About the Notion of Inverse Problem in STEM Education

Abstract

Inverse problems play an important role in STEM disciplines; although this concept is not well-defined in STEM education. For instance, Mason considers inversion as ‘undoing’, whereas Keller observes that if two problems are inverses of one another, then one of them has been studied extensively, while the other is newer and the former is called ‘direct’, while the latter is called ‘inverse’. Groetsch observes that if y is the effect of a given cause x when a mathematical model K is posited (Kx=y), then, two inverse problems arise: causation (given K and y, determine x) and model identification or specification (given x and y, determine K). This last view is an adaptation of the IPO-model, taught in Computer Science. During the last 5 years, we designed and put in practice and experience based-on inverse problems and their utilization in teachers training courses. This area is strongly connected with active learning, since as Kaur observed, an effective mathematics instruction begins when the instructors take the role of designers with the aim of facilitate active learning activities. In this chapter, we reflect on these experiences to construct a wider theoretical framework for inverse problems in STEM education.