Publikationen

In this article we outline the role evidence and argument plays in the construction of a framing theory for Proof Based Teaching of basic operations on natural numbers and integers, which uses tiles to physically represent numbers. We adopt Mariotti’s characterization of a mathematical theorem as a triple of statement, proof and theory, and elaborate a theory in which the statement “The product of two negative integers is a positive integer” can be proved. This theory is described in terms of a ‘toolbox’ of accepted statements, and acceptable forms of argumentation and expression. We discuss what counts as mathematical evidence in this theory and how that evidence is used in mathematical arguments that support the theory.

Link:  DOI: 10.1007/s11858-019-01027-x

Interactive Systems for learning offer great potentials for the use in school classes as they allow supporting teachers in addressing students at different knowledge levels at the same time, the systems can provide valuable and individual feedback and are motivating and entertaining for the students using it due to gamification elements. Nevertheless, developing learning systems for schools is demanding, as many different stakeholders need to be involved. In this workshop paper, we report from a transdisciplinary research project with computer scientists, mathematics educators and a textbook publisher, in which we investigate the potentials of using tangible user interfaces for algebra learning. In this paper, we particularly present insights from a comparative study in school, in which 22 students (grade 7) used either a touch-based or a tangible-based algebra learning system on a tablet. Our results show that both system versions generally work well and that the tangible system received higher user experience.

Link: DOI: 10.13140/RG.2.2.13000.21766

While manipulatives have played an important role in children’s mathematics development for decades, employing tangible objects together with digital systems in the classroom has been rarely explored yet. In a transdisciplinary research project with computer scientists, mathematics educators and a textbook publisher, we investigate the potentials of using tangible user interfaces for algebra learning and develop as well as evaluate a scalable system for different use cases. In this paper, we present design implications for tangible user interfaces for algebra learning that were derived from a comprehensive field study in a grade 9 classroom and an expert study with textbook authors, who also are teachers. Furthermore, we present and discuss the resulting system design.

Link: ICOM Special Issue: Tangible Interaction and its Applications

This workshop position paper presents ongoing research on using smart tangible objects for algebra learning. While mathematical manipulatives have played an important role in children’s mathematics development for decades, employing tangible objects in the classroom has been rarely explored yet. In our work, we investigate the potentials of using smart objects for algebra learning. Our smart tiles are based on traditional algebra tiles, passive mathematical manipulatives used in many schools in Northern America, and we currently extend these by 1.) multimodal input and output capabilities, 2.) dynamic constraints and 3.) adaptivity and feedback. In this paper, we give an overview on the overall system concept, the interaction with the tangible objects and their current design, as well as on the potentials of actuated smart objects for future interaction.

Link: DOI 10.13140/RG.2.2.13000.21766

We present a set of boundary objects we indentified in an ongoing interdisciplinary research and development project, where mathematics didacticians collaborate with human-computer interaction experts to develop digitally enhanced versions of manipulatives for algebra learning.

Link: Proceedings der ICTMT13 mit der Posterbeschreibung (S. 447 f.)