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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The Dynamic Number NSF Project developed 12 Geometric Functions activities designed to help students learn about functions and geometric transformations through direct experiences constructing and manipulating them. (See the four Foundations pages for the mathematical, cognitive science, technology, and pedagogical foundations of this approach.)
All of the activities listed below reside on the Dynamic Number website, and include a student sketch, a student worksheet, and extensive teacher notes. These activities require The Geometer's Sketchpad.
Many of these activities are also available in Web Sketchpad format in the Introducing Transformations unit and the Cartesian Connection unit. Web Sketchpad activities can be used with any modern browser, with no need for students to have access to Sketchpad itself.
Introducing Functions Activities
These activities introduce the function concept and the idea of distinguishing function families based on their behavioral characteristics.
Function Families Activities
These activities acquaint students with the four main geometric function families. They construct and then manipulate members of each family, describe them using function notation, identify the function behavior (particularly relative rate of change) that distinguishes one family from another, and solve interesting challenges related to each of the families.
In these activities students construct two different functions, combine them, and explore the behavior of the resulting composed function.
In these activities students create interesting original functions and explore how their new functions transform an entire input domain (in the form of a picture) into an output range.