High School Calculus in Focus: A Comparative Study of the Intended Curricula of Select Countries

Abstract

While many countries are integrating calculus into their high school curricula, there is limited research on how these curricula differ among nations with varying levels of mathematical achievement. To address this gap, this study compared the intended high school calculus curriculum of four countries: the Philippines, South Africa, New Zealand, and Ireland. Through curriculum mapping, the research identified similarities and differences in topic coverage and learning progression across these curricula. The results revealed that the Philippines and New Zealand’s Level 8 achievement standards covered the most topics, while South Africa and Ireland’s ordinary level curriculum covered the fewest. The Philippines, New Zealand’s Level 8 achievement standards and Ireland’s higher level curriculum were well-aligned, rigorously covering derivatives and integrals of both algebraic and transcendental functions. In contrast, South Africa, New Zealand’s level 7 achievement standards, and Ireland’s ordinary level curriculum focused more narrowly on
algebraic functions. Notably, none of the countries defined limits using the ε-δ definition, and only the Philippines formally defined the definite integral. Structurally, only the Philippines treated calculus as a separate subject, while New Zealand adopted a unique spiral approach to teaching calculus topics. These findings suggest the need for further investigation into how these curriculum differences impact students’ understanding of calculus.