My tutor when I was in grade 7 turned me into a mathie!
In 1984, we moved to Algeria when my father was assigned his post as the ambassador of Qatar to Algeria.
I started my education in Belgium then after 3 years in Qatar, my father wasn’t sure I’d make it through the more advanced math they taught there.
My father got us this tutor, for both me and my sister who was in grade 4.
The first time we saw him he started with these statements: “I will teach both of you how to think differently, age and school grade have nothing to do with it”. “I will not teach you to do well in school, I will teach you for your life”. “Please forget everything you got from any school, we’ll start from the beginning, and we’ll see how far you can go”.
This was so inspiring, I felt like he was letting us into a secret goal that was higher than grades at school, he kept using the word “we” and he said “the grades will come, don’t worry about them, we’ll discover Math”.
First lesson: Numbers!
He started the lesson with “Remember, I told you to forget everything you got from school”, he asked me “Osama? How many of you are there?”.
I just replied “there are many boys like me”. He stopped me “NO! How many of YOU are there”.
I felt that I was an idiot, “One?”
“Yes, exactly”. “And how many of this sister do you have?” “How many of me are there?” “How many of your dad do you have”
We start with the only number that exists, “One”. There are no other numbers!
“No but, we don’t know anything you previously learnt at school”, we only have “One”.
“What do we call you and your sister?”
unsure, I muttered “two?”.
“NO! We don’t have other numbers! you’re One and One, what about all of us here, and don’t say three!”
“One and One and One”
As a shortcut, we invent names for many Ones, let’s agree to call the first number “Two” and the second “Three”. In the same way we can invent “Four”, “Five”, “Six” and many others. They don’t exist but we invented them.
Let’s also invent something else, putting all those ones together to get a number, let’s call it addition, and assign the symbol + to it. We’ll use the symbol = to show the result of what we did:
“What about 2+3? I know it’s 5 buy why?”
“You don’t know it’s 5! you need to get there.”
Think about the numbers and your notes, I’ll see you tomorrow!
“Just like the number one we found out, let’s imagine a dot! It can be anywhere, on this table, in outer space, or even inside my mouth.” “Let’s call it A”.
“Imagine another dot! also anywhere, let’s call it B”.
“Imagine a line that goes between them, we’ll call it a line segment AB.”
“If this line started with A, passes through B, and continues forever, we’ll call it a ray”.
“Forever?” “A ray like a ray of light?”
“A ray of light stops, this one is like a ray of light, it has a direction, but it never stops!”
“What if it continued forever in both sides?”
“We can call that a line”
“We’ll also speak later about ideas of many lines and their relations to each other, as well as the shapes between them, but let’s go back to our numbers”
“To see it better let’s invent a line of numbers”, “let’s call it the number line”.
“Draw a line, and move your pen somewhere on top of it”
“What’s the first number?”
“Let’s start with that, write 1 there, put dots with equal distances between them, over each one, write the next number, 2, 3, 4, 5, …”
“What about zero?” “It doesn’t exist yet, we just start with 1”.