In his book, Hot to Solve it, George Polya, Mentioned: (How To Solve It, PartI, In the classroom Purpose,page6.paragraph 7) "It is foolish to answer a question that you do not understand."
You are more than just smart mathematician to me. Thanks for giving light to us, math teachers. Mr. Polya, you are father of every sincere teacher. Rest in Peace. I’ve read and read his brilliant books but this my first time to see video. I can help but find myself in tears.
Feeling Very Happy !sir ,today I have Observed your Lesson & learned how to get answers by students with joy and happiness in maths teaching .💐 You are Great sir.I'm proud of You 👏
Today I bought 「How to solve it」in Japanese. I went to book store because I want to know How to solve difficult problem and make an effort. I had wondered How many students solve difficult problem before I met this book! Although I am 19years old now, his books seems brilliant yet!
There is nothing more valuable than a great teacher and I put George Polya in that category. This was a wonderful video demonstrating his teaching method.
Having read Polya's book on Problem Solving, could not resist watching this video. What an absolute delight ! Anybody interested in problem solving will love this. You may also learn some geometry & maths. My takeaway is what "teaching" should be !
Yes! thanks for sharing this. I hope MAA will let this remain public. It is in many libraries in video form and so I hope the intent of sharing can be recognized here!Genuine math teachers will enjoy the video and learn from it!
So basically, guess but guess with conviction and a curious mindset that could be proven wrong at any point but possess the courage to derive a new conclusion based off of reasonable induction.
Great. Sometimes ago I saw a marvelous video showing Moore teaching 8 years old kids which is marvellous and in the same spirit, I cannot find it again on youtube anyone an idea? Note: About the move between guessing/and correcting read also "Proof and refutations" of Imre Lakatos.
"Teaching is not a science is an art...." says Professor. I believe it is an art, indeed and it is a science notwitshtanding. It compels to it not for the bragging but for the natural will to make science and knowledge worthy to any mind, approachable to any heart, however feeble and fragile that is capable to unleash the will to know in love of knowledge of life, its cause and the result of it...yourself, humanity, world and learn the laws, principles, morality, the ground and unshakeable drive to preserving it. It is a science that prepares the many on the path of science and the many on the path of their lives. However, I do believe that is beyond it, that is an art indeed. No I am going to listen to rest of his lesson.
A teacher's job is to give answers to questions. A pupils job is to remember these Q&A problems. Guess solutions to questions with no answer or incorrect formulation.
An extremely good idea, exercise and practice would be to try and to keep a timed, recorded journal of your own life, of your own each and every minutest to the most major-est of thoughts, both scientific and artistic that you have, your day to day, each and every, savory and unsavory, pleasant and unpleasant experiences and of your own reactions, responses, take aways from them , in a genuine, sincere attempt and effort to make sense of your own life as also of life in general and of this crazy world you happen to inhabit and to indwell. It would make for an engaging and engrossing maybe even an enlightening read. Even the life of the tiniest of virus is not a completely uneventful, and immemorable one.
A big fan of his classic book How to Solve it. However, I will say that his teaching was ideal, not very realistic. If he was in a high school class of today, maybe he could not conduct an instruction as well as he demontrated in the video. Who were his students? Undergraduate students and/or graduate students at Standford University. They had much stronger motivation of learning than students in many schools of today. And the knowledge base that students had in his class was much more solid than that of most students in today's schools.
I must say I'm totally disappointed in this man. I always knew about his discoveries in discrete mathematics, I learned he was a legendary teacher. So be it. But his answers on the blackboard are just wrong. I can easily prepare a set of 3 planes dividing the space into 7 parts, for instance, or 4 planes into 10 parts. He completely disregarded the question of perpendicularity posed by this very clever girl (planes being all perpendicular one to another is only the simplest case of perpendicularity!!). I also don't like how he uses the word "random", which has no application in mathematics. Let's add up 3 and 3 and hope we get 7 this time... I mean, mathematics is not a random trial. And choosing planes which aren't perpendicular is in no way "random". This is a good manual of how not to solve problems.
Yes randomness exists in mathematics, and I think you misunderstood him, of course you can contrive a scenario where 4 planes can divide space into 10 parts but then you’re not answering the question, the point of investigating something that’s random is to take into account the extreme cases as well. In other words, random in this context would mean the maximum number of subspaces that results from 4 planes cutting a space. Randomness forces you to take every case into account and assumes that anything less than the maximum can be achieved. .
@@kaiz8597 Randomness does not exist in mathematics. Mathematics can deal with randomness that supposedly exists in the external world (although that is another story). What he meant was a special case and a general case. I don't remember, now that two years have passed, what the video was about but rather than me misunderstanding Polya, I think you misunderstood my comment. Go read it again.
