Visualizing Gradient with Surfaces

Highlights of the activity

1. This small group activity is designed to provide students with a geometric understanding of gradient.
2. Students are asked to find the direction and relative magnitude of the gradient at various points on a plastic surface.
3. The wrap-up discussion focuses on comparing the gradient for different scalar fields and addresses the idea that the gradient doesn’t point toward the ‘top of the hill’ but rather, locally, in the direction of greatest rate of change; that the gradient is always perpendicular to the level curves/surfaces. The dimensionality of the gradient is also discussed.

Reasons to spend class time on the activity

This activity helps students build a geometric understanding of the gradient.

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version