When Liu Hui Meets Archimedes: Students' Epistemological and Cultural Interpretations of Mathematics

摘要

The present study aimed to investigate in what way and to what extent Taiwanese college students' epistemological views of mathematics had evolved during a history-based liberal arts mathematics course titled: "When Liu Hui Meets Archimedes-Development of Eastern and Western Mathematics." The course was designed to help college students comprehend the cultural features of mathematics by highlighting the similarities and differences in the formation of mathematical knowledge in the Eastern and Western worlds. Through comparing and contrasting collected data, we found students demonstrated different epistemological views of mathematics in three aspects: first, they were able to recognize the diverse features of mathematics; second, they better realized how mathematics had interacted with societies; and third, they tended to comprehend the different mathematical cultures that exist in the Eastern and Western worlds. However, students were unable to appreciate intuition-based inductive approaches and were less likely to acknowledge how creativity and imagination were involved in mathematical thinking.