의사 인지 이론 관점에서 본 2015 개정 고등학교 수학에서 대학 수학으로의 정적분 담론의 이행

Abstract

According to the 2015 national curriculum revision, the high school mathematics 2 textbook introduces the definite integral as the difference of the anti-derivatives at the endpoints. However, because most calculus and elementary analysis textbooks at the university level define definite integral as the limit of Riemann sums, students who learned mathematics according to 2015 curriculum revision in high school are forced to use the word “definite integral” differently in university. Sfard views mathematics as a discourse, and she explains the historical development of mathematics and mathematics learning as the change of discourse in the participationist’s perspective. This article looks at the transition problem of the definite integral from school and university in the commognitive framework of Sfard. The comparative analysis of high school and university mathematics discourse about definite integral demonstrates that the two discourses are incommensurable not only in the different word use of definite integral but also the different meta-rule of using definitions and proving. Furthermore, the historical analysis shows that this meta-level change in the transition can be traced to the mathematical revolution from 18th result-oriented calculus to 19th rigorous calculus based on precise definitions and proof. This analysis helps instructors to understand the nature and meaning of the challenges of students in the transition of definite integral between school and university mathematics, to be aware of the commognitive conflict in the communication with students about definite integral, and to design a lesson that helps student change their discourse. The commognitive perspective can contribute to instructors seeing the didactical possibilities in the transition and improve their teaching approach.