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In this paper, the formula for measuring creativity in Fermi problems is developed.
Fermi problems are open problems, treated as a type of mathematical modelling, that requires a quick estimation of an unclear quantity. The problem usually requires decomposing and transforming the initial Fermi problem into understandable subproblems. It has been suggested that such decompositions and transformations require creativity. However, there are limited studies that analyze and discuss how creativity in Fermi problems should be viewed, although Fermi problems have potential related to creativity. Therefore, the author conducted empirical studies of Fermi problems from the perspective of creativity, based on previous studies on creativity.
In previous studies, creativity is often measured by three factors: Fluency, Flexibility, and Originality. Fluency is measured by the number of ideas for solving a problem. Flexibility is measured by the number of categories of ideas for solving a problem. Originality is measured by the rarity of ideas to solve the problem. However, there are several criticisms of these measures. The first are criticisms of Flexibility. Because of the similarity between Fluency and Flexibility, some studies do not include Flexibility as a factor of creativity. Furthermore, the categorization of ideas is arbitrary, so the measurement of Flexibility could change depending on the evaluator. The second is a criticism of Originality. Most studies arbitrarily set the rarity of ideas to measure this factor. For example, some studies say that less than 5% of ideas are rare, while others say that less than 1% are rare.
The formula to measure creativity in Fermi problems, which could resolve the above criticisms, is proposed. The formula is developed by applying information theory. It does not include the concept of Flexibility, which is evaluated in terms of the number of categories of ideas. Furthermore, the formula does not set a criterion for determining idea rarity, using as it does the relative occurrence rate of ideas.
The results of the analysis using structural equation modeling, which is a statistical analysis, showed a more than moderate correlation between creativity calculated using the suggested formula and established creativity (e.g., creativity in psychology). Furthermore, the proposed formula performed better than a formula measuring creativity in a previous study.
In other words, the proposed formula could solve the issues that have been pointed out in previous studies, and the statistical analysis allowed us to examine the formula.

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.