Cognitive Analysis Of Junior Two Students In Solving Open-ended Geometry Problems

Humans have the rigorous logical interpretation thinking mode represented by the Eujili Geometry and the open creative thinking of the main representative of Newtonian micro-accumulation.Leading the development of mathematics.However,from the "dismissal of the hundred schools and the exclusive respect for Confucianism" to the spirit of the school of koans and the 1988 "Syllabus for Teaching Mathematics in Full-time Junior High School for Grade 9 Compulsory Education",which stated that "the development of logical thinking is the core of developing competence",the Chinese education sector has overemphasized the "closed nature" of mathematical reasoning.The implementation of open-ended geometry questions can therefore change the current misconceptions about education and the need to develop innovative talent.As research progressed and scholars recognized the educational value of geometric open-ended questions,they began to appear in textbooks as well as in mathematics examinations.During the internship,the author found that students have different cognitive characteristics when solving open-ended geometry problems.Therefore,this paper investigates the cognitive characteristics of second-year students in solving openended geometry problems.This paper uses literature research,questionnaires,test surveys and interviews as research methods.On the one hand,teachers’ and students’ perceptions of open-ended problems in mathematics were explored through the analysis of open-ended geometry problems to understand the types,educational value and current status of open-ended problems in mathematics.On the other hand,a developed geometry open-ended questionnaire and student interviews are used to investigate the overall level,gender differences and cognitive characteristics of second year students in solving geometry open-ended questions.The questionnaire is then combined with an analysis of the factors affecting second year students in solving geometry open-ended questions and the current state of teaching and learning,so that appropriate suggestions can be made to teachers and students.First,the analysis of test papers and student interviews based on the SOLO categorical assessment framework revealed that the cognitive level of second-year students in solving open-ended geometry problems was mostly in a single-structure and multi-level structure,and there were significant differences in the level of male and female students in solving openended geometry problems.The cognitive process of second year students in solving open geometry problems is divided into four stages.In the problem representation stage,a few students have difficulties in problem interpretation,problem representation is not comprehensive enough,and half of them have inappropriate methods of problem examination;in the model identification stage,most students lack breadth,poor reasoning and analysis skills,and incomplete cognitive structure;in the solution migration stage,students have certain problem solving skills but lack comprehensiveness,students’ problem situations lack creativity and lack the idea of combining numbers and shapes;in the solution monitoring stage,students cannot test and evaluate themselves.Secondly,a questionnaire was combined to understand the extent of teachers’ and students’ awareness of geometry open problems and the current state of education.An analysis of the factors affecting second year students in solving geometric open problems concluded that students have insufficient information extraction skills,inappropriate methods of examining problems,lack of marking habits,poor logical reasoning and analysis skills,lack of strategic approaches,incomplete cognitive structures,lack of ideas about number and geometry,lack of language expression skills,and susceptibility to the influence of the external environment.Finally,according to the cognitive level,gender differences,cognitive characteristics and influencing factors of the second year students in solving problems,teaching suggestions are made to teachers: Teachers should raise awareness of teaching geometric open problems;for the problem characterization stage: strengthen students’ awareness of problem examination and cultivate the habit of problem examination;exercise the application of problem examination strategies and cultivate students’ problem examination ability;for the model identification stage: pay attention to students’ thinking and live mathematical thinking methods;optimize students’ cognitive structure and cultivate logical reasoning ability;for the problem solving and migration stage: reform classroom teaching and create open teaching situations;consolidate Students’ foundation and arithmetic ability;for the problem solving and monitoring stage: cultivate students’ habit of retrospection and reflection.The students are also advised to establish a correct view of learning,develop good learning habits,form a learning atmosphere of self-reflection and peer support,and overcome their fear of difficulties.