数学运算规则的样例学习：实验研究与理论探索

摘要

在样例学习研究领域，作者着眼于规则的样例学习研究，尤其是对数学运算规则的样例学习做了一系列的实验研究和理论探索。最初的实验研究在小学生四则混合运算规则和“去括号”运算规则的实验中取得了预期结果。但在小学生代数运算规则的样例学习实验研究中却遇到了问题。经过对问题原因的深入分析，提出了数学运算样例中新算符及新规则设计的“解释法”“转换标记法”和“解释—标记法”，并在指数与对数转换规则和对数运算规则以及分数和比例运算规则的样例学习实验中证实了这些样例设计方法的优越性。根据上述实验研究，作者对样例学习的性质、样例学习理论的建构等理论问题以及样例学习如何兼顾学生个体差异等教学实践问题作出了明确的回答。%The authors conducted a series of experimental studies and theoretical exploration of mathematic operation rules. The initial experimental studies about elementary school student’s worked-examples learning the rules of “four fundamental operations arithmetic” and “removal of parenthesis” had acquired expected results. But the authorsd encountered problems in the experimental studies of the elementary school student’s worked-examples learning of algebraic operation rules. The authors proposed new methods that designed the new operators and new operation rules of the mathematic operation worked-examples,they were named the method of explanation,the method of converting label and the method of explanation-labels whose superiority had been verified in the experiments of the worked-examples learning of the rules of conversion form index to logarithmic, the rules of logarithmic operation,the rules of fractional arithmetic and the rules of proportion operation. On the basis of these experimental studies,the authors answered some questions in this paper,such as characters of worked-examples learning,the construction of the theory of worked-examples learning and the consideration of individual differences in student’s learning the rules with worked-examples learning.