At El Sol Academy, a charter school in Santa Ana, the 4-year-olds are working hard at learning – by playing computer games. At one computer, a girl tries to match up the numeral 3 with four trees.

California’s hottest new math teacher is an animated penguin named JiJi. Yes, it’s true. A mute, waddling, tuxedo-clad cartoon figure has been quietly taking over math programs dotting Silicon Valley, ...