An example: gradient of the tangent to a curve at a point
This is an example that shows how the gradient of the tangent to a curve at a point varies with the point. The app is so quick and easy to use that this took me 17 seconds to create (I timed myself!).
Use of smartphones in classroomsThis app presents a fantastic opportunity to put dynamic maths software into the hands of students. As I've commented on before, I think the real benefits of technology come when students are using it. In addition to this there are significant advantages when this is on a device that students have an attachment to and feel ownership of. Most people feel their own phone is a device that is very personal to them and this means students are more likely to be well-disposed to software on it.
Having GeoGebra on their phones means that students can harness the power of the software wherever they are: at home, on the bus, ... However, many teachers have reservations about students using phones in class. There are concerns that this presents a major classroom management issue. This is an ongoing debate and there is some evidence that banning phones in schools has a positive impact on achievement: http://www.theguardian.com/education/2015/may/16/schools-mobile-phones-academic-results. A lot of these arguments focus on general mobile phone use in class and it would be interesting to see some experiences based on students using subject-specific apps such as GeoGebra with effective tasks designed to improve their understanding using the software.