About 140 odd English medium schools in five metros were surveyed. 30,000 odd students from classes 4,6 and 8 were asked questions to find how much they understood the concepts in mathematics, science and English.
Not surprisingly, students fared poorly in all these questions. They could answer the questions based on their recall. Anything asked differently than in the textbook was not answered. This clearly demonstrates the difference between learning something by rote learning and understanding something.
With the advent of objective method of questioning so prevalent in today's secondary and higher secondary exams, students get extraordinary marks. But they also belie the underlying truth that the student may not have 'understood' the concepts, because that is not tested by these exams.
It is here, where parents can perhaps play a bigger role. They can help their kids 'apply' their knowledge in day-to-day matters. For instance, a kid of 5 can count from 1 to 10, but does not understand the concept of '2' or '5' until you tell him to divide 6 chocolates between him and his friend. That is where your kid understand the 'meaning of numbers'.
When students learn to understand mathematics, they learn it to apply their knowledge with real life. They understand that what they are learning has direct relevance in their lives, and therefore start seeking it. Once the students get this linkage right, they really become 'educated' and 'smart'. Or they may just remain as intellectuals.