and ending up with more exploration at the top.
Knowledge was something the Greek philosophers were keen to find, to develop, to pass on. Real knowledge for them was not simply believing the truth, but also having reason to believe it.
So many of our beliefs are not well-founded; so much of what we are told at school we believe because we are told, not because of experience or evidence or conclusiveness. Real knowledge is a precious thing.
So, it seems to me, respecting the genesis of this founded belief is really important. We have all sorts of utilitarian ideas about why schooling, or a particular kind of schooling is good. It's good because we can participate in the economy, we can be internationally competitive. As the new English National Curriculum for maths has it, "it is essential to everyday life, critical to science, technology and engineering, and necessary for financial literacy and most forms of employment." True as that may be, maths, like all subjects, can be something else, an opening of the eyes, a body of undertandings, of knowledge. Finance doesn't know. Employment doesn't know. How can they guide us? How can they weigh opinions, find truth? Maths, like no other subject, can give a sense of what certain knowledge really feels like. We need that.
Have you ever read Plato's account of Socrates defence ("The Apology")? I recommend it. It's a really essential read, short, fascinating and pivotal. In it, Socrates describes his enemy-making quest to find what people really know:
Accordingly I went to one who had the reputation of wisdom, and observed to him - his name I need not mention; he was a politician whom I selected for examination - and the result was as follows: When I began to talk with him, I could not help thinking that he was not really wise, although he was thought wise by many, and wiser still by himself; and I went and tried to explain to him that he thought himself wise, but was not really wise; and the consequence was that he hated me, and his enmity was shared by several who were present and heard me. So I left him, saying to myself, as I went away: Well, although I do not suppose that either of us knows anything really beautiful and good, I am better off than he is - for he knows nothing, and thinks that he knows. I neither know nor think that I know. In this latter particular, then, I seem to have slightly the advantage of him. Then I went to another, who had still higher philosophical pretensions, and my conclusion was exactly the same. I made another enemy of him, and of many others besides him.Read this too, from Jonathan Haidt's great book The Happiness Hypothesis:
In philosophy classes, I often came across the idea that the world is an illusion. I never really knew what that meant, although it sounded deep. But after two decades studying moral psychology, I think I finally get it. The anthropologist Clifford Geertz wrote that “man is an animal suspended in webs of significance that he himself has spun.” That is, the world we live in is not really one made of rocks, trees, and physical objects; it is a world of insults, opportunities, status symbols, betrayals, saints, and sinners. All of these are human creations which, though real in their own way, are not real in the way that rocks and trees are real. These human creations are like fairies in J. M. Barrie’s Peter Pan: They exist only if you believe in them. They are the Matrix (from the movie of that name); they are a consensual hallucination.This is why it's great that we can find knowledge that's as firm as our direct knowledge of rocks and trees. And young children have this as they explore the world. Papert, points out how Piaget's "genetic epistemology" made us much more conscious of how much young children are learning:
While we can “see” that children learn words, it is not quite as easy to see that they are learning mathematics at a similar or greater rate. But this is precisely what has been shown by Piaget’s life-long study of the genesis of knowledge in children. One of the more subtle consequences of his discoveries is the revelation that adults fail to appreciate the extent and the nature of what children are learning, because knowledge structures we take for granted have rendered much of that learning invisible. We see this most clearly in what have come to be known as Piagetian “conservations”.
(It's interesting re-reading Seymour Papert's Mindstorms, because I find things in there that I say. Now I wonder, did I get that from Papert? Or was there just a similar take on things?)
School can and should be about "understanding rather than turning the handle" (as someone has written on their Twitter profile). There will have to be some handle-turning for sure, but let's keep pride of place for the understanding, the knowledge.