Mathematics for everyone: Insights from Socratic teaching

In Plato’s dialogues, he recounts a conversation between Meno and Socrates (Cooper, 1997). In this specific dialogue, Socrates is discussing virtue with his fellow interlocutor, Meno, and whether it can be taught.

Socrates interrogates Meno, forcing him to provide definitions and clarification. Meno fails to satisfy Socrates, so they decide to tackle the problem together. But Meno is hesitant. He realises that they cannot discover what they do not know since they would not be able to verify if they truly know.

It at this point when Socrates suggests to Meno that learning is process of recollection; that all the knowledge a person learns is merely remembering what they already know. A ridiculous but compelling idea.

To illustrate this, Socrates makes one of Meno’s servants demonstrate and explain a geometry proof, knowing that the slave, a boy, has no mathematical education. To further illustrate his theory of learning, Socrates tells Meno that he will not “teach” the boy but rather ask him questions and from that, the boy will prove a known fact about a square and its double.

He goes on to question the boy and takes notes in the sand. At first the boy seems to demonstrate an adequate mathematical understanding but as soon as Socrates asks the boy to apply his understanding, the boy can only utter incorrect answers. Socrates, undeterred by this, alters his line of questioning and not long after that, the boy gains a simple understanding of squares and successfully proves a geometric theorem.

This story serves to illustrate a fundamental truth: that mathematics is a sense, an instinct that can be refined just like a sense of rhythm. In this short story, the process of mathematical education is clearly demonstrated. The student has an intuition about the world or makes an observation and thereafter decides to investigate. Through reason, the student arrives at a conclusion and has subsequently learnt more about the world.

Obviously, the guidance of an astute teacher plays a significant role in the process. We can see from Socrates example that a high quality education, especially a mathematical one, is where that student is an active participant. It is the teacher’s responsibility to instil the natural curiosity that burns within each learner by guiding them towards asking the right questions and refining their natural curiosity.

It is also important to note that the boy fails at first. But this is also part of the mathematical learning process. Refinement only comes through correction and there is no doubt that the slave boy left that scene having a slightly stronger instinct for mathematics. He did not become a mathematician but became more mathematical in his thinking.

Anyone can endeavour to refine their mathematical sense. Its starts by training their natural ability to observe, to question and to abstract.

Mathematics is the endeavour to understand reality through abstract concepts and logic. It involves the discovery of properties of abstract concepts and the use of reason to prove these properties.

Mathematics furthers our instinctive ability to abstract by formalizing it. It allows us to communicate our abstraction to others and record them in a concrete and meaningful manner. The socialization of abstractions allows for greater and more complex understanding of the concepts an individual can develop. Concepts can be reviewed, revised, or added to.

Thus, given the right teacher and learning environment mathematics is for everyone.