Students in College Algebra at Minnesota School of Business-Blaine are using an iPad app to enhance visualization of math formulas.
“Teaching students how to translate and rotate graphs, even two-dimensional ones like parabolas, is greatly enhanced if the students can visualize the graphs,” John Daley, information technology program chair, said. “You can teach students how to translate a graph, for example, but it’s much more effective if they can visualize what’s happening in real time.”
“The Desmos calculator really helps in College Algebra I,” Chiyou Moua, information technology program student, said. “It’s one thing to try and learn how the coefficients and constants affect the graph of a parabola, but seeing it on the iPad and being able to move it around easily really helps.”
After searching for a simple, effective, free graphing calculator for quite some time, Daley is using the Desmos graphing calculator on iPad to demonstrate translations of graphs.
“The Desmos app is very user-friendly, with an intuitive, effective user interface,” Daley says. “Simply typing in “y = x” immediately results in the drawing of the linear equation y = x, and then selected key for squaring transforms the graph into the associated parabola.”
“I love being able to manipulate the graph directly,” Kale Cooper, veterinary technology program student, commented. “Being able to work interactively on the iPad with an equation’s graph is way better than just using a textbook.”
Adding constants both inside and outside the parentheses of an equation like the standard form for a parabola demonstrate how such manipulations move the parabola left and right and up and down.
“Visual learners love it,” Daley asserts. “It takes an abstract concept and makes it real, right on their iPad.” Daley went on to say that showing students how graphs can be manipulated on the iPad “de-mystifies” math concepts once thought to be hard, and simplifies the learning process.
Daley added that he plans to use the graphing calculator in Introduction to Decision Systems, which he is also teaching this quarter.