**How Formal should Calculus in the School Mathematics Curriculum be:
Reflections Arising from an Error in a Calculus Examination Question**

**TOH Tin Lam*, TOH Pee Choon*, TAY Eng Guan*, TEO Kok Ming* and Henry LEE**

#### *National Institute of Education

Nanyang Technological University

Singapore

Published in The Mathematician Educator, 2023, Vol 4, No. 1, pp 66-77.

### Abstract

This paper examines the calculus curriculum in the current Singapore secondary and pre-university levels. Two concepts, (1) increasing and decreasing functions and their derivatives, and (2) the second derivative test for the nature of stationary points, are elaborated. An example of an incorrect calculus item in a national examination is brought up in relation to conditional reasoning involving calculus concepts. We reckon that the current emphasis on procedural knowledge in calculus is useful. However, we argue that formal conditional reasoning should not be introduced prematurely for school students.

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