Research On Reasonable Errors Of Mathematical Concept Learning Based On The Concept Map

Mathematical concept learning has been a hot topic in mathematical education research in recent years, no matter the learning process of concept, or the mental activity of concept learning has always been concerned by educates and researchers. Researchers confirmed that it is easier to analyses and study mathematics concept learning by stage partition of mathematical concept. In APOS theory the mathematical concept learning has been divided into four phases including Action, Process, Object and Schema, in which educators can research learners’math concept learning based on observation and analysis. Reasonable error is a covert and chronic error pattern in mathematical concept learning, with multiple different types and representation. Concept map is a kind of instructional tool, with which the learners can effectively check out some ’reasonable’errors during their mathematics concept learning. This paper aims to build the concept map and test’reasonable’errors in mathematical concept learning, based on the four phases of concept learning and some related theories.This paper aims to analyses the function of concept map in preventing’reasonable’error during mathematical concept learning,with concept map teaching, students’drawing the relevant concept map, clarifying the related knowledge and’reasonable’ errors in the mathematical concept learning in each phase. It argues that concept map can improve learners’ meaningful learning and the communication and cooperation among teachers and students, which can lead the teaching reflection. Concept map teaching can effectively check out learners’’reasonable’errors and be helpful for educators to investigate them, and then promote learners’ enthusiasm and initiatives, which is beneficial to the development of their cognitive ability. Mainly focuses on phasing research of mathematical concept learning, based on APOS theory, so it concludes that it is effective and meaningful to introduce the concept map into mathematical concept learning.Firstly to test and consider revising the’reasonable’errors research through concept map teaching and students’drawing concept maps in mathematical concept learning. During more than three months, with the students in Class1and Class5in Grade two in the first high middle school in YZ city as the object, to study their learning on vertical concepts. And the result shows that the’reasonable’errors are ubiquitous in mathematics teaching in middle school in China, which is bad for students’understanding on mathematics knowledge.’Reasonable’errors can gradually disappear, but the disappearance is faster with the external intervention, so teachers’ intervention with concept map can effectively speed up the disappearance of’reasonable’errors. Therefore, we should pay more attention on students’’reasonable’errors in mathematical teaching, improve the teaching model and view it as a long-term research subject.Based on field investigation, analysis and demonstration, it concludes as follows:1、The concept map could test students’reasonable’errors effectively.2、The concept map is helpful for teachers to interfere’reasonable’errors in mathematical concept teaching.3、The concept map could speed up the disappearance of’reasonable’ errors in mathematical concept learning.In this study, there are still some shortages to some extent, and this experiment has Some unpredictable factors,mainly because the time is limited, there is certain subjectivity involved in judging and defining’reasonable’errors, concept maps make board writing disorder, and students’Mental instability, etc.I will go on the research on’reasonable’errors based on the concept map, try to learn the advanced theory and technology actively, and explore the function of concept map in mathematical teaching in optimizing teaching,testing’reasonable’errors and innovation ability so as to enrich the mathematics teaching theory and practice.