Investigation And Research On Students' Understanding And Teachers' Teaching Of "Arithmetic Square Root" In Junior Middle School

Based on SOLO classification and evaluation theory,from the definition of the arithmetic square root,the use of the nature of the arithmetic square root,the arithmetic square root properties and "numerical value of 2^1/2 " to level four dimensions,constructing evaluation framework,the arithmetic square root level of investigation of junior middle school students understand about the arithmetic square root level;Based on the existing research results of mathematics subject teaching knowledge(MPCK),combining teaching knowledge with the specific content of arithmetic square root,the evaluation framework of arithmetic square root teaching knowledge was constructed from the content dimension,teaching dimension and student dimension,and the teaching knowledge of arithmetic square root of junior middle school mathematics teachers was investigated.Finally,the factors influencing the teaching effect of arithmetic square root are analyzed and corresponding teaching suggestions are put forward.Questionnaire test method,classroom observation method and interview method were used in this study.211 students from two schools were tested by the test paper to analyze the understanding level of the square root of arithmetic of junior high school students.Observing the arithmetic square root teaching of 30 middle school math teachers,combining with interviews,analyzing the teaching knowledge of the arithmetic square root of middle school math teachers.Through the analysis of the research results,the following conclusions are drawn:Junior high school students' understanding level of square root arithmetic :(1)Junior high school students' understanding level of square root arithmetic definition dimension is high;(2)Junior high school students have a low level of understanding in the dimension of square root of arithmetic;(3)Junior high school students have a high level of understanding on the application dimension of square root property of arithmetic;(4)Junior high school students have a low level of understanding on the dimension of "numerical value of 2^1/2 ";(5)Girls' comprehension of square root of arithmetic is generally higher than that of boys;(6)Students in key schools have a higher understanding level of square root than those in ordinary schools.The teaching knowledge of the square root of arithmetic for junior middle school mathematics teachers :(1)Teachers have a good grasp of the basic knowledge of the square root of arithmetic,but lack of depth of understanding of the content;(2)In terms of teaching dimension,the teaching methods and strategies for the concept and nature of square root of arithmetic are single,and the emphasis on 2^1/2 inquiry is insufficient;(3)From the perspective of students,teachers have a basic understanding of students' cognitive level and existing knowledge and experience,but the overall understanding is limited to a general understanding,which is not deep enough;Insufficient explanation of students' perplexed knowledge and generally low degree of student participation.The factors that influence the teaching effect of arithmetic square root are as follows :(1)the teacher's knowledge reserve of arithmetic square root is insufficient;(2)Lack of the penetration of the combination of numbers and shapes;(3)Insufficient exploration of the existence and size of 2^1/2 in the investigation,and no attention to the exploration activities;(4)Insufficient understanding of students;(5)Students are not interested in learning arithmetic square roots.Based on the research results,the following suggestions are proposed :(1)To strengthen the teaching of the definition of arithmetic square root,so that students can understand the necessity of introducing arithmetic square root;(2)integrate the history of mathematics,arouse the enthusiasm of learning arithmetic square root;(3)Pay attention to the penetration of the combination of numbers and shapes;(4)attach importance to inquiry activities and strengthen the teaching inquiry of 2^1/2;(5)Strengthen the study of the content knowledge related to the arithmetic square root.