When Euclid introduced his people Items, one of the great intellectual constructions of humanity, to Ptolemy I, King of Egypt, the response he received was: "Are there no smoother roads to geometry?" "No, there are no royal roads to mathematics," Euclid retorted.
Euclid, a wise man of humble origins, felt able to tell the successor of the Egyptian pharaohs that if he wanted to delve into geometry, he would necessarily have to follow the same path as the rest of us. In this way, he left us geometry as a democratic legacy for humanity.
Now, if there are no royal roads to geometry, there are some roads that are easier to navigate than others. Designing the best is the work of didactics.
Geometric reasoning is nothing more than rigorously reasoning with objects of a postulated reality—for example, an equilateral triangle—to discover the eternal truths implicit in their form and communicate them in precise language. Mathematical objects are conceptual fictions. Their study, therefore, goes far beyond their usefulness. When one of his disciples asked Euclid, "What good does knowing this do me?", the great geometer gave him half a drachma and dismissed him.
Precisely because geometry is a form of knowledge not subject to any extrinsic necessity, it provides us with pure experiences of order and rigor. And this, as Plato knew, is the best way to care for our soul.
Pierre-Louis Lions, a great French mathematician, often said that if we want to give opportunities to the poor, we must provide them with a good mathematical education. I agree: If we want to help the poor, let's teach them mathematics in the most accessible way possible, but without lowering its demands or rigor. We avoid designing poor curricula for the poor, because they lead nowhere.
The elements They aren't easy. But is there anything truly great—a great love, for example—that is given to us effortlessly? Look at the effort we put into caring for our bodies.
When we offer poor students a curriculum that focuses more on what is familiar or interesting than what is challenging, we are selling them a pig in a poke. We are offering them not compassion, but condescension. If there are no books at home, schools will have to be filled with books. And if the family vocabulary is very limited, classrooms will have to be filled with words.
We must open the windows of schools to horizons that transcend the family environment. We cannot deny the poor contact with Homer, Bach, Euclid, Mompou, Velázquez, and Joanot Martorell. In pedagogy, golden pills lead to cultural marginalization. School cannot be an extension of the family home, but rather a place in which to experiment with what we lack at home.
The mission of school is to help us transcend the horizons of our host world to facilitate our movement into progressively broader cultural spheres, without feeling ashamed of ourselves for our lack of resources. School is not designed to navigate within what is known, but to open avenues of exploration into the unknown. Or do our students not have the right to transcend the boundaries of their postal codes?
If schools don't encourage poor children to go beyond their usual horizons, who will? If schools abandon that mission, they are admitting that cultural capital is part of the exclusive inheritance of the fortunate.
Undoubtedly, children from culturally sophisticated homes have more tools to explore the world. But no one, looking face to face with a 6-year-old, can tell what their math grade will be in the university entrance exam. Disciplinary literacy, without reflective observation of their specific vocabulary.
The Marquis of Tamarón once asked on his blog: "To all who honor me with their comments, please avoid careless spelling." It would be terrible if there were noble paths in spelling.
It's worth remembering that the poorer our language, the poorer our thinking; that we cannot construct hypotheses without mastering the conditional; that it's necessary to strive to write well precisely because it's difficult. As Christophe Clavé insists, eliminating the nuances of our language is like gravedigger.
