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Practice, Apply, and Create Variations


I purchased 7 mangoes from a nearby fruit seller yesterday as there were that many persons in my home. There are plenty of fruit sellers around, so there is no reason of purchasing more and storing. The fruit seller was a lady in her seventies and probably had no formal education. She sold those mangoes at ₹140/kg. She weighed the mangoes selected by me. It was 1 kg 750 gm. She asked me to pay ₹245 while transferring the mangoes into my bag.

I was surprised as the time taken by her to do this calculation was practically nothing and she didn’t use calculator or pen-paper. I took more time than her to do this calculation manually and found the amount to be right. I thought, she might have got another customer earlier purchasing same quantity of mangoes, so she might just remember the amount! But, it was not so.

I was curious to know her process of doing the calculation. She said; 14*7 = 98 for 700 gm, +₹7 for 50 gm = ₹105 for 750 gm. Add 140 for 1 kg. So, 140+105=₹245. Well! She could have subtracted ₹35 for 250 gm from ₹280 for 2 kg to get ₹245 for 1 kg 750 gm. Or, there can be faster ways to do such kind of computation. This is not important here whether it was computationally most efficient method or not. She was able to do the work reasonably well without depending on any calculation devices. Practice, application and variations made her so strong in this.

Way back in the year 2004, I was interviewing a Computer Science and Engineering graduate for a suitable position in a reputed software company. He had already cleared our technical test. There was a column in the application form asking for the expected salary per annum. He had filled ₹25000 per month. I brought it to his notice that expected salary per annum was being asked, not per month. He took out his notebook and pen from his bag, wrote 25000 and below that 12, and started multiplying the way we used to multiply in our school days. I wanted him to do it faster. To this, he replied; “sorry sir, I haven’t brought my calculator today.”

Well, nothing can be generalized from these incidences. It depends on individuals as how they study, understand and apply. However, we find heavy rush in coaching institutions where students are prepared for entrance or job related examinations. Similar tricks as used by the mango seller are taught to them in subjects like numerical ability, quantitative aptitude etc. We don’t require to learn them separately. And, if we need to learn them this way, then it is extremely difficult to do good without going back to basics. So, why not study the basics right way right at the school level itself? At this stage simple things with very deep applications are taught. Mostly, the focus remains on getting the marks. Evaluation system is such that one can score very high marks without understanding the concepts properly. Students have to spend huge money and time at later stage to learn similar topics, but some of the damages done at earlier stage cannot be reversed. So, please don't make this mistake. Practice, apply and create variations. It makes Mathematics at school level highly enjoying.

 Mathematics courses for classes X, IX, and VIII at make the students understand the concepts deeply and make them enjoy the subject. Courses on Optimisation Techniques are for students of professional courses that increases their employability in a drastic way. These courses have been created by such professionals who have taught and applied mathematics at advanced level and have researched on learning problems of earlier stages that cause big hindrance in doing good at later stage. These courses address this issue right in the beginning. Cost practically nothing and can make a big positive difference. Check it yourself and help those who need this.