The Study, Based On Cognitive Load Theory Of Mathematical Problem Solving Error

Mathematics is rigorous and scientific, so it is inevitable that every student may make errors more or less in the process of learning mathematics. It is impossible and unnecessary to avoid happening errors in instruction. Mathematic errors is an natural phenomenon in the process of learning mathematics. As education and instruction must respect individual difference, it also need face of errors objectively.Cognitive load theory is one of the theories that develops rapidly in recent years abroad, which inspects of learning and problem-solving from the perspective of guiding the allocation of resources mainly, as well as provides psychology theory for the design of teaching. Although there are many about the application of cognitive load theory to the design of teaching, it is less in the field of mathematic education, especially less about study with mathematic errors. So, it has important significance and value to study cognitive load's influence on mathematic errors which integrate psychology theory with mathematic education.This study have formulated test questionnaire based on research objection.210 junior high school students were tested using natural experiment design on the basis of former researches.The purpose of this study is to inspect such factors as element interactivity and the presentation of problems which produce cognitive load and affect mathematic errors. The body of the thesis falls into 5 parts:PartⅠ:An introduction to the relevant literature. This part introduces and analysis existing mathematic errors and related cognitive load researches by review relevant literature. In addition, we get this study's inspiration from literature introduction.PartⅡ:Put forward the problem. By analyzing the problem of existing related study with mathematic errors and cognitive load, this part forms study's purpose mainly,hypothesis and ideal,analysis test questionnaire.PartⅢ:The demonstration study. We have selected 210 junior high school students as object of study and applied SPSS 13.0 to carry out data statistic analysis.The mathematical analysis part mainly includes the following problems:(1)Whether the level of cognitive load affect on mathematic errors or not in solving mathematical problems.(2)Whether element interactivity and the presentation of problems affect on cognitive load and mathematic errors or not in solving mathematical problems.(3) Whether the strategy of problem solving affect on cognitive load and mathematic errors or not in geometry problems.PartⅣ:Conclusion discussion. On the basis of data analysis, this part discusses the influence of mathematic problems on cognitive load and mathematic errors by individual experience, essential qualities of study's material (especial element interactivity), The presentation and organization of material.PartⅤ:Instruction suggestion, review and conclusion of this study. we put forward the following suggestions:reasonable use of errors as learning and instruction resource; emphasis students' understanding on definition and rule in computation instruction; utilization diversification design in geometry problems instruction.The conclusion as follows:(1) The level of cognitive load is significant between the second step and the first step at the first bracket,the first bracket and the second bracket. Errors are significant between two steps of every bracket, the first bracket and the second bracket.(2) The level of cognitive load and errors are significant in every inequality problem:There is no significant influence on the errors of multiply denominator,bracket-expansion,transposition of terms but transposition of coefficient. The errors of alteration unequal sign direction are significant.(3)There are systematic errors in mathematic calculation by above study and these errors are related with element interactivity. Element interactivity cause cognitive load which is the main reason of errors.(4)The presentation of geometry problems affect on students' cognitive load and mathematic errors:The level of cognitive load and errors are significant between indirect-proof and direct-proof; Main reason of errors is cognitive load caused by the presentation of problems; outer-strategy is significant to errors but cognitive load.