Optical illusion designers take their awareness of the way the mind works and design their illusions to take advantage of these processes. One example is the popular illusion of a white figure on a black background. The viewer is asked what he sees -- some answer a vase, and some answer two faces. Both answers are technically correct as the white figure looks both like a vase and like the space between two dark faces.
Many math classes, particularly geometry and trigonometry, require the memorization of many different shapes and formulas, without very much connection between these terms and reality. Often it's too late when students realize that knowing trigonometry will help them cut out circular windows as a construction carpenter, for example. Optical illusions help students visualize how these seemingly abstract terms will help them succeed in future careers.
Optical illusions often contain riddles that students must use critical thinking skills to solve. Deciding how many squares are present in a complicated diagram would be one example of these as students have to remember the definition of a square and look beyond the normal parameters to find the answer.
Math can be a mystifying topic for many students. Coming into a classroom at the beginning of an instructional period and finding a set of problems on the board is not nearly as much fun as finding an optical illusion up on the projector screen with a question to answer. Engaging students with optical illusions can secure their interest for an entire class period, which will increase the effectiveness of your instruction.