With Technologically Embodied Geometric Functions, students develop conceptual metaphors that directly relate computer-based sensory motor experiences of abstract function concepts. This approach relies on four foundations:
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This unit provides an introduction to geometric transformations from a functions point of view.
Students construct geometric transformations that take a point in the plane as input and produce another point as output, they vary the input and observe the output, they analyze the relative movement of the two points, and they use the language of functions to describe the behavior of the point variables.
Students begin this unit by dragging points to explore how dragging one point can affect another, and then solve several puzzles, figuring out which of four transformations belongs to a different family (reflection, rotation, dilation, etc.) from the other three. In the central activities of the unit, students construct transformations from each of the families, describing their behavior in detail and solving challenges such as finding a hidden mirror or a hidden center point. The unit concludes with a series of transformation “function dances,” in which an independent point follows a defined domain (such as a polygon) and the student drags another point, trying to match the motion of the transformed image point.
In the course of the unit, students connect transformations and function concepts. They develop a sense of points as variables, label the points using meaningful function notation, observe and describe the relative rate of change of the points, and restrict the independent variable to a geometric domain (a polygon) in order to trace the geometric range (the transformed image of the polygon).
This introductory video shows short highlights from some of this unit’s activities.
All of these activities include websketches, most have classroom-tested worksheets, and many include performance-based assessment games. None of them yet incorporate teacher-support materials, and we continue to refine the websketches, worksheets, and assessment materials as we use them with students and observe students’ successes and difficulties.
The unit includes seven activities, each requiring one or two class periods:
These activities are designed to accomplish a number of objectives. In doing them, students will:
▹︎︎ The Fine Print