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多年来,德国奥斯纳布吕克大学和数学教学法研究所,就程序编制和分析问题对学生进行实验研究,从中发现,学生对数学问题的智力分析方式存在着较大的个性差异,对此他们提出假说:这种个性差异的存在主要是因为学生认知差异的存在,在此基础上,德国著名的认知心理学和数学教学法专家英格·施万克教授(Pfof. Dr. Jnge Schwank),将认知结构区分为机能性和表语性结构。机能性思维注重行为过程和作用方式,而表语性思维则善于用关系判断考察事物。 施万克从两方面分析相关系统中概念表征的各种可能:外在的数学概念与关系网络的表达和内在心理模型。通过研究,她又提出了有关共鸣效应现象的假说,即个性偏爱某些特定的外在表征方式,这意味着他为自己建立一个能适应其认知结构的世界。
Over the years, Osnabruck University in Germany and the Institute of Mathematics Teaching Methodology have carried out experimental research on students’ compilation and analysis of problems, from which they found that students have great personality differences in mathematical analysis of mathematical problems. They put forward the hypothesis: This personality difference exist mainly because of the existence of cognitive differences in students, on this basis, the famous German cognitive psychology and mathematics teaching expert Professor Ing Schwanke (Pfof. Dr. Jnge Schwank), the cognitive structure is divided into functional and epigraphic structure. Functional thinking focuses on behavioral processes and modes of action, whereas epigraphical thinking is good at judging things by relationship. Schwank analyzed the possibilities of conceptual representation in related systems from two aspects: the extrinsic mathematical concept and the expression of the relation network and the intrinsic mental model. Through her research, she again put forward a hypothesis concerning the phenomenon of resonance effect, that is, personality favors some specific external representation, which means he builds a world for himself to adapt to his cognitive structure.