The more I learn about using technology in class, the more I think that it isn’t adding technology that is important, but rather, it is changing the way I teach that is important. I am slowly realizing the need to move away from disseminating information to having students discover it. For me, the attraction of technology is that it can allow students to do this in ways that were unrealistic 20 years ago. I think what “counts” as good use of technology is when we use it to truly create deeper learning and when it can allow students to explore and learn both independently and in groups.
For example, the environment I envision would include some structured lectures, but more group problem solving and math-speak going on in class with math writing going on outside of class (through forum discussion in an LMS or in a class blog or wiki). There is something that changes how well you understand math when you move from examples to explaining it in written words. Technology can provide a valuable venue for this kind of discussion. Technology can also provide ways for students to use trial and error in arriving at possible hypotheses more quickly than doing repeated examples by hand (for example, understanding transformations when graphing). I still feel there is a need to do work by hand and practice it, but exploration can be done more smoothly using technology. I also feel that technology can provide that just-in-time information that many students need by allowing them access to information on missing pieces as well as advanced concepts.
What I do NOT envision is classrooms where all students are working independently in isolation on computers every class, merely moving transmission of information from the teacher to the computer.
I think much of what I envision is possible in real classes but in order to allow student to learn the principles that they need to move on to higher levels of mathematics, the lessons need to have purpose and structure (guided constructivism?), as well as time for true exploration. Unfortunately, current curriculum guidelines and time constraints make it difficult to incorporate technology in ways that allows for this type of learning environment. I am currently working on baby steps as time allows.