> Now let me be clear about what I’m objecting to. It’s not about formulas, or memorizing interesting facts. That’s fine in context, and has its place just as learning a vocabulary does— it helps you to create richer, more nuanced works of art. But it’s not the fact that triangles take up half their box that matters. What matters is the beautiful idea of chopping it with the line, and how that might inspire other beautiful ideas and lead to creative breakthroughs in other problems— something a mere statement of fact can never give you.
> By removing the creative process and leaving only the results of that process, you virtually guarantee that no one will have any real engagement with the subject. It is like saying that Michelangelo created a beautiful sculpture, without letting me see it. How am I supposed to be inspired by that? (And of course it’s actually much worse than this— at least it’s understood that there is an art of sculpture that I am being prevented from appreciating).
> By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes.
> Now let me be clear about what I’m objecting to. It’s not about formulas, or memorizing interesting facts. That’s fine in context, and has its place just as learning a vocabulary does— it helps you to create richer, more nuanced works of art. But it’s not the fact that triangles take up half their box that matters. What matters is the beautiful idea of chopping it with the line, and how that might inspire other beautiful ideas and lead to creative breakthroughs in other problems— something a mere statement of fact can never give you.
> By removing the creative process and leaving only the results of that process, you virtually guarantee that no one will have any real engagement with the subject. It is like saying that Michelangelo created a beautiful sculpture, without letting me see it. How am I supposed to be inspired by that? (And of course it’s actually much worse than this— at least it’s understood that there is an art of sculpture that I am being prevented from appreciating).
> By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes.