Viel Beweisen, kaum Rechnen? Gestaltungsmerkmale mathematischer Übungsaufgaben im Studium

Abstract

Zusammenfassung Übungsaufgaben erfüllen im Mathematikstudium zentrale Funktionen. Allerdings ist bisher kaum systematisch untersucht, welche Gestaltungsmerkmale sie aufweisen und welche Ziele Dozierende mit ihren Übungsaufgaben verfolgen. In einem kontrastierenden Ansatz wurden 277 Übungsaufgaben aus vier Lehrveranstaltungen hinsichtlich ihrer Gestaltungsmerkmale untersucht und klassifiziert. Ergänzend wurden in einer Interviewstudie die zugehörigen Lernziele der Dozierenden ermittelt und mit den Ergebnissen verglichen. Es zeigt sich, dass es systematische Lücken gibt, sodass sich nicht alle Lernziele gleichermaßen in den Aufgaben spiegeln. Auf Basis der Ergebnisse werden Vorschläge für die Gestaltung von Aufgaben formuliert.

The relation between attitudes towards mathematics and dropout from university mathematics—the mediating role of satisfaction and achievement

“…In particular, Engelbrecht (2010, p. 143) stated that "most students' perception of being successful in mathematics in school does not involve much inquiry but mostly just the application of different methods". Comparing typical tasks at university with typical tasks in school, a clear shift to proving is reported (Vollstedt et al, 2014;Weber & Lindmeier, 2020). As these proving tasks usually cannot be solved by using only schematic calculations or algorithms and most students are unfamiliar with formal proofs when entering university (De Guzman et al, 1998), cognitive and affective problems can occur when students have to deal with proofs on their own: cognitive in the sense that they are not able to cope with homework tasks and affective in the sense that they do not dare to work on the tasks to avoid failures and that they are more interested in school mathematics, focusing on schematic calculations, compared to university mathematics, focusing on proofs.…”

Development of affect at the transition to university mathematics and its relation to dropout — identifying related learning situations and deriving possible support measures

“…In Germany, students have to hand in weekly homework tasks. Sometimes, by solving these tasks correctly, students can earn extra points for the final exams, or solving tasks is mandatory in order to be allowed to participate in the exams (Weber & Lindmeier, 2020). Handedin tasks are graded by teaching assistants.…”

“…This general shift involves differences in the way new content is presented during lessons and lectures as well as differences in the tasks students have to solve (cf. Bergsten, 2007;de Guzmán et al, 1998;Luk, 2005;Weber & Lindmeier, 2020).…”

“…In contrast to school, routine tasks are less prevalent at university while proof-related tasks play a bigger role (Pritchard, 2015;Thomas & Klymchuk, 2012). Weber and Lindmeier (2020) analyzed mathematics tasks from a German university and reported that nearly 70% of the tasks involve proving.…”