Active Learning and the Pythagorean Theorem Through Dynamic Geometry and Robotic Optimization

Abstract

This chapter examines the use of technology within an active learning environment. The case follows Kaitlyn, a first-year high school teacher, through a series of 3 lessons designed to develop the Pythagorean Theorem by way of an applied real-world problem involving a robotic rover. Technology is used to motivate students to want to make sense of the mathematics involved and discover patterns that they will later justify. Throughout the lessons, the students employ concepts from previous classes and integrate several mathematical ideas, including: the triangle inequality, function notation and multivariable functions, Pythagorean triples, the Pythagorean Theorem, and slope. As the lessons progresses, the reader is asked to reflect on both the mathematics and classroom practice and connect it to research on teaching and learning. The use of active learning, authenticity of tasks and questions, dynamically linked representations, and effective use of discourse routines are addressed.