Changes in Students’ Mathematical Competencies at the Beginning of Higher Education Within the Last Decade at a German University

Abstract

Mathematics plays a significant role in many study programs. However, several studies show deficiencies and a decline in beginning undergraduates’ skills in mathematics in many content domains. However, it remains unclear whether they have improved in so-called process competencies like modeling, mathematical reasoning, or using different representations instead, because there has been a shift towards the acquisition of such in many recent curricula. We investigated this issue at a university in Germany based on data from a (non-standardized) mathematics entry test taken by 3076 economics students divided into different cohorts from 2012 to 2019. Using regression analyses, we found that, on the one hand, students’ ability to carry out symbolic calculations decreased. On the other hand, their performance increased in some test questions focusing on other process competencies like reasoning, mathematizing, or using different representations, which have become common tasks at school due to a stronger emphasis on these process competencies after a curriculum reform. Our data indicate that this reform might have had the desired effect.

Exploring the interplay between vocational competence and dropout intention: insights and perspectives

“…Regarding the intention of upward dropout, domain-linked competence in the commercial domain, characterized by occupation-specific mathematical abilities, enables trainees to perceive mathematics as practical, pertinent, integrated, and capable of addressing various vocational mathematical challenges. This functional application of mathematical skills, beyond mere procedural execution, is crucial for tertiary education entry (Büchele and Feudel 2023). Additionally, given the centrality of mathematics in disciplines such as engineering, natural sciences, and economics, trainees possessing advanced math skills may recognize the potential for higher education to unlock a broader array of career prospects and academic pursuits beyond vocational training.…”