ABSTRACT
This chapter discusses common mistakes in math instruction and explains the misunderstandings behind them. The word length comes from long, and it makes sense to assume that "length" refers to the longer sides of a rectangle. The perimeter and area of a square can be calculated using the formulas for a rectangle because it is a rectangle. In comparing a rectangle to a square, Jane said this to her children: "A square has four congruent sides but a rectangle has two longer sides and two shorter sides". Although Jane realized that a square is a special rectangle, in practice she often regarded these two shapes, unwittingly, as being two different categories. For example, before presenting geometric solids, Jane wanted her children to review some common 2-D shapes so that when it came to a face on a solid, they could easily recognize that shape.
