How does technology change the way we teach and learn mathematics?

I don't think technology necessarily has an impact on the way we teach and learn math. There are poor ways to use technology and excellent ways.

But I can do some things more or better with technology than I can without it:

• More play (constructivism): Can play with ideas like the slope of a line, the parameter "a" in a parabola. Pencil and paper are slow. In a class period, a 7th grade student can only reasonably make about 5 graphs (and they would most likely complain about doing that many). With technology, they could make dozens and be able to see how changing parameters affects a line.
  
• More conceptual: Like bullet point #1. Students develop better intuition through play.
  
• More hands-on/real-world application: Students can easily measure real life objects and/or events through capturing video or photos and work with these real-life measurements. Data can be analyzed faster and more transparently. Example: Students can film someone on a swing (pumping at a constant rate), overlay a meter stick on say iMovie, share the movie with others, then at stations watch the movie and create a graph of height versus time. Hopefully they will see a beautiful sinusoidal curve!
  
• More organic sharing of products (of work): Kids can make final products like a voice thread or digital story and post online for kids to view and comment. There's no need for everyone to sit and listen to everyone's poster or Powerpoint presentation and then get bored after the third one.
  
• Less paper (but more energy use and toxic ewaste)