Research On The Structural Characteristics Of Good Mathematics Cognition Of High School Students Based On Flowchart Method

The mathematical cognitive structure is a core psychological component of a learner in the process of mathematics learning.In any case,the existing cognitive structure is the basis for the individual to learn new mathematical knowledge.And the most important characteristics of cognitive structure are its content and organization.Therefore,the study on the characteristics of the knowledge and knowledge connections in mathematical cognitive structure,particularly the good mathematics cognitive structure(GMCS),is of substantial significance.However,the results of existing researches were mainly speculative reasoning based on relevant psychological theories as well as practical teaching experience.And they were mainly quantitative instead of qualitative.Moreover,they focused mostly on sheer mathematical concepts and scarcely on other issues in cognitive structure,particularly propositions.Thus,this paper would adopt the method of flow map and conduct a quantitative analysis on characteristics of types and organization of proposition knowledge in high school students’ GMCS,further find out the features of GMCS,make pertinent teaching suggestions and give a related classroom case.With regard to methodology,this study mainly adopted the method of literature,interview,and flow map,etc..The research order of this paper is: First,related theories and review studying.Based on careful reading the releva nt literatures,write a review about the existing researches on GMCS according to the aspects of the type and characteristic of knowledge,the type and characteristic of organization and the measures of constructing a GMCS,etc..Besides,carry out comparative learning and write a review about the common methods used in researching cognitive structure,namely concept mapping,cards sorting and flow map.Second,screen and study out the investigation materials and form the interview questions in the light of flow map requirements.Third,contact the subjects and carry out the practical research,specifically,conduct a face to face audio-taping interview to each student.Forth,transform the obtained audio data to textual data and code the latter.Based on it,draw the flow maps that represent students’ mathematical cognitive structures.Fifth,Based on these flow maps,use the data statistical analysis software,EXCEL and SPSS 22.0 to quantify the characteristics of the proposition knowledge in GMCS.Sixth,explain the results of the data quantification to clarify the characteristics of the proposition knowledge and their connections in GMCS and answer the study question.Seventh,based on the conclusions and teaching practice,put forward several pertinent teaching suggestions.The main conclusions of this study were as follows.First,from the perspective of general situations of cognitive structure variables,GMCS contained a relatively larger amount of more extensive and exact proposition knowledge,between which there were more recurrent links.And the entire proposition network was more compact and integrated and easily activated to associate more knowledge.The extraction of knowledge from it was more prompt.Second,from the perspective of the amount of knowledge processed by each processing strategy,GMCS contained relatively more knowledge processed by higher-order conditional inferring and comparing and contrasting,as well as the radical defining(about connotation of basic core concepts with concrete definition or conotation),besides the majority processed by describing.Third,from the perspective of the correlation between cognitive structure variables,there were respectively relatively strong and stable positive correlations between extensiveness and richness and integratedness,between richness and integratedness,as well as between flexibility and extensiveness.It indicated the larger amount of propositions contained in GMCS not only promoted bountiful recurrent connections that made the entire proposition network more integrated and compact,but also to a large extent,let the GMCS itself become more easily activated to associate more knowledge.Forth,from the perspective of the correlation between the amounts of knowledge processed by different processing strategies,processing strategies for knowledge in GMCS were relatively independent of each other.In other words,different types of proposition knowledge in GMCS relatively distinctly corresponded to different processing strategies,which to a certain extent indicated the clearness and differentiability of proposition knowledge in GMCS in semantic organization of characters and symbols.Fifth,from the perspective of the correlation between cognitive structures and the amounts of knowledge processed by different processing strategies,there was a relatively stable and strong positive correlation between the amount of knowledge processed by conditional inferring in GMCS and the richness of the MCS.It indicated the larger amount of recurrent connections between propositions in GMCS was substantially owed to its substantial propositions processed by conditional referring.Sixth,from the perspective of main knowledge contents in cognitive structure,GMCS contained a relatively larger amount of more abstract and inclusive knowledge that could highlight and focused closer on the core concepts with more complex using conditions.Seventh,from the perspective of the concrete distribution of ideas possessing recurrent connections in students’ mathematical cognitive structures,there were more connections between whether parallel or inclusive knowledge or low and high level knowled ge contained in GMCS,especially the last one.Besides,there were evidently more recurrent connections between old and new knowledge in GMCS as well.Eighth,from the perspective of misconception in cognitive structure,GMCS contained almost no any misconceptions about connotation of core concept.Besides,there was not any misconception about important practical decisions and properties of core concept expressed in the form of theorems in GMCS.Ninth,from the perspective of the specific knowledge processed by each processing strategy in cognitive structure,GMCS contained a relatively larger amount of knowledge about properties and application of core concepts processed by conditional referring strategy and core concepts with concrete definition or connotation processed by defining strategy,while these types of propositions in average cognitive structure were substantially descriptive.In conclusion,based on the above research results and given the practical teaching,this paper pointed out students’ GMCS could be fostered from the following aspects: Firstly,highlight the instruction of extensive propositions knowledge to enlarge proposition network;Secondly,enhance the learning of core concepts and the proposition knowledge of those concepts closing to them to stick out the center of the proposition network;Thirdly,lead students to substantially grasp exact proposition knowledge to unblock the proposition network;Forth,emphasize multidimensional connections between proposition knowledge to compact the proposition network;Fifth,comb comprehensively core concepts and the knowledge ranked below and over them to stick out the predominant connections;Sixth,lead the students to use comprehensive knowledge processing strategies to enrich semantic representation of the proposition network;Seventh,help the students to clarify main processing strategies for different types of knowledge to make the proposition network clear;Eighth,stick out the strategy of conditional inferring to increase the recurrent connections between proposition knowledge.