| Table of Contents | Sample Puzzles |
One way to do this is to provide effective practice in the application of concepts, strategies, and procedures. Students must be challenged again and again to use mathematical ideas. We want students to use them in investigations, open-ended questions, creative projects, and nonroutine problems. But success with such tasks often requires time spent on more structured practice, working exercises carefully designed to teach specific ideas. Students construct meaning as they work through them, and retention is enhanced. Certain features are designed into Punchline puzzles to make this practice more effective.
KNOWLEDGE OF RESULTS. Students appreciate feedback and confirmation when they work, especially when learning new skills. Built into these puzzles are various devices for giving the student immediate feedback as exercises are completed. For example, if an answer is not in the scrambled answer list or code, the student knows it is incorrect. (S)he can try again or ask for help. Teachers are able to spend more time helping students who need help and less time confirming correct answers. Students work with greater confidence.
OPPORTUNITIES FOR COOPERATIVE LEARNING. For most topics in this book, there is a set of puzzles for cooperative groups of 2 or 4 students. Each student does essentially the same exercises but with different numbers. The process is the same but the answers are different. Each student gets part of the punchline, so that all parts must be done for a complete solution. Students are encouraged to help each other, since the numbers are different. There is interdependence combined with individual accountability, the twin hallmarks of effective cooperative learning. Together they produce an additional source of student motivation.
Punchline Problem Solving includes puzzles for most topics in today's middle school math programs. They are organized into 14 sections that correspond to chapters in many textbooks. Twenty-two of the puzzles are for cooperative groups of either 2 or 4 students. Each puzzle is designed for a specific topic listed in the Table of Contents and on the puzzle itself. Many puzzles provide space for student work. And, hopefully, their self-correcting feature will lighten the burden of correcting assignments.