Linear Change is usually what you want; that's a lesson Andrea A. diSessa (2000) learned from electronics. "In some circumstances, however, you may learn in equally dramatic fashion that you don't want linear change. You can buy volume controls with linear or nonlinear behaviors. I assumed, naturally, that linear was the correct choice and that nonlinear controls were reserved for some esoteric purpose I couldn't imagine. I was spectacularly wrong. Adjusting the linear volume control on an amplifier produced a strange phenomenon." (p. 74–75)
"The sound level seemed to leap up, and then the second half of the control barely seemed to do anything at all. Why? Because your ears hear sound based on ratios, not on repeating a constant change (linearity). A sound gets louder by the same amount if its amplitude (e.g., the voltage from an amplifier) increases by the same *factor*, not by the same *amout*. You want a control that goes 2, 4, 8, 16, 32, …; you don't want the 'usual' linear pattern that goes 2, 4, 6, 8, 10, …. Comparing these two number sequences, you can see that the linear pattern starts out close to matching the nonlinear pattern, but then it falls well short, corresponding to my volume control that 'stopped working' halfway up." (p. 75)
Next: Patterns of Change
DISESSA, Andrea A, 2000. Changing minds: computers, learning, and literacy. . Cambridge, Mass.: MIT Press. ISBN 978-0-262-04180-5.
> “While written at a level that anyone with a good acquaintance with high school science can understand, the book reflects the depth and breadth of the issues surrounding technology in education. Rejecting the simplistic notion that the computer is merely a tool for more efficient instruction, diSessa shows how computers can be the basis for a new literacy that will change how people think and learn. He discusses the learning theory that explains why computers can be such powerful catalysts for change in education, in particular, how intuitive knowledge is the platform on which students build scientific understanding. He also discusses the material and social reasons for the computer’s potential and argues for ‘two-way literacies,’ where everyone is a creator as well as consumer of dynamic and interactive expressive forms. DiSessa gives many examples from his work using the Boxer computer environment, an integrated software system designed to investigate computational literacies.”--Jacket.