Teachable Moments
This page presents several 'teachable moments,' interactive environments with which students can explore ideas in mathematics and science. I plan to add suggestions for experiments and challenges, and perhaps some self-assessment questions.
ChanceLab
ChanceLab provides an interactive laboratory in which students can experiment with coins, spinners and dice to see results for any number of trials, including large numbers (1000 or greater). Results are listed numerically and can be viewed as a bar or pie chart. By accumulating trials, for example, it's easy to discover that the probabilities of outcomes approach the theoretical probabilities for large numbers of trials. It's also easy to discover that even a large discrepancy does not necessarily imply that the next trial will decrease it (e.g., a record of 10 heads and 4 tails doesn't imply the next trial will be a tail).
ChanceLab provides an interactive laboratory in which students can experiment with coins, spinners and dice to see results for any number of trials, including large numbers (1000 or greater). Results are listed numerically and can be viewed as a bar or pie chart. By accumulating trials, for example, it's easy to discover that the probabilities of outcomes approach the theoretical probabilities for large numbers of trials. It's also easy to discover that even a large discrepancy does not necessarily imply that the next trial will decrease it (e.g., a record of 10 heads and 4 tails doesn't imply the next trial will be a tail).
ImpulseLab
ImpulseLab provides an interactive space for exploring the effect of impulse forces (or 'kicks') on an object. Kicks can be applied toward the left, right, up or down and the space-walking astronaut moves in response, just as it would using jets of gas in orbit. The astronaut's path is traced as it moves, and its velocity can be shown by an arrow. Students can observe how an impulse force changes velocity in the direction of the impulse, not position. Constant forces (e.g., gravity) can be approximated by a continuous set of kicks, allowing such motions as the flight of a projectile to be explored.
ImpulseLab provides an interactive space for exploring the effect of impulse forces (or 'kicks') on an object. Kicks can be applied toward the left, right, up or down and the space-walking astronaut moves in response, just as it would using jets of gas in orbit. The astronaut's path is traced as it moves, and its velocity can be shown by an arrow. Students can observe how an impulse force changes velocity in the direction of the impulse, not position. Constant forces (e.g., gravity) can be approximated by a continuous set of kicks, allowing such motions as the flight of a projectile to be explored.
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