If you understand Mathematics, it is not difficult ..... .
Debate Rounds (3)
At school, our syllabus was designed by The University of Cambridge Local Examinations Syndicate (UCLES). I was we can say, proficient, as you put it. At SC level it was excellent. However our school was taking part for the first time in the Australian Mathematics Competition (AMC). Practicing the preparation papers, i was astonished; there was some exercises i couldn't even attempt and i was surprised. One such exercises taken from the 2009 paper is about palindromic numbers ( 1221, 5885, ...).
In the paper it is asked how many 4-digits palindromic numbers that is divisible by 7 exists (the question was not as straightforward as that). Under the syllabus we were following, we would never have learnt it. Checking the answer booklet, i grasped (understood) the mechanism. Other variants became easy.
The point you raised is the heart of the problem. There exist the basics and complication of the basics. Examinations are unfortunately designed to prevent even those who understand the concept from passing. They take pleasure in mystifying students. Who pass then? The answer is those who understand the basics and also understand the traps/mystification of the examiners.
Such students may be those who have practiced lot of papers. After sufficient practice, they know how to proceed because they understand the setting of the question.There is the understanding of concepts and the understanding of steps/processes.
A debate is not merely to defeat an opponent but also to seek an explanation with the help of a contender. I feel that this debate is more of an explanation for a better understanding.
As you would conclude this debate, i request you to include any point i have missed and to consider the points i have brought to our attention.The task awaiting you is to present the final picture as this debate is a pioneer of it's kind and will serve as a reference for later times.
A notice to all those present: if you are experiencing difficulties in Mathematics, if possible, try the following;
1. Look for a well versed and passionate teacher.
2. Concerning a subject ask him how the subject came about/how was it discovered/it's derivation (you will be surprised).
3. Ask about it's use.
4. Ask about the mechanism well.
Make sure you understand.
5. To prove your understanding, try teaching/explaining it to somebody else.
-Thank you very much for having read this in it's integrality.
Once again, I'd like to reiterate my previous point, but in its entirety.
You bring up a lesson in which you learned how to find a quantitative amount of numbers that are palindromes and are divisible by seven.
Yes, it is true that you understand this concept, but even if I morphed the equation to be slightly more difficult you would have trouble solving it.
If I asked how many 79 digit palindromes are divisible by 3, I could give you hours tiring over a succinct way to approach a problem that you theoretically understand, but you, like many other mathematicians would be stumped.
Even if you did devise a way to solve this problem, I think it's safe to say that it took you hours and that it can be effectively classified as 'difficult'.
I am positive that you have grasped all that fundamentals of mathematics that include basic arithmetics and simple combinatorial problems but if I asked you to mentally calculate 988387 23879 = x, it is still bound to be strenuous.
I argue that geometry problems are the most difficult to tackle because they require critical and out of the box thinking, which many of us do not possess. Only a select few members of the mathematical society are able to consistently and correctly answer hundreds among and infinite selection of difficult geometry problems.
During our school studies and education, we are provided with a basic framework of concepts that revolve around surface area, side lengths of a triangle, relationships between angles and sides and relatively simple and advanced formulas.
The issue is that we are taught with the same reiterated pedagogy, and the same set of concepts and problems.
Once again, the morphing and inter-usage of mathematical concepts is impossible on a grand scale, and rapidly and accurately answering a diverse range of geometric problems is absolutely absurd to consider.
To answer all geometric problems is to have 'seen' all geometric problems and to have integrated them into your memory with nil room for error.
Even the top mathematicians in their field of study, Terrence Tao and even Newton, have been unable to disclose themselves to all of the unique derivations that geometry presents and they too, have a lot to learn about application of known concepts.
Rainman, a mathematical and memory genius, has the ability to absorb up to 99% of the knowledge he reads and store it into his active lexicon, but in an idealistic mathematical desire for perfection, that is not up to par.
And even if his memory capacity was up to one hundred and he fully understood the practical applications for the concepts that he derived from books, he would no be able to digest all of the diverse mathematical publications of the world and thus even understanding a simple concept that involves say, Absolute Values, can stump you when it is morphed into different forms.
Thanks for the great debate!
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