An Analysis Of The Difficulties In Learning Cognition Of Students In The Sixth Year

With the importance of algebra study domestic and foreign, about the research of equations also into researchers view gradually. In the early the late18 th to the early 19 th century, people have gradually understood the algebraic is the scientific study of the equation theory. Linear equation theory is undoubtedly the most basic and fundamental content. However, the current research on the linear equation mainly focused on the role in solving practical problems and the change process of thinking in this process. As well as the simple classification when the student easily makes mistakes in learning process of linear equation,and in-depth analysis and discusses the errors reasons behind.The paper mainly adopts a qualitative research method, and empirical research to cognitive errors when students learning in the linear equation process.First, collect, collate and summed the errors of examination papers, the test papers and exercise books when student learning linear equation chapter; Second,to classify and streamline different types of errors; Finally, select the most representative cases as the basis for this study. After a simple classification by the errors of examination papers, the test volume and exercise books, also based on the existing solved linear equations research, that forming analytical framework has three dimensions: mainly from the arithmetic of “operator-set”, lacking of understanding of arithmetic structured concept or strategies and lacking of algebra concept or strategies to understand. Follow three aspects to analyze and explore student cognitive errors and their reasons in learning the linear equation.These findings suggest(1) The concept confusion or operating omissions by the rule of "operator-set" in arithmetic, mainly exist in the following three aspects:Arithmetic moderate number "=" procedural understanding of the process so that students will be solving equations and algebraic computation confusion;arithmetic mixed number of "parallel" wording in the process of solving theequation is treated as an integer part and a fractional part of the multiplication;when to use the common denominator arithmetic strategies ignore the integer part of the operation.(2) The concepts or operation error caused by lacking of understanding of arithmetic structured concept or strategies mainly exist in the following three aspects: on the "+" "-" understanding of the meaning is still stuck in the "Operators", it can not be understood as properties symbol or representation of the amount of the opposite sense to the students understand the "shift key" and other concepts or "" key "shift key" action caused some interference; lack of understanding of the nature of the equation, the impact of students ’transposition’concept and operation properly understood; multiplication of the addition of the distribution ratio so that students can not understand the lack of brackets to operate properly in the course of solving the equation.(3) Obstruction of acknowledge of the concept, principle and use of strategies caused by insufficient understanding of algebra concepts or strategies,mainly exists in the following five aspects: not properly understand once linear equation "three elements"(the equation containing an unknown, unknowns number 1) need to meet, so that students can not properly understand or judge once linear equation; not correctly understand the same solution principle equations, so that students can not solve the equation of a correct understanding of the concept; not correctly understand the meaning of the parameters, resulting in students not accept algebra containing letters as an answer; you can not really understand the rules go brackets, resulting in a wide variety of student errors appear in parentheses to the process; in the course of the column equations word problems, the solution of the equation is easy to focus on the solution and ignore the problem, or when the application questions contain multiple unknowns,students often can not find the proper standard amount, you can not find a relationship between the amount of unknown unknowns, or when the application contains a number of complex issues equivalent relationship, the student is not easy the same amount off to find the correct series of equations.In conclusion, this study makes simple classification and sum up for theerrors in once linear equation course, but also make detailed summarize and analysis for these errors from the cognitive level of students. Not only for the students to understand the error occurs in the learning equation once linear, the cognitive level provides a perspective; also for teachers, professors once equations take a dollar corresponding targeted instructional strategies provide a good basis.Keywords: once linear equation, cognitive difficulties, error...