Institut für Mathematik und Informatik
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Cognitive Spacetime
(2019)
The raise of so-called artificial intelligence has made people believe that computers may some day be congenial with human beings. In the past computers were regarded as effective but soulless and unintelligent assistants to free humans from routine tasks. Computers were supposed to perform time-consuming but mechanical calculations. Today's computers are universal machines that can execute an almost unlimited variety of software. The increase of processing speed allows us to implement complex software which does not seem to have much in common with past computing machinery.
In the field of education this awakened the desire to build algorithms which didactically support learners or even emulate human-like tutors. However, despite the apparent complexity of today's software, algorithms are step-by-step procedures which in their core are purely mechanical. So before introducing just another approach for technology-enhanced learning let me reconsider a seemingly naive but fundamental question. Given the nature of how computers work on the machine-level, can we emulate human-like tutors with computers?
I believe that we can not because human beings are in possession of abilities which can not be implemented with algorithms due to their mechanical kernel and the formal systems on which algorithms are built. However, there exists a concept with which we can implement a mutual human-machine interaction that enables computers to at least adapt themselves to a learner. The result of this is what we call "adaptive systems". In this work, I present a method based on spatio-temporal data structures and algorithms which enable us to build technically simple but artificially intelligent self-adapting systems. Such systems can be utilized for technology enhanced learning but also for other fields related to human-machine interaction.
This work aimed at investigating the effectiveness of a suggested approach, which presents geometric problems through a daily-life story using dynamic geometry software to enable undergraduate students to feel the importance of geometry in daily life, to share in the process of formulating geometric statements and conjectures, to experience the geometric proof more than validating the correctness of geometric statements, and to start with a real-life situation going through seven steps to geometric proof. The content of the suggested approach was organized so that every activity is a prerequisite for entering the next one, either in the structure of geometric concepts or in the geometric-story context.