In this paper, the Singapore school calculus curriculum at the upper secondary and the pre-university levels is examined in the light of the Singapore mathematics curriculum framework. Three key features of the calculus content are discerned: (1) an intuitive approach to calculus supported by the use of technology; (2) an emphasis on techniques; and (3) an emphasis on procedural over conceptual knowledge. Following that analysis, a review of the performance of a group of pre-university students on selected calculus tasks in a calculus survey prior to and after their learning of pre-university calculus is discussed. The students’ performance in the survey shows that many students did not visually identify calculus concepts that were studied procedurally. They demonstrated a lack of conceptual understanding of the calculus procedures. This study suggests that the partial calculus knowledge acquired in the early upper secondary levels might not necessarily facilitate the acquisition of a more complete concept at the pre-university level. Furthermore, the students’ procedural knowledge of calculus did not seem to develop their procedural fluency or flexibility.

本文根据新加坡数学课程框架对高中和大学预科课程中的新加坡学校微积分课程进行了研究。演算内容的三个关键特征被识别出来：（1）使用技术支持的演算的直观方法；（2）注重技术；（3）强调程序知识而非概念知识。经过分析之后，我们讨论了一组大学预科学生在学习大学前微积分之前和之后进行的一次微积分调查中对选定的微积分任务的表现的评论。学生在调查中的表现表明，许多学生没有从视觉上识别经过程序研究的微积分概念。他们表现出对微积分程序缺乏概念上的理解。这项研究表明，在高中早期阶段获得的部分演算知识可能不一定有助于在大学前阶段获得更完整的概念。此外，学生对微积分的程序知识似乎并未发展其程序流畅性或灵活性。