Insides, Outsides, Loops, Lines

Spatial relationships are very close to the first intelligent concepts that infants grasp. To explore the world we need to recognize locations and faces. Some of the first formal mathematics learned deals with the recognition of shapes such as circles and triangles. While numbers are learned and then abstracted to do arithmetic, the generalization of shapes is almost always left out. Which is unfortunate because the modification of shapes into new forms is the foundation of much of our lives. For is the recognition of faces not the classification of a small subset of basic shapes into an infinite set of possibilities? The abstraction of shapes into topologically equivalent sets has been sadly neglected in education and this book is an important part of the cure. Children love to explore their world, taking the familiar and extending it into the unknown, developing new ideas about physical relationships that can be used in many areas. This book, containing no arithmetic problems, takes that approach and manages to teach an enormous amount of mathematics. The basic ideas of inside and outside a curve are explored in ways that forces the reader to grasp that the content is simple, but complex in the ways it can be used. The Mobius strip, which shows that objects can have only one side, forces thinking at a level that is simple while also profound. Recognizing the distortion of one object into another can also have fundamental benefits in many areas. As someone who has struggled with Chinese ideograms, I am convinced that the skills taught in this book will help open up another avenue for children. It would be very interesting to determine if children brought up writing in pictures are better at topological abstractions than those who have not. Learning mathematics can be fun if properly presented. This book truly earns the highest of possible praises: "It helps to make learning fun." It belongs in school libraries at every level. Published in Journal of Recreational Mathematics, reprinted with permission.

I gave it as a gift to my 10 yr old neice to try to expose her to another aspect of mathematics where it deals with shapes rather than numbers. She loved it and couldn't stop working on the "problems". I spent more money on the tracing paper than the book because she didn't want to mark-up the book in case she wanted to share it with her classmates.