Mathematics and science can be thought of as a search for patterns and structure. Discovery and insight comes when patterns are recognized and structure is understood. From a developmental perspective, the ability to recognize a pattern signals the transition from concrete to abstract thinking. So having students explore pattern problems helps sensitize them to the discovery process that provides a foundation for authentic learning and abstraction. These books provide rich and diverse collections of pattern problems for students to explore, investigate, discover, and create. The five types of pattern problems found in these books are:
- Pattern Predictor
- Equality Explorer
- Sequence Sleuth
- Number Ninja
- Function Finder
There are eight pages of each puzzle type, along with optional hints, and detailed solutions totaling 96 pages in each book.
The activities are independent and self-contained, but tend to build on one another and get gradually more sophisticated. This collection deliberately avoids use of variables, but the activities involve reasoning that lays a genuine foundation for algebraic thinking and technique. Calculators are never needed, and their use is discouraged.
Parents and teachers should encourage students to pursue these pattern problems with a sense of adventure and perseverance. There are many ways to solve and explain a pattern problem, and the solutions provided are not intended to be unique. In all situations, and at whatever pace and facility, the transition from concrete to abstract thinking is worthwhile.
All activities provide space for work to be shown, but students are encouraged to have scratch paper at hand in case uncovering a pattern merits deeper investigation, such as guess-and check, drawing diagrams, and making lists or charts.