Using learning progression-based interactive dynamic geometry instruction to develop quadrilateral reasoning in preservice teachers

Abstract

This study investigated the learning of K–8 preservice teachers (PTs) while enrolled in an in-person class that was integrated with an online, individualized, and interactive Dynamic Geometry curriculum (iDGi), built from empirically derived learning progressions (LP). The research examined PTs’ developing understanding of the prototypical defining properties of quadrilaterals—formal geometric attributes that align with the visually salient features students often use when identifying and reasoning about quadrilateral types and their relationships. It also explored how the curriculum supported PTs’ transition toward more precise and abstract forms of reasoning. The curriculum’s effectiveness was evaluated with 541 PTs across multiple courses, all of whom completed identical online multiple-choice LP-based assessments before and after engaging with iDGi. Findings indicated that iDGi significantly improved PTs’ reasoning about quadrilaterals. Analyses of three whole-class discussions illustrated how related in-class activities complemented and deepened PTs’ conceptual understanding.