Between School and University: Mathematical Argumentation

Several studies show that university students in Germany still have problems in reasoning mathematically although this already should be fostered at high school since the implementation of standards for school mathematics. Mathematical argumentation is a core competence and highly important, especially in academic mathematics. To foster mathematical argumentation at the beginning of university studies, competence models are needed which give more detailed insights in the skills that are necessary for reasoning. As mathematical argumentation is a complex process, especially at the higher secondary level or at university, many little steps are needed to complete a competence model for argumentation at the secondary-tertiary transition gradually. A possible step can be to initially identify several aspects of mathematical argumentation competence that influence the reasoning quality. The empirical basis for identifying those aspects is a cross-sectional study with 439 engineering students who participate in a transition course in mathematics. We address the following questions: (1) how is the quality of student's reasoning? (2) Which kind of arguments do students use? (3) What resources do students who reasoned correctly use for solving the problems? (4) Does the content of the tasks play an important role? The results show a great influence of the content on the reasoning quality, especially if the content is abstract or concrete. Argumentation quality of students decreases with an increasing level of abstraction of the content. Furthermore, the results reveal that students often use routines for solving the problems. That indicates that procedural approaches still play an important role in school mathematics. If procedures could be used for solving the tasks, students are more successful. Competence models for mathematical argumentation at the beginning of the tertiary level should, therefore, include these factors.