Ancient approaches and modern maths

Damian discusses why the process of conversation is more effective than just instructing students.

It’s important to have great maths conversations because they allow us to process, make sense of and resolve apparently conflicting ideas in order to learn mathematics.

This is an extract from Plato’s Meno C450BC in which Socrates seeks to demonstrate to Meno, a rich statesman, that learning isn’t a process of acquiring new facts, it’s one of recollection.

The full dialogue, which I’d encourage you to read, is one that fascinates me – written around 2500 years ago, it’s one of the earliest references to maths pedagogy. It also highlights something that is still true now and will likely still be true in another 2500 years to come: with the right questions, conversation can enable a student to realise they know something without actually telling them.

The dialogue, observed by Meno, is largely between Socrates and an uneducated boy. Socrates guides the boy through a task with a sequence of questions, demonstrating to Meno that, though uneducated, the boy is able to understand how to construct a square whose area is twice that of a given square without being told how.

The dialogue enables the teacher (Socrates) to see what questions need to be asked next to enable the boy (the ‘student’) to make proper sense of the situation: Socrates is assessing the boy’s prior knowledge.

Secondly, the dialogue helps to bring abstract objects out into the open, like a mathematical walk around an abstract world of mental constructs (lines, squares, lengths, equality, area etc): Socrates draws a diagram in the sand to support the boy in developing his mental constructs.

Lastly, the dialogue enables the teacher to develop the learners’ motivation and curiosity by creating a tantalising tension in the student’s mind (the cognitive conflict between the natural tendency to double the lengths to double the area, yet seeing that this cannot be the correct answer): Socrates doesn’t correct the boy but requires him to answer questions which enable him to see the contradictions in his own reasoning.

Considering the above, the modern guidance on teaching maths might easily have been written by Plato and voiced by Socrates in this same dialogue.

It’s remarkable that 2500 years ago, with no knowledge of cognition, neuroscience or modern educational research, Plato was so “on the money” with his pedagogical demonstration, but perhaps all effective teachers of mathematics learn early on that the process of conversation is much more effective than just instructing students in a method.