Particularly in mathematics, the transition from school to university often appears to be a substantial hurdle in the individual learning biography. Differences between the characters of school mathematics and scientific university mathematics as well as different demands related to the learning cultures in both institutions are discussed as possible reasons for this phenomenon. If these assumptions hold, the transition from school to university could not be considered as a continuous mathematical learning path because it would require a realignment of students' learning strategies. In particular, students could no longer rely on the effective use of school-related individual resources like knowledge, interest, or self-concept. Accordingly, students would face strong challenges in mathematical learning processes at the beginning of their mathematics study at university. In this contribution, we examine these assumptions by investigating the role of individual mathematical learning prerequisites of 182 firstsemester university students majoring in mathematics. In line with the assumptions, our results indicate only a marginal influence of school-related mathematical resources on the study success of the first semester. In contrast, specific precursory knowledge related to scientific mathematics and students' abilities to develop adequate learning strategies turn out as main factors for a successful transition phase. Implications for the educational practice will be discussed.

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Constructive error handling is considered an important factor for indi-vidual learning processes. In a quasi-experimental study with Grades 6 to 9 students, we investigate effects on students’ attitudes towards errors as learning opportunities in two conditions: an error-tolerant classroom culture, and the first condition along with additional teaching of strategies for analyzing errors. Our findings show positive effects of the error-tolerant classroom culture on the affective level, whereas students are not influenced by the cognitive support. There is no evidence for differential effects for student groups with different attitudes towards errors.Aprender de los errores: efectos de la formación del profesorado en las actitudes de los estudiantes hacia los errores y el uso individual que hacen de ellosSe considera que el manejo constructivo de los errores es un factor importante en el aprendizaje individual. En un estudio cuasi-experimental con estudiantes de grados 6 a 9, investigamos los efectos sobre las actitudes hacia los errores como oportunidades de aprendizaje bajo dos condiciones: una cultura en el aula tolerante a errores, y esa condición junto con la enseñanza de estrategias para analizar los errores. Encontramos efectos positivos de la cultura tolerante a errores en el nivel afectivo, mientras que el apoyo cognitivo no tuvo influencia a los estudiantes. No hay evidencia de efectos diferenciales para grupos de estudiantes con actitudes diferentes hacia los errores.Handle: http://hdl.handle.net/10481/27879Nº de citas en WOS (2017): 3 (Citas de 2º orden, 1)Nº de citas en SCOPUS (2017): 5 (Citas de 2º orden, 1)

The transition from school to tertiary mathematics courses, which involve advanced mathematics, is a challenge for many students. Prior research has established the central role of prior mathematical knowledge for successfully dealing with challenges in learning processes during the study entrance phase. However, beyond knowing that more prior knowledge is beneficial for study success, especially passing courses, it is not yet known how a level of prior knowledge can be characterized that is sufficient for a successful start into a mathematics program. The aim of this contribution is to specify the appropriate level of mathematical knowledge that predicts study success in the first semester. Based on theoretical analysis of the demands in tertiary mathematics courses, we develop a mathematical test with 17 items in the domain of Analysis. Thereby, we focus on different levels of conceptual understanding by linking between different (in)formal representation formats and different levels of mathematical argumentations. The empirical results are based on a re-analysis of five studies in which in sum 1553 students of bachelor mathematics and mathematics teacher education programs deal with some of these items in each case. By identifying four levels of knowledge, we indicate that linking multiple representations is an important skill at the study entrance phase. With these levels of knowledge, it might be possible to identify students at risk of failing. So, the findings could contribute to more precise study advice and support before and while studying advanced mathematics at university.