[Dedicated to all my friends who know me really well and were with me during the times described below, all my teachers who loved me for what I was, and to all my students who liked me for the reasons only they know :) Happy Teacher's Day!]
"Is There a ‘Right’ Way to Learn Math?" - I read this article today and I could relate to this article so much that I felt I was writing the first few paragraphs myself..
The exact example of the relation between multiplication & addition happened with me too, and incidentally that was my first thrilling experience with the subject. When I discovered that 2 x 3 is the same as 2 + 2 + 2, I was thrilled, but when I realized that is is same as 3 x 2 and further that all of these also equal 3 + 3, I wanted to jump out of joy. The excitement continued for a few days, those few nights were my best sleep nights.
And my fascination for Mathematics continued, for a really long time particular fascination of numbers remained, while other areas like Trigonometry & Calculus enjoyed their own share of charm as well. Whatever the teacher taught in the class, used to just get imprinted on to my mind (I have a good memory people say, I agree too though it is slightly fading away - as much as I don’t want to admit, people grow old and I am no exception! :) I do have a strong photographic memory too), I never needed any repetition of any concept, anything. Once, was enough, most likely because I was in love with the subject. While I was a really studious student, I used to religiously revise what was taught in school that day and read things myself - before & after type of a thing to understand the basics of the concept taught. I would rightly guess exactly what questions would come in the exam, and when I come out of my exam I would know exactly how much would I score because I knew exactly how many marks would be cut for what kind of mistake. I never got anything without hard work, real hard work. If at all I missed a small concept, small snippet of something, that one small little thing will appear in the exam. The pattern continued through my childhood and I got real tight slaps from my mother when I lost marks because I didn’t revise that one little tiny thing. Many of my classmates did really well even without studying as religiously as me. I realized ‘luck’ wasn’t for me. I grew up to become even more studious hence. While in college, I used to sit with the calculator (the scientific calculator - it was Orpat, this one) for hours together just like that playing with numbers, I discovered the pattern:
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987...
The differences between say 12 x 6 and 16 x 2; 15 x 7 and 17 x 5 and why those patterns and so on, by myself.
Unfortunately, I didn’t have anyone around to share my excitement. There was something about the subject, about those numbers, all types of numbers, those theorems, the parabolas, the hyperbolas, the tan thetas and sin thetas and cos thetas. Questions like ‘why was the derivative of sin theta, cos theta?’ - I would think of these questions myself and I would find answers. It was true nirvana! Two specific instances I remember from my college days are:
1. f(x) = 1/ax: My professor who used to teach us Linear Algebra, asked a question casually once on something on some function. He described some unique thing about that function and asked us to guess and let him know the next day. All that day - during the class, after the class, during my commute to home after college, doing my household chores I kept on thinking. Suddenly, while I was doing the dishes at home late evening that day, there was a spark in my mind. I had the answer. The function was f(x) = 1/ax. Next day in the class, he asked and I answered. I was confident it was true because it was satisfying all the clauses mentioned. My professor reacted ‘Vhery good’, and he would almost jump off the dias. ‘Very good’, he repeated!
2. Two lines of regression: Related to Mathematics, my profound love to Statistics also grew. I was particularly in love with Regression as a topic. And while reading through this book Fundamentals of Mathematical Statistics by Gupta & Kapoor (this book), I found something very different from what I usually worked on. Usually, there is a regression line and we have a dependent variable and an independent variable. At least I, never thought of the case when we interchange the roles of the 2 variables. Hence, comes the concept of 2 lines of regression. This was not my discovery though, but there was something about this concept. I read the entire chapter twice and thrice to just multiply the thrill. I wished before the exam that that question should come and I would answer, and it did, and I answered like I achieved nirvana! I had this thing, I would leave all simple questions, pick up the ones that are challenging, and answer them first. Feel the nirvana and then answer the rest of them which didn’t matter much, from the nirvana standpoint. It worked, my hands ached after every exam because my mind ran faster than my hands & fingers and my hands & fingers used to feel literally racing with my mind. In that exam, I scored 58/100, for some reason all my answers were incorrect but I was extremely happy because that one question was there and I had the opportunity to answer that.
I grew up to teach Mathematics at school, both Maths and Statistics at college and so on. I loved teaching too, but never wanted to teach the regular topics, though some of my students felt the same way I felt as a student, on some concepts that I would consider basic by then. So, I could relate. I loved teaching because I liked learning, the thrill remained though not that much because I was ‘working’ and always chasing a deadline, in this case covering up the entire syllabus.
Anyway, life after that wasn’t as interesting.
"Is There a ‘Right’ Way to Learn Math?" - I read this article today and I could relate to this article so much that I felt I was writing the first few paragraphs myself..
The exact example of the relation between multiplication & addition happened with me too, and incidentally that was my first thrilling experience with the subject. When I discovered that 2 x 3 is the same as 2 + 2 + 2, I was thrilled, but when I realized that is is same as 3 x 2 and further that all of these also equal 3 + 3, I wanted to jump out of joy. The excitement continued for a few days, those few nights were my best sleep nights.
And my fascination for Mathematics continued, for a really long time particular fascination of numbers remained, while other areas like Trigonometry & Calculus enjoyed their own share of charm as well. Whatever the teacher taught in the class, used to just get imprinted on to my mind (I have a good memory people say, I agree too though it is slightly fading away - as much as I don’t want to admit, people grow old and I am no exception! :) I do have a strong photographic memory too), I never needed any repetition of any concept, anything. Once, was enough, most likely because I was in love with the subject. While I was a really studious student, I used to religiously revise what was taught in school that day and read things myself - before & after type of a thing to understand the basics of the concept taught. I would rightly guess exactly what questions would come in the exam, and when I come out of my exam I would know exactly how much would I score because I knew exactly how many marks would be cut for what kind of mistake. I never got anything without hard work, real hard work. If at all I missed a small concept, small snippet of something, that one small little thing will appear in the exam. The pattern continued through my childhood and I got real tight slaps from my mother when I lost marks because I didn’t revise that one little tiny thing. Many of my classmates did really well even without studying as religiously as me. I realized ‘luck’ wasn’t for me. I grew up to become even more studious hence. While in college, I used to sit with the calculator (the scientific calculator - it was Orpat, this one) for hours together just like that playing with numbers, I discovered the pattern:
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987...
The differences between say 12 x 6 and 16 x 2; 15 x 7 and 17 x 5 and why those patterns and so on, by myself.
Unfortunately, I didn’t have anyone around to share my excitement. There was something about the subject, about those numbers, all types of numbers, those theorems, the parabolas, the hyperbolas, the tan thetas and sin thetas and cos thetas. Questions like ‘why was the derivative of sin theta, cos theta?’ - I would think of these questions myself and I would find answers. It was true nirvana! Two specific instances I remember from my college days are:
1. f(x) = 1/ax: My professor who used to teach us Linear Algebra, asked a question casually once on something on some function. He described some unique thing about that function and asked us to guess and let him know the next day. All that day - during the class, after the class, during my commute to home after college, doing my household chores I kept on thinking. Suddenly, while I was doing the dishes at home late evening that day, there was a spark in my mind. I had the answer. The function was f(x) = 1/ax. Next day in the class, he asked and I answered. I was confident it was true because it was satisfying all the clauses mentioned. My professor reacted ‘Vhery good’, and he would almost jump off the dias. ‘Very good’, he repeated!
2. Two lines of regression: Related to Mathematics, my profound love to Statistics also grew. I was particularly in love with Regression as a topic. And while reading through this book Fundamentals of Mathematical Statistics by Gupta & Kapoor (this book), I found something very different from what I usually worked on. Usually, there is a regression line and we have a dependent variable and an independent variable. At least I, never thought of the case when we interchange the roles of the 2 variables. Hence, comes the concept of 2 lines of regression. This was not my discovery though, but there was something about this concept. I read the entire chapter twice and thrice to just multiply the thrill. I wished before the exam that that question should come and I would answer, and it did, and I answered like I achieved nirvana! I had this thing, I would leave all simple questions, pick up the ones that are challenging, and answer them first. Feel the nirvana and then answer the rest of them which didn’t matter much, from the nirvana standpoint. It worked, my hands ached after every exam because my mind ran faster than my hands & fingers and my hands & fingers used to feel literally racing with my mind. In that exam, I scored 58/100, for some reason all my answers were incorrect but I was extremely happy because that one question was there and I had the opportunity to answer that.
I grew up to teach Mathematics at school, both Maths and Statistics at college and so on. I loved teaching too, but never wanted to teach the regular topics, though some of my students felt the same way I felt as a student, on some concepts that I would consider basic by then. So, I could relate. I loved teaching because I liked learning, the thrill remained though not that much because I was ‘working’ and always chasing a deadline, in this case covering up the entire syllabus.
Anyway, life after that wasn’t as interesting.
