References: Young, pp. 178-188.

VI. Method

1. The Meaning of Method.

2. How the Ancients probably taught Calculation.

a. Various forms of the abacus.

b. The abacus at the time of the Renaissance.

c. The effect upon arithmetic of abandoning the abacus in western Europe.

3. Causes of the Rise of the Rule.

4. Revival of Objective Teaching.

Trapp (1780), von Busse (1786), and Pestalozzi (about 1800).