ABSTRACT
The knowledge of the Chinese teachers seemed clearly coherent while that of the United States (US) teachers was clearly fragmented. Verbal explanation of a mathematical reason underlying an algorithm, however, seemed to be necessary but not sufficient for the Chinese teachers. The Chinese teachers were skilled in adding and removing parentheses and in changing the order of operations in a mathematical sentence. The Chinese teachers tended to justify mathematical statements both verbally and symbolically. For all the arithmetic topics, the Chinese teachers indicated that although a standard algorithm may be used in all cases, it may not be the best method for every case. The US teachers tended to focus on the particular algorithm associated with an operation, for example, the algorithm for subtraction with regrouping, the algorithm for multidigit multiplication, and the algorithm for division by fractions.
