An Empirical Study On Mathematical Errors Based On Cognitive Load Theory

In the process of high school mathematics learning,it’s quite common for students to have problem-solving mistakes.And there’s a deeper reason behind this phenomenon:students are the subject of the teaching activities,and it’s easier to find out the reasons for the study of wrong questions by combining the research with them.Against this background,with the guidance of Cognitive Load Theory,this research takes the students’ mathematics errors as the object and takes both students and teachers into consideration in order to explore the real reasons behind the mathematics errors,and we hope that it can offer some strategies for the teaching.Through literature review,comparative analysis and other research methods,this research get some reference from the existing relevant theory and strategy,and then we can provide a basis for further researches.In the teaching practice,we record the errors of two classes in Grade 3 in real time in the Vector chapter and sort the wrong questions in error rate order,and further analyze the number of people making errors.After the first understanding of wrong question conditions,we make analysis from three aspects:wrong question itself,students who have made mistakes and the teacher.And further analyze the knowledge points,the solution methods and Error-prone point.In this way,we find that the common methods are this three:base vector method,coordinate method and geometric method.Through interviewing the students that have made mistakes,we can know more about these students’ thinking and their own understanding for their mistakes.There are four main reasons for this phenomenon:the vague concept of knowledge,the isolation of knowledge,the confusion of memory and the lack of putting what one has learned into practice.Meanwhile,we also make an interview with this two classes’ school-teaching teacher and other mathematics teachers to make sure the above-mentioned four reasons’ rationality or make supplement for them.Then we will gather some relevant teaching experience about the wrong questions and catalogue them into "policies".Based on the research findings described above,in order to gain further insight about wrong questions’ case study,this paper have made longitudinal study and found that as the student’s error rate reduces,the corresponding cognitive load decreases accordingly.The wrong question has a great relationship with the cognitive load of students,and then we will choose three classic mistakes to measure the cognitive load.What’s more,there is an innumerable links among faulty reason,knowledge and the theory of cognitive load:the vague concept of knowledge is the essential reason and we need to eliminate the Redundancy effect;the isolation of knowledge is the connective one and we should take control of the internal cognitive load;the confusion of memory is the basic reason and it will lower the external cognitive load;the lack of putting what one has learned into practice showed the application and we should increase the related cognitive load.Based on the cognitive load theory,this paper proposed the wrong topic teaching strategy:cause the essential reason is the vague concept of knowledge,we should eliminate the redundancy effect;to control intrinsic cognitive load,we need to build a knowledge system;opening a "multichannel" teaching method can reduce extraneous cognitive load effectively;and putting what one has learned into practice is the way to improve the relevant cognitive load.