„Mathematische Weltbilder” bei Studienanfängern — eine Erhebung
„Mathematische Weltbilder” bei Studienanfängern — eine Erhebung
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Studienanfängern 的“数学世界图片” — eine Erhebung
DOI：
10.1007/bf03338808
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Stefan Grigutsch
中科院分区：
文献类型：
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作者：
G. Törner;Stefan Grigutsch
“数学世界观”研究的出发点是，这些“数学世界观”在个人学习和做数学中起着中心和重要的作用。对一年级学生（数学和化学）进行了调查，其中确定并测量了几个数学概念（“Vorstellungen”）。可以证明，这些成分部分地构成了一种“世界观”，并对做数学有影响。结果表明，“词观”各因素对其他因素的影响不是单因的，而是构成成分复合体的因素。一个复杂的涵盖态度（“Haltungen”）有关的问题是否和在多大程度上数学是一个过程（认知，智力进步和建设理论）或一个系统（例如，“工具箱”和“公式”以及抽象的，正式的理论）。第二个情结是对“数学教育乐趣”的态度（与“不要将学校数学与数学分开”有关）、“对当前数学表现的自我评估”和“学习不仅仅是为了笔试;推导和证明并非不重要”。因此，“数学世界观”事实证明，它是一个复杂的结构，从本质上影响着数学的学习和实践，上述两种复合体都是“数学世界观”的原型，这是数学表现的理想。“数学世界观”包含了一些对数学学习和数学实践或有害或有益的态度。特别值得怀疑的甚至是严重的，虽然并不令人惊讶或意外的是，事实上，“世界观”的“化学家”（相比，“数学家”）提供了明显较差的条件，学习和做数学。“化学家”表现出更有限的“世界观”，通常是针对用户和“客户”，而“数学家”则是数学的生产者。
The starting-point for research on “mathematical world views” („mathematische Weltbilder”) is the thesis that these “mathematical world views” play a central and significant rôle in the individual learning and doing of mathematics.An investigation on first-year students (mathematics and chemistry) has been carried out in which several conceptions („Vorstellungen”) of mathematics have been identified and measured. It can be proved that these components partly constitute a “world view” and do take effect on doing mathematics. The results show that the factors of a “word view” influence others not monocausally, bu reciprocally whereby complexes of components are constituted. One complex covers the attitudes („Haltungen”) concerning the question whether and in how far mathematics is a process (of cognition, intellectual progress and building theory) or a system (e.g. a “toolbox” and a “formulary” as well as an abstract, formal theory). A second complex consists of the attitudes with respect to “pleasure in mathematics education” (connected with “don’t separate school mathematics from mathematics”), “self-assessment of the current mathematical performance” and “learning not only for the written class test; derivations and proofs are not unimportant”.Thus a “mathematical world view” turns out to be a complex structure which essentially influences the learning and doing of mathematics, and both of the mentioned complexes characterize a prototype of a “mathematical world view” which is ideal for mathematical performance.The students’ “mathematical world views” contain some attitudes which have either detrimental or more promoting attitudes concerning learning and doing of mathematics. Especially doubtful or even serious though not surprising or unexpected is the fact that the “world view” of the “chemists” (compared to that of the “mathematicians”) provides clearly worse conditions for learning and doing mathematics. The “chemists” show a more restricted “world view”, typically for users and “customers”, whereas the “mathematicians” rather turned out to be producers of mathematics.