Croatian math and computer science teacher Maja Cvitkovic is not
content with the same old math lessons. So when she recently had
the opportunity to use Mathematica with a group of teenage
students at a workshop in Zagreb, she devised a lesson that gave
them a chance to play. The assignment: Create a picture using
random dots. "A common calculus exercise is to present a
function and have students plot its graph," explains Cvitkovic.
"But this is too passive for me." To help students gain greater
insight into functions and their corresponding graphs, Cvitkovic
turned the traditional exercise "upside down," as she describes
it. Her students began by envisioning an image and then were
asked to find the function that would create that image when
applied to a list of random dots. After settling on and
sketching an image on paper, students identified where the
points required to create that image would be more dense and
where they would be more sparse. The next step is where
experimentation began: Using what they a