A Study of Good Mathematical Cognitive Structure Based on Flow-Map Method Taking Spatial Line as an Example
[1]
Zezhong Yang, The School of Mathematics and Statistics, Shandong Normal University, Jinan, China.
[2]
Yanqing Zhang, The School of Mathematics and Statistics, Shandong Normal University, Jinan, China.
In this paper, the flow-map method is used to analyze the characteristics of good mathematical cognitive structure (GMCS) of high school students by taking the spatial line as an example. According to the requirement of flow-map method, the sound data obtained from the investigation are converted into text data for preliminary coding analysis. After that, the coding analysis is carried out, and the flow map of students' MCS is drawn on the basis of the analysis. Then, the flow map related data are quantified and analyzed. The contents of quantitative analysis mainly include the universality, richness, integration, misconceptions, knowledge retrieval rate, flexibility and knowledge processing strategies used in organizing knowledge. Through the quantitative analysis, this study concludes that the GMCS has the following characteristics: 1) It contains more extensive propositions with higher accuracy and recurrent linkages, and the whole propositional network is more integrated, compact, efficient and easier to activate association with more knowledge. 2) It not only contains knowledge of using describing, but also contains more knowledge of using conditional inferring, comparing and contrasting. 3) It contains more advanced propositional knowledge with more complicated conditions, but the MCS of middle and general level students is a relative lack of such knowledge. 4) It not only has the knowledge of parallel relation (E. g., the knowledge of parallel and vertical propositions between straight lines and planes in space), but also has the knowledge of inclusion relation or lower level knowledge and higher level knowledge. Moreover, there are more recurrent linkages between the old and new knowledge in GMCS. The typical propositional knowledge is the knowledge of hetero-plane lines, parallel lines and intersecting lines. 5) There is no misdescription about the basic meaning of the core concept in GMCS, and no misdescription of propositional knowledge about important applications of core concepts, such as property theorems and so on.
Flow-Map Method, Good Mathematical Cognitive Structure, Spatial Line
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