Ask questions that might help students incorporate conceptual knowledge into their visual-reasoning processes. Also, when discussing a concept such as that of a triangle, make sure to use a variety of different examples, such as many different sizes and shapes of triangle in non-standard orientations. This approach will help students evoke dynamic images when reasoning about concepts. When students have become familiar with mathematical transformations, they can be encouraged to describe their mental transformations using mathematical terms. Many of the tasks that we have presented to students in our research and curriculum-development projects can promote students' coordination of visual imagery and conceptual knowledge.
Some examples follow.
Ask students to draw a square in Logo. Then ask them to draw a tilted square. Do the same for rectangles. Give students a procedure RECT that draws a rectangle when the two dimensions for the rectangle are given as input. Give the students a Logo procedure that draws figure A and let them test it on a computer.