Facilitating the development of Preservice teachers' proportional reasoning in geometric similarity problems using augmented reality activities

摘要

The literature reports preservice teachers' overuse of proportionality when solving geometric similarity problems with nonproportional relationships. Changing this type of error is reported as difficult even after applying certain interventions. As a solution to this type of error, this study used augmented reality activities to facilitate the development of preservice mathematics teachers' proportional reasoning. The data of this qualitative study included 17 preservice teachers' written responses to a paper-and-pencil test with five problems, which had been applied before and after the implementation of the augment reality activities, and video recordings collected during the augment reality implementation process. A case study methodology was used in designing the study in which the collected data were analyzed using a content analysis method. The preservice teachers' first test responses showed that although they were good at solving problems with regular figures, they had difficulty solving the problem with irregular figures. In this specific problem, the preservice teachers expected a proportional relationship between the areas of the two irregular figures. Their difficulties appeared to be a result of not being able to calculate the areas of these two figures by tiling or multiplying length and width that they used for regular figures. After the implementation of the augmented reality activities, which provided a dynamic representation of similar figures, the preservice teachers' overuse of proportionality drastically decreased. This finding suggested the contribution of the augmented reality technology on the development of the preservice teachers' proportional reasoning.