„Mathematische Weltbilder” bei Studienanfängern — eine Erhebung

Abstract

The starting-point for research on “mathematical world views” („mathematische Weltbilder”) is the thesis that these “mathematical world views” play a central and significant role 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.