Designing problems introducing the concept of numerical integration in an inquiry-based setting

Abstract

Research literature argues for the benefits of inquiry-based approaches to provide opportunities for in-depth understanding of mathematics. This paper studies the design of mathematical problems for the purpose of introducing the concept of numerical integration in an inquiry-based setting. We present a series of six developmental stages (represent, refocus, area, accumulate, approximate, and refine) indicating a natural trajectory for students to follow when inquiring on the concept of numerical integration before any formal introduction to the topic. Further, we present a sequence of three problems illustrating how the developmental stages can be applied in problem design.