Problem solving is considered as one of the most important topics in STEM (science, technology, engineering, and mathematics) education, and this is especially relevant when problems require modeling skills in order to be solved. Also, it should be noted that in many branches of science and technology, typical problems are posed in an inverse form. Then, combining both characteristics, the so-called inverse modeling problems deserve to be studied deeply, particularly in their potential for task enrichment. For those reasons, since 2016, a research project was carried out, by using inverse modeling problems to develop prospective teacher’s task enrichment skills. The results of this experience that took place in 2017 showed nine different groups of proposals where only few participants were very creative, whereas many others posed trivial problems or simply imitated examples analyzed previously. After that, a new research design was proposed during 2018 and implemented during the first months of 2019, with the aim of avoiding—or at least attenuating—those difficulties observed in the previous fieldwork. The new results showed interesting differences and few similarities when compared with the other experience. In this chapter, both experiences are analyzed, and lastly, findings and final conclusions are reported.
Part of the book: Theorizing STEM Education in the 21st Century
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.