Research On The Internal Mechanism Of Cognitive And Understanding Errors In Mathematical Concepts

Concepts have been a vital part of math learning as always.Only when students correctly understand the mathematical concept can students step into next stage of learning and applying,and the incorrect understanding of mathematical concept is a very common problem in middle school.Incorrect understanding is the final result which caused by the internal change of student.The internal change is also interfered or guided by the external change..Therefore,it is necessary to clarify the internal changes of the student.If find out the internal change of students how they made incorrect understanding,then teachers can arrange his teaching more reasonably,guiding students learn mathematics knowledge in a correct way and effectively avoid incorrect understanding when new knowledge appears.The research methods adopted in this study are mainly: literature method,survey method,concept map method.The research sequence of this paper are as follows:Firstly,the research on mathematics comprehension and the study on related theory of concept map;Secondly,compiling questionnaires and materials of Antiprism and Semi-positive polyhedron;Thirdly,select a number of representative middle school students to conduct pre-surveys and improve survey design;Fourthly,collate and count the concept maps and questionnaires;Fifthly,statistical analysis of the concept map from the following aspects: the other concepts of the new mathematical concept connection,the position of the new mathematical concept in the concept map,the conceptual diagram form,the logical connection between concepts;Sixthly,the author analyze the characteristics of the concept map of middle school students,and then summarize the difference produced by correctly and incorrect understanding that students made in this aspect.Seventhly,we propose teaching suggestions for the process of incorrect understanding of middle school students,and attach an instructional design example.After research,we believe that the internal psychological process of middle school students' cognitive understanding of mathematical concepts should be such aprocess: When middle school students learn a new mathematical concept,they will firstly connect the new mathematical concepts with existing old mathematical concepts in the cognitive structure in the form of association or extraction of new mathematical concept features.These old mathematical concepts are mainly advanced concepts or at the same level.The concept then forms a hierarchy of cognitive structures,starting with new mathematical concepts in a way that links between concepts.Finally,based on the above research results,we can start from the following aspects in the daily mathematics teaching so that avoid the middle school students' incorrect understanding of the new mathematics concept: Firstly,provide key concepts for learning new math concepts before class;Secondly,guide secondary students to find out the mathematical concepts with direct connections in case of having a leap-type connection;Thirdly,emphasize the concept of mathematical superiority and collocation;Fourthly,analyze the knowledge of new mathematical concepts from multiple perspectives to form a comprehensive understanding;Fifthly,increase the connection between mathematical concepts;Sixthly,correct the right from wrong according to the specific situation of students.