Learning Math
I will provide a caveat before I start rambling, I am not a teacher or an educator. But... I have taught occasionally and I have learnt!
Everyone knows that the way we learn at school, I can at least speak for India, is not the best possible way. We are taught to pass exams, we are taught to follow or memorise instruction manuals, but not taught to be creative and to understand and appreciate stuff.
But what our educators don't realise, or may be they do realise but don't care about, is that most of what is taught in schools are basic life skills!
Take mathematics, for instance. We use it every single day! We apply the basic principles unwittingly because they are so intuitive.
But, we are not taught in the same intuitive manner.
I want to scream / scold / rebuke / kill? everyone who made us learn 'steps' and formulae, who made us memorise tables, who taught us long form of division without explaining what it means to divide and when do we do it.
Anyone who has a basic cellphone (that means practically everyone) owns a calculator. So why do people lay so much stress on arithmetic. I want to laugh back at people who laugh at me when I can multiply 37 by 26 in my head, or who think being able to divide 658 by 14 in their heads is 'cool'. Point is I know what it means in real life terms to multiply 37 by 26. You'd be surprised to see how many people don't.
I repeat myself, these are life skills! This is not some high level mathematics, that you need that kind of a brain. You need these skills to be able to survive in this world.
Take weighted averages. Anyone who has painted knows the concept intuitively. If you mix two parts red with two parts white you get a deeper pink as compared to one part red and three parts white. It is such a simple visual concept that a 5 year old can appreciate it! But here lies that problem. In school we are taught a formula, X= (X1*N1+X2*N2+X3*N3)/(N1+N2+N3). What the hell that means?
Every child learns differently. The painter would learn to appreciate and learn to consciously apply this concept with the colours' example. A more literal person would need to understand it in language. Or just simply be told that if you want the tea to be sweater just put more sugar in it!
Half the time students are left wondering why are they being taught something. But when they face a problem in real life then they do not know what do with it. When one learns that the h sq = a sq + b sq as the Pythagoras theorem, one never realises or is made to realise that one would be using its applications every single day! What do you do to decide the shortest path from point A to B? Apply the Pythagoras theorem! What do you do to find out how much you owe the guy who painted your house? Use surface area! What do you do to find out how much salt to put in a dish for ten people when you have only cooked only for four before? Use ratio and proportions! Or fractions! Or weighted averages! It's the same concept in different contexts! Do we even realise that!
It is impossible to plan your savings, cook food, stitch a dress, play and follow sports, build or buy a house, buy anything! and make important decisions in your life without having a working knowledge of mathematics! And we all have that! It is just that when we were kids and were taught all of this in school, and then college, and then post grad (!), we never realised what it was for. That is because nobody took the time out to do so. Our school teacher taught us to pass board exams. (Practice, practice, practice!) Our coaching teacher told us 'short-cuts' to 'solve problems' in a jiffy. Our college teacher was so jaded and uninspired, and by that time we also got used to learning (or rather, memorising) a certain way.
I cringe when I look at my younger cousins, who are in school, memorising steps or formulae. I never wasted my time doing that. There were far too many formulae for me to remember! Far simpler to take the logic route.
I cringe even more when I see grown adults in several contexts trying to remember steps to do something at work. Not paying attention or asking questions (and right questions!) in training sessions, being annoyingly passive learners and later complaining that 'systems' are too complicated or dysfunctional! Blaming their inability to make decisions on wrong systems and not on their inability to process information.
But it is not their fault. Some of us were lucky to receive the right kind of conditioning when we were kids by some sensible adult. Maybe a parent, maybe a maverick teacher. Some of us have a 'math' brain. Some of us read and conditioned ourselves. But there are scores of us who have not been conditioned to think creatively in everyday situations. It is such a sorry state of affairs that our education systems attempts to make doctors, engineers and MBAs out of everyone, but cannot even make fully functional adults who are well-quipped with basic life-skills.
Everyone knows that the way we learn at school, I can at least speak for India, is not the best possible way. We are taught to pass exams, we are taught to follow or memorise instruction manuals, but not taught to be creative and to understand and appreciate stuff.
But what our educators don't realise, or may be they do realise but don't care about, is that most of what is taught in schools are basic life skills!
Take mathematics, for instance. We use it every single day! We apply the basic principles unwittingly because they are so intuitive.
But, we are not taught in the same intuitive manner.
I want to scream / scold / rebuke / kill? everyone who made us learn 'steps' and formulae, who made us memorise tables, who taught us long form of division without explaining what it means to divide and when do we do it.
Anyone who has a basic cellphone (that means practically everyone) owns a calculator. So why do people lay so much stress on arithmetic. I want to laugh back at people who laugh at me when I can multiply 37 by 26 in my head, or who think being able to divide 658 by 14 in their heads is 'cool'. Point is I know what it means in real life terms to multiply 37 by 26. You'd be surprised to see how many people don't.
I repeat myself, these are life skills! This is not some high level mathematics, that you need that kind of a brain. You need these skills to be able to survive in this world.
Take weighted averages. Anyone who has painted knows the concept intuitively. If you mix two parts red with two parts white you get a deeper pink as compared to one part red and three parts white. It is such a simple visual concept that a 5 year old can appreciate it! But here lies that problem. In school we are taught a formula, X= (X1*N1+X2*N2+X3*N3)/(N1+N2+N3). What the hell that means?
Every child learns differently. The painter would learn to appreciate and learn to consciously apply this concept with the colours' example. A more literal person would need to understand it in language. Or just simply be told that if you want the tea to be sweater just put more sugar in it!
Half the time students are left wondering why are they being taught something. But when they face a problem in real life then they do not know what do with it. When one learns that the h sq = a sq + b sq as the Pythagoras theorem, one never realises or is made to realise that one would be using its applications every single day! What do you do to decide the shortest path from point A to B? Apply the Pythagoras theorem! What do you do to find out how much you owe the guy who painted your house? Use surface area! What do you do to find out how much salt to put in a dish for ten people when you have only cooked only for four before? Use ratio and proportions! Or fractions! Or weighted averages! It's the same concept in different contexts! Do we even realise that!
It is impossible to plan your savings, cook food, stitch a dress, play and follow sports, build or buy a house, buy anything! and make important decisions in your life without having a working knowledge of mathematics! And we all have that! It is just that when we were kids and were taught all of this in school, and then college, and then post grad (!), we never realised what it was for. That is because nobody took the time out to do so. Our school teacher taught us to pass board exams. (Practice, practice, practice!) Our coaching teacher told us 'short-cuts' to 'solve problems' in a jiffy. Our college teacher was so jaded and uninspired, and by that time we also got used to learning (or rather, memorising) a certain way.
I cringe when I look at my younger cousins, who are in school, memorising steps or formulae. I never wasted my time doing that. There were far too many formulae for me to remember! Far simpler to take the logic route.
I cringe even more when I see grown adults in several contexts trying to remember steps to do something at work. Not paying attention or asking questions (and right questions!) in training sessions, being annoyingly passive learners and later complaining that 'systems' are too complicated or dysfunctional! Blaming their inability to make decisions on wrong systems and not on their inability to process information.
But it is not their fault. Some of us were lucky to receive the right kind of conditioning when we were kids by some sensible adult. Maybe a parent, maybe a maverick teacher. Some of us have a 'math' brain. Some of us read and conditioned ourselves. But there are scores of us who have not been conditioned to think creatively in everyday situations. It is such a sorry state of affairs that our education systems attempts to make doctors, engineers and MBAs out of everyone, but cannot even make fully functional adults who are well-quipped with basic life-skills.
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