Understanding Math: How to Overcome Fear of the Abstract
Far from the prying eyes and ears of the court, Varys and Tyrion Lannister discuss the power games in King’s Landing that led poor Ned Stark, yet King in the North, to be beheaded in public. from the library.
Tyrion: “I don’t understand how the Maesters can read all these books. It gives me a headache. »
Varys: “That’s because you don’t know the formula. »
Tyrion: “The formula? What are you talking about ? »
Varys: “The formula for reading. Each book is like an equation, with a beginning, a middle and an end. You must find the unknown to discover the solution. »
Tyrion: “You sound like a Maester, Varys. How can I find this unknown? »
Varys: “By asking questions. Looking for answers. By connecting the dots to form a coherent whole. You will see, once you understand the formula, reading will be a breeze. »
In this 3rd book of Game of Thrones “the Battle of the Kings”, it is the destiny of the two men that is at stake. Varys, intelligent and manipulative character, wants to emphasize the importance of education and knowledge to Tyrion Lannister mischievous offspring but despised by the crown.
The solution is in reading. Reading books, to read men.
How to thwart cruel political games and survive? The method is the key: state the dilemma, identify the clues and find the solution or the unknown.
And everything is solved like a math problem.
A revelation which, in the 9th century, seduced the court of Caliph Al-Ma’mun.
Algebra to the Rescue of the Kingdom of the Thousand and one nights
Once upon a time …
A request of the utmost importance
In the streets of Baghdad, Muhammad Al-Kwharizmi descends the steps of the palace. Caliph Al-Ma’mun asked for it expressly. As he greets the Abna al-Dawla guards, one of them announces his presence.
“O Commander of the Faithful, here is the Honorable Al-Khwarizmi, mathematician and philosopher of the stars, who has come to pay homage to your person”.
Despite the urgency of the monarch’s request, the scholar enters without apprehension because he knows the Caliph’s propensity to work for the well-being of his subjects. Founder of the famous “House of Wisdom”, Al-Ma’mun dreams of a harmonious and balanced, highly educated and cultured Islamic society.
His passion for science and the arts is unparalleled. Thus he sees in Al-Khawarizmi and his knowledge the vehicle which will enable him to improve the daily life of the kingdom and to promote science and mathematics in the world.
Caliph: Greetings, Al-Khawarizmi.
Al-Khawarizmi: God’s blessings be upon you, your highness.
Caliph: Your dedication and expertise are invaluable to our society. I entrust you with an ambitious project. The people face several challenges on a daily basis in agriculture, trade or construction. So I am considering a book bringing together mathematical methods to solve all their problems with their solutions. This work will be of great use to all of us and to “Al-Mustaqbal”, future generations.
Al-Khawarizmi: Your words touch me, Your Highness. I will do my best to write a manual that honors your trust and is useful to our people.
Over the following months, the mathematician works to list the usual questions and problems encountered with their resolution techniques. As for example, the equitable land shares, the exchange between merchants or the distribution of an inheritance.
A priceless work
But what will bring this book into the pantheon of humanity of works and into posterity is the purely theoretical part with which he introduces his manuscript: he describes in an abstract and methodical way the resolution processes that are put into practice in concrete problems:
“Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala” – “The summary drunk on calculation by restoration and comparison”.
Then as time passed, traveling to the West, his title was shortened by Latin-speaking mathematicians to al-Jabr wal-Muqabala. Finally, we kept only the first 2 letters: al-Jabr, algebra.
A field, a little boy and fabric
But what kinds of problems are solved in this book?
Concretely
Consider the following 3 questions:
- A rectangular field has a length of 8 and an area of 40. What is its width?
- A 40-year-old woman is 8 times her son’s age. How old is the boy?
- A fabric merchant bought 40 kg of 8 identical rolls. How much does a roll weigh?
These 3 questions bring the same number in response: 5
- Length x width = 40 therefore 8 x width = 40 therefore width is 5.
- Son’s age x 8 = wife’s age so son’s age x 8 = 40 so boy’s age is 5.
- 8 rolls x weight of a roll = weight of the rolls therefore 8 x weight of a roll = 40 therefore the weight of a roll is 5.
In fact, these 3 examples answer the same question :
What multiplied by 8 is 40? It’s 5.
Concretely, the number 8 and the number 40 may well be dimensions of cloth or lands, ages, tanks, computers or anything else. No matter, the mathematical treatment is the same: we divide 40 by 8 and we find 5.
It is the genius of Al-Khwarizmi, to have stripped these riddles of all their contextual clothing to derive the mathematical expression from them :
8 x “unknown” = 40.
or again : 8x = 40.
Haaaaa here is this famous unknown x! In the centuries that followed, these riddles took the name of equations.
Symbolically
And Al-Khwarzimi goes even further. The scientist asserts that these equations may not even depend on any numerical data :
Let’s look for a number (unknown named x) which multiplied by a quantity 1 (here 8) gives a quantity 2 (here 40).
And this is how abstraction in mathematics officially came into being.
So that’s algebra: proposing methods for solving this type of mathematical riddle or “equations”… which find answers to everyday difficulties.
And since that day…
Today in the 21st century, many children encounter difficulties with its algebraic equations.
It’s as if we were calm counting our candies, our cubes, our apples and our lemons and hop we end up with x’s, y’s, z’s, ” zunknowns “.
How to Understand Math – Learn Differently
Fortunately, many alternative methods offer active learning through concrete activities and creative approaches with students.
Let us note, the Montessori pedagogy: it bases its method on 3 essential principles for learning: the free choice of activity by the child, work at his own pace and the manipulation of objects. So to solve an algebra problem like the equation x + 4 = 18 and find the value of x, we will provide beads or cubes to the student.
The Steiner Method emphasizes experiential learning and holistic teaching to understand math. Students are encouraged to explore mathematical concepts through creative activities such as drawing and drama. To find the solution to this same equation x + 4 = 18, we will use for example the drawing of a balance with 2 weights One weighing x + 4 and the other 18.
The Singapore method, which is inspired by many innovative pedagogies, bets on the use of diagrams and drawings, or on the proof of the formula in the real world to help students understand abstract mathematical concepts. Will use these two methods for example
But you can also do algebra every day, everywhere, at home, in the street, at sports, on a walk, at the cinema, on the way to vacation…
How to Understand Maths – Everyday
In the kitchen
Mathematical equations in the kitchen ? Yes. All the time. Recipes for cakes and other pies and flans are full of ¼ liter of milk, kilograms, grams and spoonfuls that must not only be quantified but adjusted or even multiplied to satisfy the gourmets that we are (click here for the article ) .
At the store
Is your pre-teen watching his pocket money to buy the latest Playstation? Knowing that it costs 350€ and that he will receive 60 from grandma for his birthday in addition to the 20€ of weekly pocket money from the parents, he will finally be able to buy it in … Bravo! He does algebra… and he’s motivated!
On holiday
“When are we getting there?” Repeated dozens of times since your departure from Paris for the sunny beaches of Montpellier, this sentence begins to hit you on the system. Let’s take a deep breath and ask the following question “we have 200 km left and we are driving at 130 km/h, when will we arrive at our destination?” » Silence. Long sigh. Let’s try this: “when we arrive, knowing that the Fenocchio glacier closes at 8 p.m., will we have time to stop there? Now their brains are thinking: the equations of the 1st have a taste of vacation.
In sport
The “stats” of his favorite basketball player Lebron James are astounding with a record of 23,119 points! statistics are a branch of algebra that allow players to be evaluated but also to plan their training. For example for the athletes, one will calculate thanks to equations the loads of training, the times of recuperation, the distances traversed… All this with a view to future performances.
Epilogue
As the war against Cersei Lannister rages on, Varys carefully reviews the strategy and plan of attack. He worries that Tyrion is underestimating the enemy fleet. It is then written for the young Lannister:
“the numbers do not lie” .
Algebra has this particularity, it manipulates numbers to better extract itself from them. And make sense of it.
Generous, it becomes abstract to serve as many people as possible.
But at any time, it can become real again as soon as it is needed to find answers to your problems.
It was created by brilliant human minds to help men in their daily lives and your child uses it constantly without even paying attention to it.
So you wonder how to understand math? By realizing that we do it every day. So keep going!
Did you like this article? Share your thoughts and experiences in the comments below!
Sources
The Great Math Novel: From Prehistory to the Present. Mickaël Delaunay, Flammarion, 2016.
A game of thrones – The battle of kings. RR Martin, Dargaud, 2022.
