Teaching Methods

In the beginning, the teacher answers the questions, later (s)he questions the answers. My ex-Dean in MBA School used to say that.
My question, why shouldn't the teacher question the answers in the beginning itself?

Yesterday a friend's daughter was having trouble with a Profit & Loss Problem.
"A shopkeeper buys 200 shirts for Rs 180 each and sells 100 at a 10% profit. at what price should he sell the balance to make an overall of 15% profit"
She knew the answer but not the steps. I gave her the steps without actually solving it for her.
It is a question from arithmetic point of view. While I could solve it faster using algebra- (10% + x%)/ 2 = 15%.
But would the teacher award her marks if she solved it that way?
I explained alternate methods- algebraic and ratio-proportion but she decided to stick to the longer one.
At school level, we are taught the method and therefore if you get the steps right but not the answer you may still get 80% marks for the question because you have understood the concept.
While if I were to attempt this question in my MBA entrance examination where the emphasis is on selecting the right answer out of the multiple choice given, I would have got a zero if I would have selected the wrong answer. And I could have used any method, algebraic, arithmetic or trial and error or pure guess work.
And if I were to be given this problem while I was doing an MBA, I could have used several methods and arrived at several possible solutions and still scored marks. The emphasis here is appreciation of the problem from various angles.
And at work, I could have even suggested ways to invest the profit in his next consignment and ways to negotiate for credit terms or advance payment terms. The emphasis in business situation is to make as much money possible out of a single transaction, via actual profit, profit after tax, credit, stock clearance etc.
Any problem in Physics can be solved using simple arithmetic or using formula or even calculus - I understand it is fastest to use calculus but somehow I have never been coached well enough in calculus to appreciate that or even solve via calculus. So it is still an enigma to me.
After yesterday's incident I am having a mental debate with myself.
Why don't teachers emphasise that appreciaton of the problem is more important than the method?
My answer- at school level, it is important to get the basics right. Each teacher teaches as per a pre set syllabus and their goal is to finish the syllabus on time. Discussing exhaustive methods to solve a particular question will never enable them to complete the syllabus. At that level, Mathematics is all about practice till you are perfect and till you have mastered formulae. History is dates and they really don't take them as people who existed albeit a very long time ago. Physics is what Newton invented after sitting under the apple tree or what other great men did long time gao and left behind series of theories, laws and formulae for us to mug up. Chemistry is also rote learning of equations and the observations that are supposed to happen in the practicals if you do all the steps correctly. No self discovery. Civics/ Economics is a set of acts and bills without really understanding where the tax money is going or how the government has made use of the education cess or why prices fall or rise and why dollar rate is important from business point of view. If a teacher were to explain all this the syllabus would never be completed and then there are exams where the answers are pre set along with the questions and the marks will be awarded according to the number of points one has covered.
Once you move to corporate life, one has no ready made answers, every thing is put down to experience. If one has spent "x" years in the industry, (s)he is supposed to be capable of working at "y" level in the organisation and expectations on the ability to sort issues are formed based on industry experience. The Dean whom I mentioned in the beginning used to take 'Strategic Management" classes for us. It happened 9 years ago but I don't remember what was the syllabus or what syllabus he used to cover during that 1 hour but I definitely remember the other real world issues he used to blend into his lecture.
As students we are taught to attend a class from the point of view of "the taught" rather than the 'teacher or knowledge worker". We like classes where we can shut up, take notes, assimilate information for our answers for test questions. We don't like to be quizzed and put in the hot spot. Test is a necessery evil and class participation is for bonus marks not for ourselves. Does it ultimately boil down to teaching methods or UGC syllabus?
What did olden day Gurukul or today's Montessory style do? Practical, all round, application based syllabus.
Ultimately everything boils down to what i am going to do for Ojas & Tejas?
Will I have the time to make them appreciate the problem and solve it using all possible methods rather than just as per the chapter title? Or more important, will they appreciate my interference and will they have the courage to tell the teacher that my method is also right?