ABSTRACT
This chapter discusses mistakes in math instruction and explains the misunderstandings behind them. When Jane was teaching perimeter, she drew a few geometric figures on a grid. Her first figure was a rectangle. The next figure was a triangle. For lower-grade children, a simpler way would be to draw figures on the grid's horizontal and vertical line segments only. After her children had enough experience with 2-D shapes, Jane started exposing them to 3-D ones. During a lesson on coordinate geometry, Jane described to her children how to plot a point on the coordinate system. A coordinate system is nothing more than two regular number lines put together, with one laid out horizontally and the other laid out vertically, intersecting at 0 for both of them. During her lesson on line symmetry—the most common form of symmetry discussed in elementary school classrooms—Jane gave a definition.
