小学生解决万以内退位减法错误类型及影响研究

Study of the Error Patterns and Influences of Primary School Students in Performing Subtractions with Regrouping for Numbers Less Than Ten Thousand

解决退位减法问题是运算的基础之一,国际学者非常重视退位减法问题研究.以Carla Fiori等人研究结果为基础,利用问卷调查方法对天津市4所小学455名学生进行测验.结果表明,学生解决退位减法问题包括5类错误:退位错误、使用运算法则错误、位值理解错误、混淆退位含义、其它错误;经过回归分析和相关分析发现退位错误对总失分影响最大.退位减法教学策略建议:明确跨0退位减法运算程序,多维度渗透位值制,利用图示表征退位减法算理,鼓励学生创新问题解决方法.

Solving subtraction problems with regrouping is one of the foundations of mathematical operations.International scholars attach great importance to the study of subtraction with regrouping.Based on the results of Carla Fiori et al.,455 students were tested using a questionnaire survey.The findings demonstrated that students solved subtraction problems with regrouping with five patterns of errors:regrouping errors,algorithm errors,misunderstanding place value,confusing the meaning of regrouping,and other errors.After regression and related analyses,it was found that the regrouping error had the greatest impact on the total loss.Based on an analysis of the cause of the error,the following teaching strategies for subtraction with regrouping are proposed:clearing the operation procedure of cross-zero subtraction with regrouping,penetrating the place-value system with multiple dimensions,graphically representing the arithmetic of subtraction with regrouping,and encouraging students to innovate problem-solving methods.