In the Real World:

. How do people "do math"?

Discussion with others, drawing pictures, sharing (conferences, email, etc) intuition, basic picture, "how" and "why" in writing, etc, as well as symbols galore.

(Not by a strict textbook read-exercises-read process!)

How do we learn languages?

--We Listen to others.
--We Try to form our own sentences.
--We interact with others, gaining knowledge and sophistication.
(Not a strict textbook/listen to lectures method either!)


--Language as a Natural Human Behavior

--Mathematical thinking as a natural human behavior

(The Rassias Method...)


Centrality of (and interrelationships) among expressiveness (symbolic, written, graphical, oral,...); understanding; and communication in human learning.


(Next)