Visual Mathematics

I believe that mathematics should be taught in a more visual manner. For many hundreds of years, studying mathematics meant studying Euclid's Elements. Euclid's Elements and other ancient writings used geometrical interpretations even for problems that dealt with number theory. For example, Euclid treated the numbers as line segments while the Pythagoreans were interested in displaying various numbers as figures (square numbers can be displayed as squares, triangular numbers as triangles etc). I believe that by trying to find geometrical or visual interpretations to various mathematical concepts, the concepts become more tangible and easier to understand.

SEEING AS UNDERSTANDING: The Importance of Visual Mathematics for our Brain and Learning
This is a good paper to start reading if you are interested in visual mathematics and education. It cites other papers that show the relationship between mathematical thinking and visual thinking or processing. At the end it has a few helpful tips for teachers who want to apply visual techniques in their classroom.

This is a link to an article, but I see that the authors made a book on the same topic. The main thesis of the article is that "The Scientific Revolution was kick-started by geometry". It discusses diagrammatic reasoning in the historical context. The article is about 50 pages long and it has a lot of information about diagrammatic reasoning and history of sciences.