn how the topic is organized. Things from social studies and humanities and biology are things not-too-neat. Things like the physical sciences or mathematics already are presented in a very structured way, so this should be easier to focus onto and to learn...but this does not mean that these subjects are easy. Just that the structure of what you are studying is more apparent.

Something that Mathematics and the physical sciences require you to do is to DRAW diagrams and figures, and sometimes to make tables of data or charts. This type of thing is very powerful for learning and communicating. Always remember that. Never turn into one of those types of people who ignore the making of drawing and figures to help analyze things.