I'm following this discussion on whether using technology could possibly be conveyed as cheating. I have a dishwasher, a car, and a vaccuum cleaner. I know that the dishwasher is best used for cleaning eating utensils and the vaccuum for cleaning the floor. As long as I don't confuse these roles and try to use the dishwasher for cleaning the floor, I feel as if I have a sufficient handle on the technology. I do NOT need to know HOW the dishwasher works..beyond what buttons to push to set it into motion for it to be effective. I think there is an analogy to technology here.>I'm satisfied if students know that the quadratic formula is a way to generalize the solution to where a quadratic function crosses the x-axis and to know when they might want to know where the function crosses the x-axis. It's fine with me if they want to program the quadratic function into their TI-82. In fact, I'll even use the linking cord and transmit the program on my TI-82 to their TI-82. I don't think that students have to demonstrate that they can derive the quadractic function from ax^2 + bx + c = 0 in order to be able to use it anymore than I think consumers have to prove that they know the mechanics behind a dishwasher before they are allowed to operate it to wash their dishes. I do expect consumers to be responsible and recognize that using a dishwasher to wash one glass at a time is not energy efficient. Likewise, I expect students to recognize that using the TI-82 quadratic formula to solve x^2 = 25 is not efficient.
-- Linda Dodge Math Consultant Frontier Regional High School South Deerfield, MA