Yin-Yang Taoism, adopted the Tai Ji symbol as the fundamental of their basic belief, enriched the Yin-Yang co-existence and exchange cycle idea. Lao Tzu, was the first (in writing) to point out that everything was born from void. Not only Yin Yang depends on each other in existence but existence depends on non existence to exist. There is no absolute good or bad. Existence is not better than void. Order is not better than chaos. The best thing we can do is not to do anything at all! This philosophy is known as Taoism, heavily rooted in I-Ching, the great book of change. 
On the other hand, Confucius, inspired by the idea of great harmony, dream of building a perfect orderly society through the process of building perfect human being. His political and government philosophy depends on the moral building of human thus education. Totally opposite to Taoism 'do nothing' idea, Confucian is heavy on intervene. He build the first public school and prescribed I-Ching (in his own words) together with music and history as the basic curriculum. The Confucianism has become the main stream philosophy in the beginning of Han dynasty in 206 BC. Supported by the government, thousands of public schools were established and Confucian version of I-Ching and Chinese history were the most important to be taught. As you may have noticed, the students of Confucian seems to have left the math out.

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