How I used Desmos to move up the levels of SAMR:
The ANCIENT method is to use graph paper to get a visual representation of a function. I used to use this method to teach the skill of graphing lines in Algebra 1. I typically do not spend too much time in my Algebra 2 class using the paper and pencil method because the goal is to understand how the transformation form (vertex form) changes the parent function. Using paper and pencil is so time consuming and I really struggle to wait for students to use it (especially when they all love to use rulers)
Substitution is to use a TI graphing calculator to speed up the process of graphing functions instead of using a paper graph. I can remember being a senior in high school and having my pre-calculus teacher required us to purchase a graphing calculator. I think it was the TI-82 and the students knew more than the teachers. It was the first time we got our hands on technology in the classroom and it actually changed how I viewed my math classes. We require Algebra 2 students to have one but with the implementation of chromebooks TI might become obsolete in our classrooms with the accessibility of free online competitors.
Augmentation is to use Desmos to increase the ability to graph multiple functions at the same time (addition of color as well). Desmos blows the TI out of the water when it comes to so many functions. Multiple graphs, accessibility, easier saving, printing, sliders, function forms (doesn’t have to be y=), etc. TI has a better battery life than my laptop but that is about all I could come up with.
Modification is to create a “picture” using multiple functions with domain/range restrictions. My students loved this project. We had great conversations about domain and range restrictions and limitations of functions. I know how uncreative the paper and pencil project would have ended up. My students weren’t afraid to try different functions and could quickly restrict the parameters without fear of “wasting time’ or paper. It also opened my eyes to the power of Desmos and I have never turned back.
Redefinition is to have a student create graph(s) and have another student try to recreate by writing the functions or using Desmos to graph the exact same picture. Also, Daily Desmos does this on a daily basis from easy to complicated so it would apply to every level of student.