Technologically Embodied
Geometric Functions
About this website

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:

Use the Materials, Support the Work

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.

Geometric Functions Presentations

Functions are an essential part of mathematics curricula, yet research shows that students struggle with this topic. Students’ early experiences with geometric transformations (reflections, rotations, translations) are rarely used to develop function concepts, but provide compelling kinesthetic experiences and opportunities for explicit discourse about important function ideas. Dynamic geometry programs such as Sketchpad and Web Sketchpad enable students to transform a point, drag it as an independent variable, and explore properties of the resulting function, fulfilling CCSS-M Standard G-CO2: students should “describe transformations as functions that take points in the plane as inputs and give other points as outputs.”

Invited presentation by Scott Steketee at the Korean National University of Education 2015 Math-Education Conference

This invited presentation explores how Web Sketchpad (WSP) can be used to create effective online activities and lessons that engage students in creating and manipulating the mathematics they are learning. It features WSP's natural interface (with no menus and no extraneous tools) and includes a sample lesson involving several student tasks supported by the WSP interface. The presentation demonstrated how The Geometer's Sketchpad (GSP) serves as an authoring environment for WSP activities, allowing GSP users to specify an activity's pages and tools and easily export them to a web page.

Presentation by Daniel Scher and Scott Steketee at the 2015 Annual Meeting of the National Council of Teachers of Mathematics

How better to explore rate of change than as independent and dependent variables dancing together? We’ll vary x and y by doing both real and computer-based dances based on geometric transformations, dynagraphs, and Cartesian graphs of various functions. Bring a laptop or iPad with Sketchpad. Leave with student-ready geometry and algebra activities.

Presentation by Scott Steketee and Daniel Scher at the 2015 Annual Meeting of the National Council of Teachers of Mathematics

In grades 7–12, CCSSM expects students to understand transformations as functions. This profound link allows students to build a transformation, drag its input (a point), describe the output's behavior, restrict the domain to a number line, and voilà!—end up with a linear function and its Cartesian graph. Leave with student-ready activities for The Geometer's Sketchpad (GSP) and Web Sketchpad (WSP).

Invited presentation by Scott Steketee at the Symposium Honoring Zalman Usiskin, University of Chicago, November 2014

This invited presentation explores how the vision of Zalman Usiskin's ground-breaking Geometry: A Transformation Approach is even more compelling now than it was over 40 years ago. Students can use dynamic mathematics software to create and drag the two-dimensional variables of geometric transformations, they can compose the resulting functions, and they can restrict the variables to number lines to create linear functions and even to construct their Cartesian graphs. Given our current understanding of cognitive science and of pedagogy, it's time to bring to every student Zal's vision of connecting geometry and algebra through function concepts.

Presentation by Scott Steketee and Daniel Scher at the 2014 Annual Meeting of the National Council of Teachers of Mathematics.

Presentation by Scott Steketee at the 2013 Fall Conference of the Association of Teachers of Mathematics of Philadelphia and Vicinity.

Presentation by Scott Steketee and Daniel Scher at the 2013 Regional Meeting of the National Council of Teachers of Mathematics.

Update History:
08 September 2015: Created the page, initially including presentations dating back only to fall 2013.