• The Mathematical Education
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• v.63 no.2
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• pp.139-163
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• 2024

The purpose of this study is to examine the capabilities of ChatGPT as a tool for supporting students in generating mathematical arguments that can be considered proofs. To examine this, we engaged students enrolled in a mathematics pathways course in evaluating and revising their original arguments using ChatGPT feedback. Students attempted to find and prove a method for the area of a triangle given its side lengths. Instead of directly asking students to prove a formula, we asked them to explore a method to find the area of a triangle given the lengths of its sides and justify why their methods work. Students completed these ChatGPT-embedded proving activities as class homework. To investigate the capabilities of ChatGPT as a proof tutor, we used these student homework responses as data for this study. We analyzed and compared original and revised arguments students constructed with and without ChatGPT assistance. We also analyzed student-written responses about their perspectives on mathematical proof and proving and their thoughts on using ChatGPT as a proof assistant. Our analysis shows that our participants' approaches to constructing, evaluating, and revising their arguments aligned with their perspectives on proof and proving. They saw ChatGPT's evaluations of their arguments as similar to how they usually evaluate arguments of themselves and others. Mostly, they agreed with ChatGPT's suggestions to make their original arguments more proof-like. They, therefore, revised their original arguments following ChatGPT's suggestions, focusing on improving clarity, providing additional justifications, and showing the generality of their arguments. Further investigation is needed to explore how ChatGPT can be effectively used as a tool in teaching and learning mathematical proof and proof-writing.

• Journal of the Korean Institute of Landscape Architecture
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• v.33 no.3 s.110
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• pp.65-77
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• 2005

Deokjin Park in Jeonju City was the site of a pond during the Koryo Period. Although Jeonju City has developed rapidly in modem times, Deokjin Pond was preserved and was developed into a park It can be theorized that Deokjin Pond's latent character has made it possible for it to adapt to the changes it has undergone throgh the years. In this study, the placeness of Deokjin Park is determined by examining its role in the adaptation process. Placeness can be determined by examining the objective character of a certain environment and the subjective experience related to it. For this paper, documents about the history of Deokjin Park were examined so that the facts related to it could be established. In addition, a number of Jeonju citizens were asked about their memories of Deokjin Park since memories reveal people's subjective experiences. The results of this study can be summarized as follows. Deokjin Pond is an ideal space for Feng Shui. It is a holy place because the tomb of the founder of the Chosun Dynasty is close to it. In addition, it has scenic value as it is part of the Jeonju Palkyoung (eight sceneries). To this day, we can see people washing their hair in the pond, proof that Deokjin Pond is still the subject of folk beliefs. When Korea was under Japanese rule, Deokjin Pond became Deokjin Park because of its ideal location, scenic value, and grand possibilities as an amusement center. Over the years, though its scenic value decreased after the death of its pine trees. Jeonju City, however, was able to revive the park's charm though a series of renovation projects and through the addition of several facilities. Deokjin Park is now surrounded by many cultural buildings. The significance of Deokjin Park can be expected to evolve with these changes. This study helps to predict the future of Deokjin Park and to elucidate the importance of landscape architecture from the point of view of an "evolving place."

• 기호학연구
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• no.54
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• pp.7-36
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• 2018

Michael Polanyi's idea of tacit knowledge came from the realization that scientific objectivity and critical philosophy had become too restrictive for philosophy, especially in the realm of meaning, which is beyond positivistic proof and contains more non-critical elements than critical ones. In social life, people still share certain kinds of knowledge and beliefs which they obtain without making or learning those explicitly. Contemplating the role and significance of tacit knowledge, he called for a post-critical philosophy that integrates the realm of meaning and thereby appreciates the intertwined nature of tacit and explicit knowledge. Polanyi's position towards skepticism and doubt shows similarities with Charles S. Peirce's thinking about the relationship between belief and doubt. Although Peirce's semeiotics stands firmly in the tradition of critical philosophy, he affirms that doubt cannot be a constant state of mind and only belief can form a basis for a specific way of life. Polanyi's approach differs from Peirce's by focusing on the impossibility of scientific knowledge based solely on principles and precision, and his emphasis on the crucial role of the community of scientists. Nevertheless, the deeper implications of Peirce's contemplations on belief and doubt have myriad ramifications on the philosophy of science as well as the sociology of science.