The Incorrigible children actually were.

Turning sixteen is a bittersweet occasion for Miss Penelope Lumley: Her parents remain disappointingly absent, and her perfectly nice young playwright friend, Simon Harley-Dickinson, has not been heard from since he went to visit his ailing great-uncle Pudge in the old sailors' home in Brighton.

Luckily, an invitation to speak at the annual Celebrate Alumnae Knowledge Exposition (or CAKE) at the Swanburne Academy for Poor Bright Females provides just the diversion Penelope needs.

Optoomuchstic as ever, Penelope hopes to give her CAKE talk, see some old friends, and show off the Incorrigible children to Miss Mortimer, but instead she finds her beloved school in an uproar. And when Penelope is asked by the Swanburne Academy board of trustees to demonstrate the academic progress of her three wolfish students so the board can judge the true worth of a Swanburne education, the future of her alma mater—and of her job as governess to the Incorrigibles—hangs in the balance.