> I think it can be hard to empathize with what it's like to be a beginner. In a similar vein, there's pi ≈ 3 (within 5% error). When we've an issue with high

> I think it can be hard to empathize with what it's like to be a beginner. In a similar vein, there's pi ≈ 3 (within 5% error). When we've an issue with high-school students having an infirm grasp of the very concept of volume, it seems an odd allocation of effort to have middle-school students struggle with 4/3 pi r^3, while failing to tell early primary-school students that "the volume and area of a ball are about half that of the box that wraps it".