Using contextual problems to develop preservice mathematics teachers' understanding of exponential and logarithmic concepts

Understanding a mathematical concept in real-world situations is of practical importance and would be helpful to learn the concept in depth. One potential way to help students learn mathematical concepts in real-world situations would be to engage them with contextual problems. Exponential and logarithmic concepts are essential topics in higher secondary and university curricula, and most students seem to have a procedural understanding of them, and their interpretation in real-world situations has less attention. We examined preservice teachers' understanding in designing contextual problems for exponential and logarithmic statements. We conducted the study in two countries: Czech Republic and Iran. The process of this study included an initial interview, implementing a set of activities, and an exit interview. The results of the initial interview showed that the preservice teachers did not have enough understanding of exponential and logarithmic statements in real-world situations, but the class activities helped them to develop their understanding of these concepts in real-world situations. Indeed, the results of the exit interview showed that the preservice teachers came to a conceptual understanding in addition to their previous procedural understanding. We report characteristics of preservice teachers' understanding that would be productive in teaching and learning exponential and logarithmic topics through contextual problems.