| The multiplication and division of integral expressions is one of the important bases of algebraic operations,the continuation of knowledge of rational number operations and integer addition and subtraction,and the necessary foundation for the subsequent learning of fractions,equations and functions,etc.In the process of learning the content of integer multiplication and division,it is found that students have great learning difficulties in the application of integer multiplication and division inverse operation,resulting in slow learning progress,high error rate and repeated mistakes when students solve problems and,serious frustration of students' learning enthusiasm,even loss of interest in learning,serious differentiation of mathematical achievements,so that some students have become underachievers,seriously affecting the follow-up study of mathematics.It is imperative to solve difficulties in learning the inverse operation of integer multiplication and division.Therefore,it is necessary to investigate and study the causes of the errors in the application of the inverse operation of integer multiplication and division of the first grade students in junior middle school,and make scientific analysis according to the causes of the errors to seek the teaching countermeasures to solve the problem,thus help students reduce the errors in the application of the inverse operation of integer multiplication and division,improve their interest in learning mathematics and enhance the teaching efficiency and teaching effect of teachers.Firstly,186 students in the first grade of Lianhe School in Laiwu District of Jinan City were investigated by questionnaire.The statistical results show that there are some difficulties and problems in the application of inverse operation of integer multiplication and division arithmetic are as follows:the confusion of formulas of similar rules due to many and miscellaneous inverse formulas,poor formula memory due to mechanical rote learning,unclear understanding of examination questions,difficulties in selecting formulas of inverse operation rules,difficulties in determining operation order and symbols,difficulties in basic numerical operations.Through mathematics test case 10 excellent students select 10 performance and error serious students for interviews,according to the result of interview,observation,analogy analysis found that the students in the integral expression,inverse operation application error reasons: formulas of the principle of the present teaching students to memory only do not take the reverse formula to the laws of memory;Students memorize obfuscation rule formula by rote and do not pay attention to the rule summary of inverse operation formula.When students read the questions,they are limited by the dominant conditions in the stem,and tend to ignore the details or recessive conditions.When applying the inverse formula,it is only mechanically followed by feeling,and the selection of the formula lacks flexibility.The incomplete analysis results in incomplete solution when inverse operation is applied..To three different schools mathematics teacher has carried on the questionnaire survey,according to the results concluded that the cause of students' errors are:teaching only positive formula derivation,and the introduction of inverse formulas was not emphasized enough,understanding depth is not enough to reverse the formulas,inverse operation application generalization error affected the law,the teacher does not pay attention to potential rule conclusion,teaching content only textbook knowledge,do not take the inverse operation of examples and exercises.In view of the above reasons,the author puts forward teaching suggestions: to determine reasonable teaching objectives,improve the degree of attention to the application of inverse computing;While mastering the rules and formulas,pay attention to the inverse teaching method of adding formulas.It emphasizes the first application error of inverse operation and advocates students' self-correction and self-reflection.Strengthen the guidance of the method of memorizing the approximate formula of the integral multiplication and division inverse operation;Supplement the knowledge of inverse operation to perfect the system and reasonably integrate it in stages;Reasonable optimization of the stage summary,the construction of reverse operation knowledge system: we should pay attention to the reverse operation formula and test link,pay attention to the penetration of mathematical ideas;We should pay attention to understand the essential characteristics of inverse operation formula and reduce the influence of generalization law. |
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