A Study On The CPFS Structure Of Triangle Knowledge In Junior High School

As the most basic and important figure in plane geometry,triangle serves as a link between the preceding and following of “graphics and geometry” in junior high school.But triangle has a fragmented course distribution.Triangle content structure of the students is not clear,then students can not grasp the essence of math concepts and mathematical proposition.Which reflect the students cognitive structure is not good.Therefore,the teacher need under the guidance of the whole thinking to help students grasp the triangle related content and build a good cognitive structure of triangle.CPFS structure is a representation of the special connotation of mathematical knowledge,and also a good cognitive structure with mathematical characteristics.Therefore,this research will under the guidance of the whole thinking to explore the knowledge structure of the triangle,compile test students triangle learning tool,and through the test to understand students' awareness of triangle structure.Research mainly discusses the following two questions:(1)What's the knowledge structure of triangle under CPFS structure?(2)How about students' the CPFS cognitive structure of triangle?For the first problem,text analysis method is mainly adopted.Firstly,combing structure of triangle content based on the level of curriculum standard requirements and combined with the content distribution of the textbooks of Beijing Normal University edition.Secondly,on the basis of the three different characteristics(mathematical objects?mathematical relationship ? mathematical proof)tease out the triangle unit.Lastly,in the CPFS structure theory,according to the abstract relationship between concepts and the deductive relationship between propositions,the triangular knowledge network is obtained.For the second question,mainly using the testing research.First,according to the two dimensions of students' mathematics understanding and CPFS structure,establish the effect evaluation tool of triangle study.Then,combing with knowledge structure and evaluation tool tests 410 students in L school and interviews some students.Finally,put forward to revelation according to the analysis of the test and interview results of the cognitive structure of the students of triangle knowledge structure.The results show that:(1)By combing the contents of triangles,the knowledge structure relation of triangles is obtained(2)establish the evaluation tool of learning effect matching with the content of triangle and find that it is feasible to evaluate triangle learning from the perspective of cognitive structure.Furthermore,according to the analysis of the test results,I find that the level of student cognitive structure in L school is low.For example,confusion with concepts and propositions in triangle and the understanding of the isolated proposition or proposition is weak,leading to proposition application flexibility poor.The research has the following enlightenment for the practice of mathematics teachers:first,in the aspect of teaching preparation,we can use the CPFS structure to grasp the triangle teaching content as a whole.The second,in the teaching process,emphasizing the formation background of knowledge and multi-angle expression of concepts and propositions,in order to grasp the nature of mathematical knowledge;Emphasis on knowledge induction and arrangement to help students grasp triangle knowledge as a whole.Third,in the aspect of learning evaluation,we can use CPFS structure to detect the learning effect and process of students in triangle.The above enlightenment can also be tried to apply to other mathematical knowledge modules.