By Tim Hickey, posted July 5, 2016 —

Toolbelt Theory and SAMR, two of the foundational ideas for my district’s Educational Technology Plan, will guide the integration of technology into our schools over the course of the next few years. I have worked on developing both concepts in a tangible way in my classroom recently.

Toolbelt Theory asserts that educators have a responsibility to help students develop both a “lifespan toolbelt” as well as the ability to choose tools in that toolbelt. Thus, in addition to understanding both the nature of a given task as well as the environment and skills required to accomplish that task, students must have command over a variety of technological tools and the ability to readily find and apply those tools. In my May 9, 2016 post, I describe the Coffee Cup Optimization problem that I pose each year in my calculus classes (students are required to build a 16-ounce coffee cup with a minimum surface area). The calculus solution is roughly the same for each group that approaches the problem, but the method and materials used in building the cup is left entirely up to them. I do, however, deliberately encourage students to choose a method with which they are unfamiliar. This puts them in the position of having to reflect on the state of their toolbelt, and it simultaneously provides them the opportunity to add to their toolbelt. I have had students add 3D printing, carpentry, laser cutting, and ceramic skills to their toolbelts via this project. If we as math teachers always stop at pencil-and-paper solutions, we are missing out on a meaningful opportunity to arm our students with powerful lifelong learning tools and the ability to choose the right tools for a given task.

The SAMR Model, developed by Dr. Ruben Puentedura, is a way to conceptualize teachers’ progression in integrating learning technology into our lessons to enhance student learning (i.e., not just technology for technology’s sake). The acronym stands for Substitution, Augmentation, Modification, and Redefinition. As an example, consider the topic of cross-sections on a base in calculus. In calculus, I have always asked my students to find the volume of a solid formed by building semi-elliptical cross-sections on a region enclosed by the graphs of two given curves. A mere substitution of technology would not change the teaching or learning that would have taken place in the absence of the technology. For instance, projecting this problem on a screen adds almost nothing to students’ experience. Augmentation captures some functional benefit to the addition of technology. Providing “clickers” to students to enter their answers in a way that allows a teacher to capture and analyze the class data adds some benefit, particularly for the teacher in terms of assessing understanding. Modification, however, results in a significant functional change in the classroom. Requiring students to use Desmos to model the curves in the problem, a laser cutter to engrave those curves into a piece of wood, and a 3D printer to generate some cross-sections necessitates the use of computer technology to accomplish the now-altered task of building a model. Finally, redefinition of a task fundamentally changes the role of technology from an end to a means. Here, the teacher might require students to build both the model described above in the modified task as well as a complete three-dimensional model of the solid showing an infinite number of cross-sections. The construction of the complete 3D model requires translating the calculus into code that 3D printing software can comprehend. It is a previously incomprehensible task, and the technology is the means to accomplish the task.

So, I suggest considering Toolbelt Theory and SAMR when developing lessons in your mathematics classroom. You may become a better teacher and, by the way, your students may find some joy and inspiration in the process.

  Tim Hickey is a Nationally Board Certified Teacher and the math department chair at Monticello High School in Charlottesville, Virginia.