Leading Productive Discussions with Web-Based Dynamic Geometry Tools (LEAD DG) > Module 1
LEAD DG Module 1 – Introduction to DGEs & Tools
In this module, teachers explore the perpendicular bisector using physical tools, Desmos, GeoGebra, and Web Sketchpad to examine how different tools shape mathematical exploration and reasoning. Through these experiences, teachers consider how technology can support geometric understanding and learn to align learning goals, tasks, and tools to support meaningful mathematical learning.
Module Elements
| 1.1 Physical Tools: Construction & Goals Teachers explore the perpendicular bisector using paper folding, a compass and straightedge, and a mira to investigate its role as a construction, a locus of points, and a line of symmetry. This section highlights how physical tools support different kinds of geometric reasoning and introduces the relationship between tool choice and instructional goals. | |
| 1.2 Desmos: Testing & Constructing Teachers use Desmos Geometry to construct perpendicular bisectors and investigate the idea of equidistance through dynamic exploration. The focus is on using technology to make conjectures, test ideas, and reason about geometric relationships. | |
| 1.3 GeoGebra: Construction, Invariance, & Why it Holds Teachers investigate multiple ways to construct a perpendicular bisector in GeoGebra while examining how different construction methods emphasize different mathematical ideas. This section focuses on invariance under dragging and selecting construction approaches that best align with the intended learning goal. | |
| 1.4 Web Sketchpad: Constraint as a Pedagogical Decision Teachers use Web Sketchpad to compare constructions completed with different sets of available tools and experience how restricting tool access can shape mathematical thinking. This section explores how author-controlled tool libraries can be used as intentional pedagogical decisions to support specific learning goals. | |
| 1.5 Evaluating Alignment: Does this task, with this tool, serve the goal? Teachers analyze how learning goals, task design, and dynamic geometry environments work together to influence students’ mathematical thinking. This section introduces a process for evaluating whether a technology tool is being used with pedagogical, mathematical, and cognitive fidelity to support the intended learning goal. |
