The quality of prospective mathematics teachers' dynamic geometry tasks in terms of the coordination between mathematical depth levels and technological actions

Abstract

Background: Teachers must have the skills to find, select, design and use technology-based mathematical activities that focus on high-level cognitive demands—supportingstudent reasoning. However, they experience various difficulties in creating, planningand making decisions about how and when to utilize technological affordances.Objectives: This study aims to examine the quality of prospective school mathemat-ics teachers' (PMTs) tasks containing the use of dynamic geometry software throughthe analysis of the coordination between mathematical depth levels (MDLs) and tech-nological actions (TAs), according to Trocki and Hollebrands', Digital Experiences inMathematics Education, 2018, 4, 110–138, Dynamic Geometry Task AnalysisFramework.Methods: Within groups, PMTs designed lesson plans that included dynamic geome-try tasks (DGTs) based on the learning outcomes of the middle school mathematicscurriculum. They then created micro-teachings of these tasks. The participants' DGTsand transcripts of their microteaching videos were the main data sources.Results: We found that many prompts included no TA or a single TA, regardless ofthe prompts' MDLs. Moreover, the results showed that the high-depth promptsaimed to contribute to students' reasoning processes on geometric concepts throughthe TAs, which required specific tools such as dragging and sliding to get generaliza-tions. Although the groups differed in the quality and number of DGTs, the groups'lesson plans mostly contained low- or medium-quality DGTs regarding the coordina-tion between MDLs and TAs.Conclusions: Informing PMTs about high-quality technology tasks and increasingtheir awareness on this matter is a priority to encourage them to incorporate innova-tive technological activities in their mathematics instruction.