You may want to check-out the first-ever book about the use of GeoGebra on the teaching and learning of mathematics: Model-Centered Learning: Pathways to Mathematical Understanding Using GeoGebra by Ligguo Bu and Robert Schoen.

Supported by new developments in model-centered learning and instruction, the chapters in this book move beyond the traditional views of mathematics and mathematics teaching, providing theoretical perspectives and examples of practice for enhancing students’ mathematical understanding through mathematical and didactical modeling.

Designed specifically for teaching mathematics, GeoGebra integrates dynamic multiple representations in a conceptually rich learning environment that supports the exploration, construction, and evaluation of mathematical models and simulations. The open source nature of GeoGebra has led to a growing international community of mathematicians, teacher educators, and classroom teachers who seek to tackle the challenges and complexity of mathematics education through a grassroots initiative using instructional innovations.

The chapters cover six themes: 1) the history, philosophy, and theory behind GeoGebra, 2) dynamic models and simulations, 3) problem solving and attitude change, 4) GeoGebra as a cognitive and didactical tool, 5) curricular challenges and initiatives, 6) equity and sustainability in technology use. This book should be of interest to mathematics educators, mathematicians, and graduate students in STEM education and instructional technologies.

STEM – Science, Technology, Engineering, Mathematics

Wikipedia on model-centered instruction:

The model-centered instruction was developed by Andre Gibbons. It is based on the assumption that the purpose of instruction is to help learners construct knowledge about objects and events in their environment. In the field of cognitive psychology, theorists assert that knowledge is represented and stored in human memory as dynamic, networked structures generally known as schema or mental models. This concept of mental models was incorporated by Gibbons into the theory of model-centered instruction. This theory is based on the assumption that learners construct mental models as they process information they have acquired through observations of or interactions with objects, events, and environments. Instructional designers can assist learners by (a) helping them focus attention on specific information about an object, event, or environment and (b) initiating events or activities designed to trigger learning processes.

I’m not sure if the book cites research cases that show how using Geogebra or interacting with applets help students build those mental models. It would be interesting if somebody will really do a study on this.

Read more about model-centered instruction.