Framework for examining the transformation of mathematics and mathematics learning in the transition from school to university: An analysis of german textbooks from upper secondary school and the first semester

Abstract

Many first-year students experience the transition from school to university as a challenging enterprise. This is especially true for mathematics programs. Comparatively high dropout rates of freshman students after the first or second semester indicate that this transition is the main obstacle for students to finish their studies in mathematics. For example, in Germany, universities and mathematics departments are faced with dropout rates of up to 50 % of first-year students in mathematics. According to surveys, students report that this is mainly caused by the enormous pressure to perform and a lack of motivation (Heublein et al. 2009). However, most of the surveys do not use instruments detecting the specific situation for the subject mathematics. We assume that the high dropout rate during the transition from school to university is rooted in the necessity of coping with two discontinuities: the discontinuity of the learning subject and the discontinuity of the way of learning. Accordingly, managing the transition from school to university successfully means individually developing two ways of transformation to overcome these discontinuities. First, a transformation from school mathematics to academic mathematics, so that academic mathematics can be recognized as an extension of school mathematics and the individual mathematical knowledge learned in school can serve as a basis for further learning (Deiser and Reiss 2013, Chap. 3).