By now we carried out two STACK related projects at the University of Bern. One was meant to accompany the theoretical weekly homework of the first year Linear Algebra course, thus significantly reducing the workload of the assistants. The outcome of the second project is an online self-assessment aimed to help future university students make a more informed decision regarding their potential mathematical studies. Concerning these two use cases of STACK we are currently collecting students’ feedback. We will present our first conclusions on this matter, which will serve as a basis for further adjustments of the material.

After our initial experience in training students to perform algorithmic calculations, we became interested in designing STACK questions of a higher abstraction level. The online self-assessment was the first step, after which we started addressing the following well-known issue. First year bachelor students (in mathematics, physics, computer science) struggle with the transition from high school mathematics to university level mathematics. One of the main causes is that mathematics in school deals mainly with calculations and problem solving, while at university one carries out argumentation on a more conceptual level. The goal of this project is to bring together students and theorems and proofs by providing an online module focused on mathematical reasoning.

The project TU-WAS at TU Darmstadt has been deploying STACK exercises for nearly two years. Its objectives were threefold: First, guaranteeing assistance for students by offering digital homework including an elaborate error-adaptive automated feedback which induces continuous engagement in the teaching material, second, providing the option of exam training with a collection of randomized exercises, and, third, supporting tutors in their correction work. The primary target group of the project are mathematics courses for first-year engineering students, which are characterized by a sizeable number of participants, especially at TU Darmstadt.

This article provides an overview of the steps and expenses required to realize the project and names associated milestones. These comprises the necessary personnel ressources and measures relevant for the creation and includes embedding and maintenance of the digital assignments. Further, the required technical resources regarding the handling of the learning-management-system (in our case: moodle) and maxima, as well as an efficient handling of student assistants for the quality control of the created assignments is discussed. To investigate possible effects on students' learning and study behavior as well as the workload of tutors due to the complementary digital task arrangement, controlled intervention studies have been conducted over the course of three semesters. The results of the longitudinal analyses of the courses in mathematics for mechanical engineering and mathematics for civil engineers will also be presented briefly in this article.

STACK offers various features to provide differentiated and individual feedback to learners. As literature shows, the focus is often on retrospective (error-related) information on the content level. Further aspects beneficial to learning such as self-regulation and consideration of the different capacities of working memory of heterogeneous learners are not yet sufficiently addressed. This contribution illustrates how feedback in STACK might be designed to close this gap. According to the feedback model of Hattie and Timperley the discrepancy between current understandings and intended learning goals can be reduced by answering the three feedback questions “Where am I going?” (Feed-Up), “How am I going?” (Feed-Back) and “Where to next?” (Feed-Forward). Within the contribution it is discussed how these questions can be addressed either on the question level (specific feedback, general feedback) or on the quiz level (overall feedback). Furthermore, following Carless and Boud’s concept of feedback literacy, learners are given the opportunity to choose a particular type of feedback, taking into account important principles of instructional design theory, namely from the cognitive load theory and Mayer’s cognitive theory of multimedia learning. The concept is developed and proven as part of the interdisciplinary project IdeaL at the OTH Amberg-Weiden that is founded by the Stiftung Innovation in der Hochschullehre. A STACK question from a formative assessment on basic properties of functions serves to illustrate the concept.