International Comparative Study of Geometrical Reasoning in Mathematical Textbooks of Six Versions in Middle School Level
Logical reasoning is the key element of key competency of mathematics and study activities. How to choose the proper presence of geometrical knowledge in mathematical textbooks， which is functional education of logical reasoning， is one of heated topics focused by mathematical curriculum reform and implemented. This comparative study is in two dimensions， and one is the reasoning pattern with six types: visual discrimination， experimental demonstration， induction reasoning， analogic reasoning， deductive reasoning， deductive proof， the other is the levels of reasoning depth: level 1、level 2、level 3 and level 4， which is worked on six different versions of geometrical textbooks used in Chinese mainland C-PEPM， Hong Kong H-XSDM， Singapore S-SM， England E-ML， Australia AU-HMZ and America A-CM in middle school level. It is found that visual discrimination， experimental demonstration， induction reasoning and deductive reasoning have comprehensive using， but only the first two of them have highlighting in using percentage. Deductive proof was used in C-PEPM and H-XSDM mostly. The percentage of the former is nearly 30%， the latter is near to 10%. The most weakness is analogic reasoning using in whole comparative books because the highest percentage is 3.91% in C-PEPM. The depth levels of six textbooks are focus on level 2 and level 3， and the former percentage is more. C-PEPM and H-XSDM are only two versions which have level 4. The decreasing ranking of reasoning depth is C-PEPM、A-CM、H-XSDM、S-SM、AU-HMZ and E-ML.
|關鍵詞||初中数学教科书、几何推理、推理呈现方式、推理深度、国际比较、mathematical textbooks、geometrical reasoning、reasoning pattern、reasoning depth、comparative study|
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