# Working with Concept-Based Curricula for Mathematics

**Chee Wee Tan**

**Objective**

The purpose of this chapter aims to address some of the challenges of delivering a concept-based curriculum in a typical mathematics classroom in a secondary school in Singapore, as well as documenting some of the teaching strategies that educators can use to promote conceptual understanding in students.

## Background

The definition of mathematics as a discipline has changed and evolved over time. One that has stood for centuries was by Greek mathematician and philosopher Aristotle, who defined mathematics as the science of quantity. Indeed, early works in the discipline had been focused in counting (arithmetic) and measurement (geometry) and were widely used in fields such as construction and navigation in ancient times.

It was not until the nineteenth century that new abstract areas of mathematics were studied, such as analysis (calculus), non-Euclidean geometry and set theory (logic). Subsequently, the definition of mathematics varied from one scholar to another in varying perspectives. For example, Russell (1903) claimed that mathematics was, essentially, symbolic logic. However, not all share the same view. Sawyer (1955), for example, focused on observations of patterns and structure, and he defined the discipline as the classification and study of all possible patterns.

C.W. Tan (*)

Hwa Chong Institution, Singapore, Singapore e-mail: This email address is being protected from spam bots, you need Javascript enabled to view it

© Springer Nature Singapore Pte Ltd. 2017

L.S. Tan et al. (eds.), *Curriculum for High Ability Learners,* Education Innovation Series, DOI 10.1007/978-981-10-2697-3_12