Visual Explanation of the Week #2: Graphical Algebra

Even a short glance over visual data yields a wealth of information, such as the number of represented objects. The ability to grasp that number in but a moment is called subitizing. Research on the phenomenon has shown that humans can usually identify the quantity of objects up to five, and up to eight with training.

The product of two numbers adjacent to a median, is one less than the square of the median. For example, 52=25, and 6×4=25-1=24. Algebraically, this is because (n+1)(n-1)=n2-1. Geometrically

Cognitive shortcuts like subitizing are employed in the fabulous graphics made by Oliver Steele for his children. A series of block calculations serve to illustrate basic laws of algebra. These visual explanations are kin to physical bricks that see use in elementary schools and as such readily understandable. At the same time, the two-dimensional graphic design can visualize transitions far better (to my judgement at least).

It is not entirely clear to me why such trivial, yet great explanations are used so little. All the more praise for Mr. Steele and his understanding for naÏve mathematicians.

References:

“The Number Sense: How the Mind Creates Mathematics” (Stanislas Dehaene)