The role of teaching, learning, and assessment with digital technology has become increasingly prominent in mathematics education. This survey paper provides an overview of how technology has been transforming teaching, learning, and assessment in mathematics education in the digital age and suggests how the field will evolve in the coming years. Based on several decades of research and educational practices, we discuss and anticipate the multifaceted impact of technology on mathematics education, thus laying the groundwork for the other papers in this issue. After a brief introduction discussing the motivations for this issue, we focus our attention on three lines of research: teaching mathematics with technology, learning mathematics with technology, and assessment with technology. We point to new research orientations that address the issue of teaching with technology, specifically describing attempts to conceptualise teachers’ mathematical and digital competencies, perspectives that view teachers as designers of digital resources, and the design and evaluation of long-term initiatives to support teachers as they develop innovative teaching practices enhanced by digital technologies. Our examination shows that learning with technology is still marked by new conceptualizations raised by researchers that can further our understanding of this complex issue. These conceptualizations support the recognition that multiple resources, ranging from paper and pencil to augmented reality, participate in the learning process. Finally, assessment with technology, especially in the formative sense, offers new possibilities for offering individualised support for learners that can benefit from adaptive systems, though more tasks for conceptual understanding need to be developed.

Storytelling is a long-established tradition and listening to stories is still a popular leisure activity. Caused by technization, storytelling media expands, e.g., to social robots acting as multi-modal storytellers, using different multimodal behaviours such as facial expressions or body postures. With the overarching goal to automate robotic storytelling, we have been annotating stories with emotion labels which the robot can use to automatically adapt its behavior. With it, three different approaches are compared in two studies in this paper: 1) manual labels by human annotators (MA), 2) software-based word-sensitive annotation using the Linguistic Inquiry and Word Count program (LIWC), and 3) a machine learning based approach (ML). In an online study showing videos of a storytelling robot, the annotations were validated, with LIWC and MA achieving the best, and ML the worst results. In a laboratory user study, the three versions of the story were compared regarding transportation and cognitive absorption, revealing no significant differences but a positive trend towards MA. On this empirical basis, the Automated Robotic Storyteller was implemented using manual annotations. Future iterations should include other robots and modalities, fewer emotion labels and their probabilities.

As Internet of Things (IoT) devices become ubiquitous, they face increasing cybersecurity threats. Unlike standard 1-to-1 communication, the unique challenge posed by n-to-n communication in IoT is that messages must not be encrypted for a single recipient but for a group of recipients. For this reason, using Secure Group Communication (SGC) schemes is necessary to encrypt n-to-n communication efficiently for large group sizes. To this end, the literature presents various SGC schemes with varying features, performance profiles, and architectures, making the selection process challenging. A selection from this multitude of SGC schemes should best be made based on a benchmark that provides an overview of the performance of the schemes. Such a benchmark would make it much easier for developers to select an SGC scheme, but such a benchmark still needs to be created. This paper aims to close this gap by presenting a benchmark for SGC schemes that focus on IoT. Since the design of a benchmark first requires the definition of the underlying business problems, we defined suitable problems for using SGC schemes in the IoT sector as the first step. We identified a common problem for the centralized and decentralized/hybrid SGC schemes, whereas the distributed/contributory SGC schemes required defining an independent business problem. Based on these business problems, we first designed a specification-based benchmark, which we then extended to a hybrid benchmark through corresponding implementations. Finally, we deployed our hybrid benchmark in a typical IoT environment and measured and compared the performance of different SGC schemes. Our findings reveal notable impacts on calculation times and storage requirements without a trusted Central Instance (CI) in distributed/contributory SGC schemes.

Graph Drawing is a field of research that has application in any field of science that needs to visualize binary relations. This thesis covers various problems arising when drawing graphs, both in theoretical and applied settings. In the first and more theory-based part, we start by discussing how and to which degree graph drawings can be used to visually prove graph properties (such as connectivity) in an effective manner. Both for these visual proofs and for graph drawings in general, the visual complexity determines how well humans are able to perceive and process them. We find it thus paramount to minimize the visual complexity of drawings. For example, one measure for the visual complexity of a straight-line node-link diagram is the number of segments used. We prove lower bounds on the segment number of some planar graph classes. These bounds tell us how (visually) complex node-link diagrams (a traditional drawing style) of these graphs must be at least. Next, we consider obstacle representations, which can be far less (visually) complex in some cases, however, (usually) at the expense of being harder to understand. Next, we investigate the coloring of mixed and directional interval graphs. While this in itself is not a drawing problem, it has, among others, application in the Sugiyama framework, which is a widely used framework for layered orthogonal graph drawing. In the final chapter of the first part, we consider drawings of level graphs on few levels under a given set of precedence constraints. The two problems considered in the second part are motivated by applications in biology. First, we propose a drawing style for visualizing multispecies coalescent trees, which are composed of a species tree and associated gene trees, and then investigate various drawing algorithms. Second, we propose a model for visualizing geophylogenies, that is, species trees that label sites on maps, and then analyze various variants and algorithms to draw them.

This cumulative dissertation presents interdisciplinary research in the field of human-computer interaction that is located in both, computer science and psychology. It investigates the implementation and subsequent evaluation of Intelligent Virtual Agents (human-like, interactive characters) with mixed-cultural backgrounds (multiple cultural backgrounds combined in one individual, e.g., as a result of migration). On the one hand, methods from computer science were applied to develop two novel tools that allow for the automatic generation of synthetic non-native speech and for the efficient implementation of Wizard-of-Oz-based interactive scenarios with mixed-cultural Intelligent Virtual Agents (IVAs). On the other hand, methods from psychology were applied to investigate how users perceive cultural behaviours in IVAs and whether their response is congruent to the one seen in human-human interactions. Additionally, to use IVAs in cultural interventions, effective intervention strategies from social psychology were adapted for interactive scenarios with IVAs. The research contribution is divided into two levels: On the first level, basic research on the design and subsequent perception of mixed-cultural IVAs is conducted. With non-native speech being the most reliable cultural marker of mixed-cultural individuals, this dissertation presents work on the design and perception of synthetically generated non-native speech for IVAs. Focusing on the two most salient markers of non-native speech, grammatical mistakes and non-native accents, it evaluates how users perceive IVAs exhibiting these patterns of non-native speech. Furthermore it investigates in which cases non-native accented synthetically generated speech can be used as a cost-efficient and flexible alternative to non-native accented natural speech. To simplify and standardise basic research on the perception of mixed-cultural IVAs with non-native speech, this thesis presents a novel tool for automatically generating mixed-cultural speech for IVAs. The tool enables fast and reliable generation of grammatically incorrect and non-native accented synthetic speech based on empirical research. On the second level, this dissertation presents novel applied research that for the first time implements virtual interactive interventions using mixed-cultural IVAs to raise inter-cultural empathy and reduce implicit cultural bias. Based on previous research from the social sciences and human-computer interaction, this dissertation also presents the implementation of a Wizard-of-Oz prototyping tool for fast and reliable implementations of complex interactive scenarios with mixed-cultural IVAs. This dissertation makes a significant contribution to research on the implementation and perception of mixed-cultural IVAs and their application to reduce implicit cultural bias. Presenting the two newly developed tools to automatically generate non-native speech and design interactive scenarios with convincing mixed-cultural IVAs, it also makes an important technical contribution for agent-based research.