During a literature review for the class I am taking this semester I ran across this bit.
The teacher or textbook may say that it is important to do such things as to "draw a diagram," but they seldom say why, and the student can see that the answer comes from a formula, so why bother with a diagram? (1987, p18)
One of the best parts of this school year has been my students drawing pictures. I have never had so many pictures. I had so many I complimented them and scratched my head about why. I wonder if because we have entered all our topics with real questions about the world and started by looking at the world as a real place and noticed how hard it is to describe it mathematically if the pictures became important. My students are starting their problem solving by relating it to the real world, with diagrams. All I really know is that they are drawing more and better diagrams this year.
Hestenes, D. (1987). Toward a modeling theory of physics instruction. American journal of physics, 55(5), 440–454.
I am never sure how to cite offline work, so at the bottom please find the APA cited reference. A link to Amazon (or WorldCat or Better World Books if you would like to reduce commercialism) means so much more today than a cite.