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Be Connected with Your Roots (Back to Basics) - Life Lessons from My Parents Applied in School Mathematics


Be Connected with Your Roots -- Back to Basics

My parents used to take us to our village (ancestors house) and nearby quite often. The lesson was to be connected with the roots. Being with our own people there, listening to them, understanding their way of living, embracing their way of caring etc. used to create so many valuable memories that I still consider those experiences on the top of the list of valuable experiences. These memories provide new energy, new way of looking at various situations and help in understanding the nuances of various challenges in life better. This doesn't mean that one should leave his present projects of life and go back to the roots. But, going back to the roots (physically or mentally) provides such understandings that helps in handling present challenges better. We take few examples from Cricket and Mathematics to substantiate it. Here, being connected with roots translates to going back to the basics.

The same applies everywhere. I remember, when great cricketer Sachin Tendulkar was out of form, expert used to suggest that he needed to work on his basics. That time he had most of the batting records in his name. Can he achieve this without having the basics right? But, even at most advanced level the problems can be better understood and handled by revisiting the basics and getting some clue from there. Even after scoring several hundreds in international cricket, he found that changing or modifying the way he holds the bat can help him come out of the run drought. Was he not holding the bat properly earlier? When we go back to basics from an advanced level we understand those basics with some greater nuances that helps in handling advanced topics better.  

While applying to school mathematics too, being connected with roots translates to keep getting back to basics. Getting back to basics doesn't mean that one has to again memorize multiplication tables from 1 to 40, or again learn how to draw a triangle etc. Let us see a classic example.

As a trainer I work with professionals on various topics related to analytics. And it is found frequently that the concept of Average needs to be revisited to avoid some serious problem at advanced level. Let us take one of my favorite questions below: 

You drive your car from Mumbai to Pune at a speed of 100 km/hr and drive back through the same route at a speed of 80 km/hr. What is your average speed? In the form of multiple choice question, I provide the choices as a) less than 90 km/hr, b) more than 90 km/hr, c) 90 km/hr, and d) you need to know distance to answer this. The frequency at which this basic question is answered wrong is alarmingly high. Most of the time people simply add 100 and 80 and then divide the resulting sum 180 by 2 to get the average as 90. This is wrong. 

If you have to find the average of two given numbers, adding them and dividing the sum by 2 is fine. But, if these numbers are being used to quantify certain properties, you need to understand the nature of the property before applying this concept of average blindly. There is an average speed in this question. When you drive faster you reach earlier. The distance traveled at the two given speeds are same. So, in this question, you are spending more time on slower speed than faster. So, the average speed has to be lesser than 90 km/hr. Average speed is equal to total distance driven divided by time. You can assume the distance between the two cities as x and find the time taken at both the speeds. You can compute the exact value of average speed and see that it's less than 90. 

I have seen people making serious errors in sales planning and similar decision situations by applying concept of average in wrong way. It may help going back to basics. Decisions being taken at advanced level go wrong because of deviating from the basics of average. It is rarely identified as people keep finding problems at the advance level only and compromise heavily on performance.

Another classic example of how going back to basics can help mastering certain concepts is related to number system. Those who have studied basics of computers must have studied various number systems like binary, octal, hexadecimal etc. They must have also learnt binary to decimal conversion, octal to decimal conversion, hexadecimal to decimal conversion, decimal to binary conversion, decimal to octal conversion, decimal to hexadecimal conversion and so on. Learning steps to do these conversions, solving various numerical problems to practice them, recalling the steps while solving some question when required and applying these steps to solve them is a very torturous way of learning this. Most of the books have separate subheadings in the chapter related to conversion of numbers to cover each of such conversions. 

Just go back to basics to learn the conversions. You have studied decimal number system in your early school days. You have learnt how to write a number in expanded form. Same thing as having unit's place, ten's place, hundred's place, thousand's place, ten thousand's place etc. Why are they 1, 10, 100, 1000, 10000, etc.? Something to do with 10; the base of the decimal number system. Understand the logic again. What happens if the base changes to something else like 2 for binary number system, 8 for octal number system, 16 for hexadecimal number system, or any other base. Just stick to the basics and you can do all the conversions without remembering any of the steps given in the books. In fact, you can do some magical things with mixed radix numbers where the base changes with positions in a number. This only needs revisiting the number system and understanding the nuances of it. 

Suppose you drive 200 km in which 40 km road is bad. In this you are able to drive at a speed of 10 km/hr. Rest of the road is good and you drive in that part at a speed of 80 km/hr. You spend 4 hours to drive through 40 km of bad road and 2 hours to drive remaining 160 km of good road at a speed of 80 km/hr. So, out of 6 hours of your journey 4 hours is on bad road and only 2 hours is on good road. Just 1/3rd or 33.33% of your journey time is on good road. But, the team maintaining that stretch of road gets appreciation for their great work.  In fact only 40 km out of 200 km of road is bad. Which is just 20% of that stretch. So, the idea that you make about your travel experience by understanding the proportion of the bad road to the total road length is not a correct idea. Your actual experience may be quite bad than what you expected with this logic. Similarly, the maintenance team performance is not that great if the goal is to make travel comfortable. If you look around yourself, you may find quite a few such examples where people unknowingly are deviated from the basics and keep making incorrect conclusions.

Focusing on the basics will help you simplify and streamline your efforts. The takeaway is this: when you're feeling lost or overwhelmed, go back to basics. Be connected with the roots. Apply first principles to understand the nuances.