1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

International Mathematical Olympiad.

  1. Apr 3, 2013 #1
    Hello all.

    Long time back, I was looking for a book on psycology of problem solving. I was trying to understand as to what it takes to be able to solve contest problems like that in the International Mathematical Olympiads. I wish to share here with you a great book that I discovered. It is titled "Mathematical Problem Solving' by Alan Schoenfeld. For me, the main takeaway from this book are the following points.

    1. Metacognition is a must have quality for problem solving. He calls it "Good Control". Just reading about it in his book helped me immensely to be able to solve tough IMO level problems. Typically, a novice simply tries one approach and then keeps trying that approach senselessly without even realizing that he has to give up that approach and try another one. He calls it the "Wild Goose Chase". An expert on the other hand looks at one approach, then backs off. He/she then thinks as to what other approach might work. Finally, an attempt is made only after they see a light or get an insight into the problem. These behaviors between an expert and a novice are very nicely explained in this book and in very great detail.

    2. Practice alone won't help. Good training is necessary for preparing for IMO. Usually, the problem appears daunting. Kids look at it, spend most of the time being frightened and also fascinated thinking "I solved my math text exercises orally..... he must be a real genius whoever solves such problems". Then after a day's work, he gives up. Looks at the solution. This will happen a few times and then he eventually gives up thinking that he won't be able to make a beginning. How then is practice going to help? All the student does is just stare, get more frightened, and then give up and look at the solution. There is more to it than just doing the above. But what is that quality which is required of a student to become a good problems solver?

    The main quality that kids develop with training is to achieve great control. There are books written by G. Polya and according to me, his books titled "Mathematical Discovery" I and II are the best in the series; however, it is not possible to become a good problem solver just by knowing the heuristics. Good control is necessary which comes only with training.

    3. Having control alone won't help. Sometimes, a problem might need an insight which alone can help in the solution of the problem. This insight comes only with good preparation in terms of good foundation in basic math. He talks about it referring to the insight as "Resources".

    When Polya's "How to Solve it" came out, it became a big hit. I think it is the "Mathematical Discovery" I and II which are the more useful books for contests. But one thing that people found was that it helped the already good problem solvers become more familiar with heuristics but it did not help a whole lot for a novice. I solved exercises from my math textbook in my tenth grade orally. All of them. I could not solve a single IMO problem. Not even a single problem. It is the same case with a LOT of people that I have known. What makes the difference? Does Polya's book help for contests? No. It does not. Training is a MUST. Alan Schoenfeld, a professor at UC Berkeley found that this is a question that needed an answer. Why does the heuristics approach not work for novice students? Mind you. A novice is defined as someone not used to problem solving. Solving exercises does not make a kid an expert. Problems are different from exercises.

    Hence Prof. Schoenfeld took up the research to figure it out. He then found answers which are given in this book. I found it amazing and I felt like sharing it with you. It is something which can potentially make a difference for someone who is preparing for a contest or for a math major. I am not sure if a highschool kid will be able to fully appreciate the content of this book if he is not an expert problem solver already; however, he will realize that it is not his lack of ability but it is due to lack of training and guidance because of which he is failing in contests. It is a common sensical thing but it took a while for me to figure it out. It became more obvious to me after I read this book.

    I could never solve a single problem from the IMO. I have solved many problems from Putnam and IMO lately. Thanks to this book. I know that some of you might say "well the first problem from these contests are generally easy...." but I have solved many of the tough ones. This book is really very useful. I think that it will help anyone who is a math major and is banging his head against the wall as to why he cannot be better at solving the tougher problems in say Analysis. I highly recommend this book. It is truly one of a kind and I have not found anybody else who has even attempted to shed light into this matter. He may not talk about Analysis or any higher level math but his main focus is on the qualities that training/course on problem solving can impart on the students which is what truly makes the difference between an expert and a novice problem solver.
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted