| A pinwheel in a rainstorm with lightening, a fire-breathing dragon, a snowman, Mickey Mouse, Snoopy, a car, a cat, a turtle, Bugs Bunny – these are not the images of a typical precalculus class. But then, this is no ordinary math class.|
Students in Lynn Adsit’s Honors Precalculus class at Mercer Island High School were given the “Make a Face Mini Project” to apply their understanding of transformations of functions and restricted domains to create an identifiable picture on their calculator screens. Using the Nspire graphing calculator, the students calculated which functions would translate their rough hand-drawn pictures into mathematically accurate images that could be inputted into their calculators and projected on the front board for all to see. Adsit could then evaluate their understanding of transformations (vertical shifts, vertical stretches and shrinks, horizontal shifts) by how accurately they drew their pictures, incorporating as many parent functions as possible.
This all sounds rather abstract until you see the actual images. One student created a turtle, complete with crisscrossed lines across its back, “so you will know it’s a turtle and not a blob with legs,” she said. But each line on the turtle’s back corresponds with a function, which this student recorded on the side of her paper. Could you do this whole exercise with pencil and paper? “Yes” she said, “but it would be easier to cheat and write a function that may not correspond with the image. The calculator tells you right away if your function is accurate.”
According to Adsit, “I think the most challenging thing about the assignment is quantifying mathematically the hand-drawn illustrations. Students need to use all twelve identified functions at least once, so they have to think about how to incorporate those shapes into their drawings and how to adjust the parent function to become part of the drawings. Restricting the domain is part of the process, but that is how the resulting value ends up where they want it to be.”
Even though the project is challenging, these students seem to really appreciate the opportunity to apply their knowledge in a new way. “This is fun!” they said. “We enjoy using our imagination to create pictures with math.”
Who knows, some of these visual mathematicians may go on to be animators, architects, engineers, designers, or some other career we don’t know about yet. What we do know is that they are learning the building blocks for higher math in a new, different and very fun way.
|Some of the student drawings created by... math!|
|Translating hand-drawn pictures into mathematically accurate images using the Nspire graphing calculator.|
|Projecting mathematically calculated drawings onto the front board.|