Funville is a math-inspired fantasy adventure by A.O. Fradkin and A.B. Bishop, where functions come to life as magical beings. After 9-year old Emmy and her 5-year old brother Leo go down an abandoned dilapidated slide, they are magically transported into Funville: a land inhabited by ordinary looking beings, each with a unique power to transform objects.
The siblings discover that Funville is full of surprises; one never knows when something will be shrunk, flipped upside down, turned into an elephant, or erased! As Emmy and Leo explore this exciting new world, befriending many Funvillians along the way, they discover that despite being able to do some very impressive tricks with their powers, Funvillians often get stumped by situations requiring more than just the straightforward use of a single power. Emmy and Leo think outside the box to solve problems by using combining multiple powers, as well as using ideas that do not involve powers.
While on the surface, Funville Adventures is just a fairy tale, the powers of the Funvillians are a vehicle for introducing children to the concept of a function. Each power corresponds to a transformation such as doubling in size, rotating, copying, or changing color. There is even a Funvillian whose power is to change other Funvillians' powers. Some Funvillians have siblings with opposite powers that can reverse the effects and return an object to its original state, but other powers cannot be reversed. In this way, we introduce kids to the mathematical concepts of invertible and non-invertible functions, domains, ranges, and functionals without mathematical terminology.
The concept of a function is truly fundamental, and accessible to children from a young age. It is unfortunate that for many of them, their first encounter with it is in high school or late middle school, often in a dry, technical manner. We present this material in a form that will appeal not only to kids already interested in math, but also to who are missing out on mathematical adventures.