So, beginning last September, every student in my classes had a tablet. The ratio of iPads to other tablets was about 12:1. Due to the nature of the courses I taught in the fall, we seemed to gravitate to Desmos as our App of choice. While I prepared some demonstrations using Desmos, what the students produced on their own was far more impressive. Using an Apple TV and projector, students were eager to display what they had produced.
Here's an example: in Mathematics 431, the third term of an accelerated/honor calculus class, we consider circles of curvature for various curves. We begin with finding the center and radius of the circle of curvature for y = cos (x) at x = 0. Eventually, students are asked to find the center and radius of the circle of curvature for y = kx^2. Here is what one student produced (to see the list of commands, click the link):
There was no question that being able to visualize these problems helped students to understand the concepts better than simply doing them paper and pencil. Using sliders and being able to dynamically change the position of the point where the tangent, and therefore the normal, intersects the graph is a powerful way for students to understand the process.
In the winter term, I taught Mathematics 220 which is essentially a geometry course which meant the emphasis was on GeoGebra. I was fortunate to have a student with lots of experience in using GeoGebra and she became the tutor for others in the course. Once again, students were happy to share what they had done on their homework via the Apple TV. We used version 5 of GeoGebra and so had the ability to work in three dimensions.
The experience of this academic year has made me no less a fan of using technology in my teaching. In fact, I'm more enthusiastic than ever. However, because we don't have a strong, school-wide policy regarding the use of tablets - teachers were told they didn't have to use them in their classes - there are some difficulties to overcome. This spring, on the first day of class in Mathematics 330, a course I taught in the fall and one in which we made great use of Desmos, I told the students that we would be using this App as well as GeoGebra, possibly. When I asked if they had experience using these Apps, all but one student raised a hand. I was mystified that a student could have actually gone through two terms of mathematics this year and not used Desmos. Sigh. But, fortunately because Desmos is so easy to master, it has not been a problem.
While I have been referring to Desmos and GeoGebra as Apps, in fact I use the web versions of both. This means I, and my students, can create a free account and save graphs and constructions. In Desmos, I have the ability to print, share, and embed graphs (that's how I created the link above). Recently, Desmos has produced a Test Mode version.