World views of mathematics held by university teachers of mathematics science

The present empirical study deals with the question of the (world) view of mathematics (i.e. the image of mathematics) held by university mathematics teachers in countries of German as a first lan-guage. The basis of this study is a voluntary survey by means of a closed questionnaire of 119 persons during an annual meeting of mathematicians. This questionnaire was on the whole employed for two other studies on mathematics teachers (N= 300) and pupils (N=1650).

Four to five dimensions were defined by means of factor analysis and subsequently verified as relevant dimensions of the view of mathematics. These dimensions can be called the formalism aspect, the schema aspect, the process aspect, the application aspect and the Platonism aspect of mathematics. Attitudes towards these aspects differ on average, so that the "average" view of mathematics of university teachers is clearly accentuated in these five aspects. The process aspect acclaims the highest agreement, whereby the aspects formalism and application claim an average to above average assessment. In contrast, the Platonic aspect receives only weak to very weak agreement, and the schema aspect is on the whole rejected.

Furthermore the structure of the view of mathematics resulting out of the relations between the dimensions is investigated. The part of the view of mathematics that is considered here contains two different viewpoints in content, namely the static view of mathematics as a system and the dynamic view of mathematics as a process. In contrast to the observa-tions in the other two populations the two viewpoints are not opposites. Mathematics is in the view of university teachers a comple-mentary toge-therness of both viewpoints. Their view of mathematics is insofar broader differentiated than the two other populations.


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