The two ideas that Mason considered important in math — rightness and reason — are connected. It is our reasoning that convinces us an answer is right or wrong. How do we know we got a sum correct? We can take the numbers apart and add them another way, to see if we get the same answer. Or we can subtract one of the numbers from the sum and see if we get the other number. Or … well, how would you prove it?
More than anything else, Mason wanted her students to discover in math a sense of immutable truth, a truth that stands on its own, apart from anything we say or do, a truth we can explore and reason about but can never change.
This sense of rightness, of solid, unalterable truth, inspires a feeling of wonder and awe — she calls it “Sursum corda,” a call to worship — that delights our minds. It’s that “Aha!” feeling we get when something we’ve been struggling with suddenly fits together and makes sense.
From the very beginning, children should be doing this sort of informal proof, explaining how they figured things out. Don’t wait until high school geometry to let your children wrestle with ideas.
