LEAD DG Module 1 – Introduction to DGEs and Exploring Triangles

In this module, teachers explore key triangle concepts and constructions using dynamic geometry environments while examining how technology can support meaningful mathematical reasoning. The module emphasizes developing clear instructional goals, selecting cognitively demanding tasks, and anticipating student thinking to lay the foundation for teaching geometry with technology.

Module Elements


1.1 Exploring Triangles and Developing Instructional Goals Teachers explore a task in GeoGebra to deepen their understanding of the conditions needed to have a triangle while examining how technology can help develop this idea. They also focus on crafting clear instructional goals that meaningfully connect content, technology, and student reasoning.	Class Slides Student Handout

1.2 Introduction to DGEs and Constructing Triangles Teachers construct isosceles, equilateral, and right triangles using GeoGebra, WebSketchpad, and Desmos Geometry, comparing how different tools support geometric constructions. This section emphasizes understanding how dynamic features such as construction and dragging influence reasoning, not just accuracy.	Class Slides Student Handout

1.3 Cognitive Demand and Selecting Technology-Based Tasks Using GeoGebra tasks focused on various triangle concepts, teachers analyze and compare technology-based tasks for cognitive demand and goal alignment. They critique and refine tasks, including AI-generated tasks, to ensure technology promotes deep reasoning rather than procedural use.	Class Slides Student Handout

1.4 Anticipating Student Thinking Teachers are introduced to anticipating students’ thinking as they consider ways students might determine the area of a triangle. They also watch a video where a teacher shares about engaging in the practice of anticipating and how important it is to consider possible strategies, misconceptions, and opportunities for generalization while preparing for instruction.	Class Slides Student Handout