Teaching mathematics is a big problem around the world. Researchers and teacher are very interested in different ways to improve the teaching of mathematics. Rule-of-four is a strategy to teach math with different representations. The different representations are numerically, graphically, symbolically, and verbally. For the graph representation, I belief visualization is a way to help students build their mental picture of the mathematical object.
I agree that focusing on representations is key to improving our math teaching. One of my favorite activity for teaching Algebra II using the Rule-of-Four is Function Matching on the NCTM Illumination website http://illuminations.nctm.org/ActivityDetail.aspx?ID=215
When the student use this web activity they are given the problem in the graphically representation — match the blue graph on the red graph. They must give their solution in the symbolic by changing the coefficients of the blue equation. For extra information they can click on the graph and get coordinates which is the numeric. All that is left is the language (oral or written). So when I use this to teach I allow student to work in groups and encourage them to talk and guide their conversations with hints.