Research On The Development Law Of Junior High School Students' Geometric Transformation Understanding Level

under the research background of "mathematics understanding",in view of the important position of geometric transformation in the teaching material and the enlightenment of international mathematics education reform,this paper takes the perspective of the combination of quantitative research and qualitative research,explore the law of geometric transformation understanding,in order to provide reference for teaching materials and teaching design,promote understanding teaching.First,consider combining Wiggins' "Understanding Six-Dimension Theory" and Duval geometric thinking level with SOLO theory to create an evaluation framework of geometric transformation understanding level for junior high school students.Secondly,the questionnaire of geometric transformation understanding level was compiled based on the framework and two-way list,and 296 students in grades7,8 and 9 were tested and investigated.Then,vertical and horizontal analysis were adopted to explore the development trend and understanding characteristics(including level distribution,knowledge difference,understanding difficulties and gender difference)of junior high school students respectively.Finally,the development law of the geometric transformation understanding level of junior high school students is summarized as follows:(1)For the argumentative understanding of geometric transformation,with the rise of grade,junior high school students' comprehension level developed slowly,and reached the highest in the eighth grade.Students of all grades have a relatively balanced development in the discussion and understanding of the three transformations,and there is no significant difference.Most students can accurately describe the concept of geometric transformation,but more than half of the students still have difficulty in understanding the relationship between transformations.(2)For the operational understanding of geometric transformation,junior high school students' understanding level increases with the increase of grade,with the fastest growth rate between grades 7 and 8.Specifically,the first grade 8 students are significantly improved in the appearance operation of the three changes compared with the seventh grade students.On the whole,except for the students in grade 7 who have difficulties in changing the appearance,most students in grade 8 and 9 are at the highest level,so grade 8 is a key period to further cultivate students' geometric and intuitive ability.At the same time,the development of operational understanding of students in the three transformations is not balanced,which shows that the operational understanding level of axisymmetric and translation is higher than rotation.(3)For the application understanding of geometric transformation,the understanding level of junior high school students increases with the increase of grade,among which the seventh and eighth grades grow the fastest,and the individual differences are large.At the same time,the development of applied understanding of students of all grades is unbalanced,that is,the level of applied understanding in axisysymmetry,rotation and translation decreases successively.Specifically,for the understanding of axisy-symmetry and rotation,only one third of students in grade 7 can apply their ideas correctly;for translation,most students are at level 1,that is,they cannot understand the meaning of the question.Most students in grade 8 and grade 9 can use axisymmetric and rotating ideas to solve their problems,but only about half of them can solve the application of translation ideas smoothly.Junior high school students have some problems,such as lack of dynamic thinking,weak comprehensive analysis ability,inaccurate expression of mathematical language and lack of thought promotion ability.(4)There is no significant gender difference among junior high school students in the transformation level of understanding.