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:
We’re working hard to create the sketches, worksheets, and support materials for these Web Sketchpad activities. Ours is a volunteer effort on the part of everyone involved, both curriculum developers and field testers, and we make these activities freely available for you to download and use with your own students.
As we develop, revise and expand the activities, we need your help. Email your commentary (What worked well? What didn’t?) and your suggested improvements to the webmaster.
Enacting Functions from Geometry to Calculus to the Complex Plane
Mathematics Dept. Colloquium at Texas State University (21 October 2016)
In this colloquium Scott Steketee presented an innovative technology-enabled enactivist approach to teaching function concepts. Based on Web Sketchpad and initially developed for secondary students, this visual sensorimotor approach can be extended to more advanced courses, providing students opportunities to enact differentiation, integration, vector operations, operations on complex numbers, and even to build a visual demonstration to determine the value of `e^(i theta)`. In today’s environment college courses increasingly expect students to be active learners, rendering activities such as these particularly useful. Accordingly, the colloquium actively involved participants in creating and manipulating mathematical objects by passing a Bluetooth mouse.
We use the online paper from ICME-13. Each figure in the paper is a fully functional websketch that we used to create and explore mathematical objects, but if you’re reading this online you will likely find it simpler to use the links to access each illustration as a complete activity with a student worksheet and hint videos.
We paused for small-group discussion and rumination about this approach to introducing functions geometrically and then connecting them to algebra: the mathematics, the pedagogy, the technology.
Several small groups reported some item from their discussion back to everyone.Part 3: On to Calculus and the Complex Plane
We were a bit rushed here to stay within our allotted time, so we explored only two of the planned four activities below.
[Note: as of this writing, these activities are in draft form. None of them has a worksheet yet, and most don't yet have hint videos.
We concluded with an opportunity for general discussion, questions, suggestions, and so forth.Requirements