In this paper, the authors summarized the study progress of the worked example learning , com- mented on the value of the worked example learning theories, advanced the theory that the pupils could study the new operational rules of mathematics by the mathematical operational worked example and proved the scientificity of the theory by their experimental results. The authors opined that the pupils could study or insight the new operational rules of mathematics by the mathematical operational worked example to be designed elaborately and they had possessed the mathematical operational rules. Designing the key step in the mathematical operational worked examples were the key to the mathematical operational worked example learning. We could designed the key steps by the methods of resolution, inverse operation and explanation to promote the pupils to study or insight the new operational rules of mathematics.%概述了问题解决样例学习研究的进展，评述了已有样例学习理论的价值，提出了学生可以通过数学运算样例学习新的运算规则的理论解释，并用自己已有的实验研究结果论证了理论解释的科学性。认为学生可以通过精心设计好的数学运算样例并根据已知的数学运算规则顿悟或推断出新的数学运算规则。关键运算步骤的样例设计是数学运算规则样例学习的关键。根据数学运算规则的逻辑特点，可以分别采用分解法、逆运算法和解释法设计运算样例中的关键步骤，从而促进学生对新运算规则的顿悟和运用。
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