数学教育学报
數學教育學報
수학교육학보
JOURNAL OF MATHEMATICS EDUCATION
2013年
3期
8-11
,共4页
具体化%符号化%形式化%认知发展
具體化%符號化%形式化%認知髮展
구체화%부호화%형식화%인지발전
embodied%symbolic%formal%cognitve development
Tall称具体化、符号化、形式化3种认知发展形式为数学三个世界。他在继承前人成果的基础上提出该理论，重新解释了人的认知发展过程。他认为抽象知识间是可以相互转化的，结晶体概念是转化的根源，并验证了其教学有效性。目前该理论处于结构稳定，内容不断完善阶段，已得到国际认可。
Tall稱具體化、符號化、形式化3種認知髮展形式為數學三箇世界。他在繼承前人成果的基礎上提齣該理論，重新解釋瞭人的認知髮展過程。他認為抽象知識間是可以相互轉化的，結晶體概唸是轉化的根源，併驗證瞭其教學有效性。目前該理論處于結構穩定，內容不斷完善階段，已得到國際認可。
Tall칭구체화、부호화、형식화3충인지발전형식위수학삼개세계。타재계승전인성과적기출상제출해이론，중신해석료인적인지발전과정。타인위추상지식간시가이상호전화적，결정체개념시전화적근원，병험증료기교학유효성。목전해이론처우결구은정，내용불단완선계단，이득도국제인가。
Tall called three cognitive development modes three worlds of mathematics. They were conceptual-embodied, proceptual-symbolicand axiomatic-formal.He showed the development process of three worlds of mathematics, and explained the process of cognitive development again by studying. He thought abstract knowledge could convert to each other; crystalline concepts were the origin of converting, and showed the validity of this theory. At present this theory is on the stage of matural structure and content perfected constantly and approved in the world.
