Technology in Service of Mathematics
We live in a time when technology is rendering much of our ability to do routine, mechanical tasks unnecessary. Just as few of us need to have skill in washing dishes or walking long distances, the time has come when we do not need much skill mundane mathematical tasks such as solving simultaneous linear equations or adding four-digit numbers. To carry the metaphor further, just as the ability to wash some pots and pans will always be needed, we certainly must understand the ideas behind solving those equations, and perhaps it can be quicker at times to do it in our heads than to pull the computer out of our pockets. Nonetheless, modern instruction in mathematics should be predicated on the assumption that the students will always have computers at their fingertips.
This new situation is abhorrent to many mathematicians. We have spent so much of our lives building courses around those mechanical skills that it is difficult to change our tactics to adapt to the times. On the other hand, I believe strongly that we should embrace the new technology and build our courses around it. The point is that we never cared much whether our students could manipulate the formal expression \(2x+1=2\) to evaluate \(x\); instead we wanted them to come to this equation from a question such as: "a salad dressing recipe calls for one cup of oil and equal parts ordinary and balsamic vinegar. The recipe makes two cups. How much of each kind of vinegar is required?" We wanted them to understand that the solution to this problem is unique. The details of finding that unique solution we should be happy to leave to a machine.
This site is dedicated to discussing mathematical technology, and developing approaches to its incorporation in 21st century mathematics courses.