Question 6: Should technology change the mathematical content we consider important? My general response to this question is no, but with an exception: I see technology as a tool to assist the student in either learning more math, or learning the same math more deeply. New technology should be used only when the time spent teaching the technology is adequately justified in time saved in delivery of instruction.
I see things like dynamic software as expanding both the range and depth of learning. Many students who have difficulty with geometric ideas are able to be more successful with this type of interactive technology. A student can say, "I see." and mean it very literally. I see graphing calculators in much the same way. My students see more graphs in a year than I saw in my entire HS education. I believe this increased exposure enhances their understanding of the mathematical ideas at play. On the other hand computer technology brings with it a downside that causes me some concern. I see teaching postions being lost and replaced with "educational technologists". I think that technologies that become pervasive in a society do not have to be taught; we have no classes in "cell phone", there is no "TV 102". I think teaching "computers" or "computer literacy" has little effect on the use and understanding that students have of computers .
The exceptional case, in my mind, occurs when technology changes the way a discipline is practiced, then it may need to become part of the instruction for that discipline. In mathematics this may be happening when the idea of "proof" expands to accept computer proof such as the four-color thm. If practicing users of math employ the technology, and it seems they are more and more, it may be necessary that there is some training in the technology in schools.
Pat Ballew, Misawa, Jp
"Statistics means never having to say you're certain."