Virtual Inverted-Classroom Courses vs. Face-to-Face Courses in German Higher Education: Comparing Students' Learning Progress and Perspectives on Mathematics Preparatory Courses

Virtual Inverted-Classroom Courses vs. Face-to-Face Courses in German Higher Education: Comparing Students' Learning Progress and Perspectives on Mathematics Preparatory Courses

Moritz Brüstle, Gerhard Götz, Myriam Hamich
DOI: 10.4018/978-1-6684-4446-7.ch003
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A comprehensive three-layer concept of constructively aligned preparatory mathematics courses in a German higher education institution and its implementation are presented. The core of it is a virtual inverted-classroom course featuring learning videos and auto-adapting computer-assisted self-study training modules. This virtual course was developed in response to the pandemic and implemented for the first time in the year 2020. An evaluation was performed on three different levels and with three different approaches: a quantitative analysis of the mathematical performance gains, a qualitative analysis of the students' perspectives on the courses, and the analysis of the usage data of the auto-adapting training modules. It turned out that these courses are comparable to previous years face-to-face courses in terms of the students' satisfaction with the courses and their growth in mathematical skills as well as in terms of the knowledge gains. The process of designing, planning, executing, and evaluating this virtual course will be illustrated in this chapter.
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In German higher education there is, in addition to universities and universities of applied sciences, a third branch, the so-called cooperative universities which have attracted an increasing number of students in the last 20 years due to their combination of university and workplace training. Many higher education institutions face an increasing dropout rate which they try to cope with by offering preparatory courses in the pre-study phase for newly enrolled students.

The Cooperative State University Baden-Württemberg (DHBW) is the first higher education institution in Germany to integrate academic studies with on the job workplace training. Students are not only enrolled at the university but are also paid employees at one of many local partner companies and thus spend approximately half of the year in workplace training instead of having long term holidays as they do at other universities. With over 32,000 students (2021), about 9,000 corporate partner companies and social institutions and over 145,000 alumni, the DHBW is the largest higher education institution in the German Federal State of Baden-Wuerttemberg (Baden-Württemberg Cooperative State University, 2021). It comprises nine locations, spread out all over the state of Baden-Württemberg, one of which is in the city of Mosbach.

In Germany, drop-out-rates for technical bachelor study programs are higher than 30% (Heublein & Schmelzer, 2018; Meyer et al., 2018; Deuer et al., 2017). Even though not all of the drop-outs may be due to student performance, there is a known relation between prior mathematical skills and the success in studying a subject in science, technology or engineering subject (e.g. Trapmann et al., 2007; Ackerman et al., 2013; Moser-Fendel et al., 2019). Based on these facts, many higher educational institutions offer tutoring or courses before students begin their studies to smoothen the transition from secondary school to higher education. In order to reduce the heterogeneity in first year students’ prior mathematical skills, the DHBW offers such preparatory courses especially in mathematics. 
The virtual inverted-classroom concept (Mazur, 1997; Crouch & Mazur, 2001) presented herein was developed and implemented first in the year 2020 at the DHBW Mosbach, when the COVID19-pandemic caused the cancellation of all face-to-face courses abruptly and required the provision of adequate digital substitutes (Brüstle et al.; 2021). In this chapter we thereby focus on the following three key aspects: Firstly, a quantitative analysis of the increase of mathematical skills based on a pre-/post-test design. Secondly, an analysis of the student's perception of the courses which was gained through a questionnaire. And thirdly, the impact of auto-adapting, computer-assisted self-study training modules on the individual learning process.

Key Terms in this Chapter

Constructive Alignment: Constructive alignment refers to a specific approach of designing courses. The goal is to align learning outcomes, learning activities and assessment tasks. In order to do that, the following steps must be taken ( Biggs & Tang, 2011 , p. 100): describe the intended learning outcome in the form of a verb (learning activity), its object (the content) and specify the context and a standard the students are to attain; create a learning environment using teaching/learning activities that address that verb and therefore are likely to bring about the intended outcome; use assessment tasks that also contain that verb, thus enabling you to judge with the help of rubrics if and how well students’ performances meet the criteria; transform these judgements into standard grading criteria.

Inverted Classroom: Learners learn the content provided digitally by the instructors on their own, usually at home. A following event (usually face-to-face) is used to consolidate together what has been learned individually. Used synonymously: Flipped Classroom.

E-Learning and Computer-Assisted Learning (CAL): All environments and procedures that use computers and computer software to aid or enable student learning. This can be courses taught online, materials provided online, specific programs that run on a computer or comparable device etc. The notion of computer-assisted learning has become interchangeable with online learning, or e-learning.

Preparatory Courses: Specific courses which are offered before the students start their actual study programme at a university. Mostly, these courses are provided to facilitate the transition from secondary to tertiary education for students. They can be on any given subject, most commonly they are offered in the context of rather difficult subjects such as Mathematics or Physics.

Learning Management System (LMS): Learning platforms or learning management systems, as opposed to mere collections of teaching scripts or hypertext collections on web servers, are software systems that have the following functions: A user administration (login with encryption), a course management (courses, content management, file management), a role and rights assignment with differentiated rights, communication methods (chat, forums) and tools for learning (whiteboard, notebook, annotations, calendar, etc.), the presentation of course content, learning objects and media in a network-compatible browser.

Learner-Centered: Learner-centered refers to a specific way of designing classes. It shifts the focus from the teacher to the learner by giving them a major part of the responsibility for their successful learning path. This could be done by offering a variety of learning paths to the students and letting them decide, which one they take. This enables students to choose a better fitting path for themselves while demanding and thus promoting a range of self-learning and -management skills. Used synonymously: student-centered.

Self-Study: According to Landwehr and Müller (2008) AU44: The in-text citation "Landwehr and Müller (2008)" is not in the reference list. Please correct the citation, add the reference to the list, or delete the citation. , three forms of self-study can be differentiated: Free self-study is characterized by students freely engaging with specific topics and content, which can be completely independent of specific modules and are not prescribed in the curriculum. Thus, engagement in free independent study is primarily dependent on students' individual interests and personal commitment. Nevertheless, universities can support such activities by awarding credit points for them, for example, by offsetting them in the ECTS total in the context of theses, service learning, or campus credits. Individual self-study is assigned to individual modules, but not through specific structured learning activities. Accordingly, there is no structuring assignment guidance and no contact support by instructors. In accompanied self-study , students work in a self-organized manner - individually and in groups - to complete given assignments. Here, a further distinction is made between “accompanied self-study time” (with contact guidance by teachers) and “unaccompanied self-study time” (without contact guidance).

Auto-Adapting Training Modules: Auto-adapting training modules are software-based self-study training programs for students, mainly focusing on performing tasks. These modules take the users’ previous performance into account and, based on that information, automatically provide the most suitable tasks. In doing so, these modules individualize and thus improve the students’ learning process without any further assistance by tutors or lecturers.

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