Math is all about practice…isn’t it?
Well, yes and no.
Practice in math does help. Yes, but one can over-compensate the lack in understanding through practice. So in school tests/ exams the scores of a ‘high practice, low real understanding’ student can be pretty impressive.It becomes a self-fulfilling prophesy! We look at the score and exclaim, “see, practice makes perfect!”
The gaps in understanding start glaring when the exam has ‘out of syllabus’ kind of questions! That is where very few do well and these are those children who understand well, and think on their feet.
Let us demonstrate what we mean when we don’t over emphasize practice. How practice without understanding takes away intuition and makes one dull!
Ask a 3rd, 4th or maybe even a 5th grade student who has done ample practice in math with additions and multiplications….
The total of the ages of say, 5 members of a family is 100 yrs. What will be the total …after 3 years?
Most children mechanically (and erroneously) respond with 300 or 500….
Because that’s what seems like the smartest thing to do. That is what they have done in situations that didn’t seem simple enough to allow addition! That’s what they have been patted for!
All ‘good, obedient’ students have religiously learnt that LCM is least common multiple while HCF is highest common factor…They have done ample practice on finding LCM, HCF and also plenty of word problems to apply their newly learnt skill! They seem to have understood well, after all, have they not solved so many problems correctly, that too from so many different books and publications? Why, is that not a true testimony to their understanding?
Give these students a simple problem….What’s the least number of equal-sized, square tiles required to pave the floor of a hall that is 28 ft X 36 ft?
What’s the response?
Haven’t they come up with the LCM though it has absolutely NO relevance in the given context?
Well, this was your typical ‘out-of-syllabus’ question… It didn’t behave predictably… How unfair!!!