This paper aims to examine the impacts of a liberal arts course about East-Asian mathematical cultures on university students' mathematics beliefs. The course, taught at a comprehensive university in Taiwan, explored pre-modern East-Asian mathematics, with a special focus on traditional Korean mathematical culture. This study employed a survey research method, whose subjects were 46 students in a comprehensive university who took the liberal arts course about East-Asian mathematical cultures, and research tools included a questionnaire of mathematics beliefs divided into two dimensions of the "nature" and "values" of mathematics, and two rounds of students' written reflective reports. The quantitative data were analysed using descriptive and inferential statistics, while the qualitative data were read with the content analysis method to provide interpretative evidence for quantitative results. The surveys were administered before the teaching of Japanese mathematics, so the influences shown in the results were due to Chinese and Korean mathematical cultures. Research results show that, generally speaking, for the dimension of the nature of mathematics, students had a more diversified understanding of the justification of mathematical knowledge; for the dimension of the values of mathematics, students tended to agree more on the links between mathematics and traditional cultures, humanities and social sciences, and real-world applications. The authors also provide suggestions to future studies and to the teaching practices for general liberal arts courses about mathematical cultures.

This study begins with the observation that the perception of directions in the past differs from that of the present. Due to the diverse ways in which directions have been expressed across different cultural and historical contexts, variations in the four cardinal directions can be found in place names and in the directional indications of Yangan. To explore this in the context of Joseon mathematics, this study analyzed problems from Cheungnyangdohae, a mathematical text that provides diagrammatic solutions to problems involving directional concepts, thereby allowing the author's perception of direction to be inferred. The analysis revealed that, in addition to the commonly used "south-up" orientation, the "south-down", "south-right", and "south-left" orientations also appeared. This diversity may be attributed to the visual representation of key mathematical concepts such as "gougu" and "jung-cha", as well as to the efficiency of spatial arrangement on the page. These findings are expected to shed light on another distinctive feature of mathematics in the Joseon era.