|Algebra students need to master a boggling array of procedural skills. In addition, they need to deepen their understanding of underlying concepts. Perhaps the best way for them to build meaningful concepts is within the context of carefully designed problems. In the process of exploring a problem, students experience important mathematical ideas. We believe, though, that an excellent adjunct to this method is the use of carefully structured and sequenced sets of practice exercises. Students construct meaning as they work through the exercises. And some skills, we believe, must be practiced until they are automatic. Certain features are designed into Punchline puzzles to make this practice more effective:
CAREFUL EXERCISE SELECTION. Exercises are sequenced to guide students in incremental, step-by-step fashion toward understanding of the concept or procedure involved. Students practice through an appropriate range of applications for the topic, and important variations and discriminations are highlighted. Exercise sets are designed to be challenging but doable, though the amount of instruction required will vary with the experience of the students.
KNOWLEDGE OF RESULTS. We all need feedback and confirmation when
we work, especially when learning new skills. Built into Punchline 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. The student 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.
||MOTIVATING GOALS FOR STUDENTS. Why Was the Nearsighted Snake Unhappy? Each puzzle title is an engaging riddle. Students construct the punchline in the process of checking their answers. The humor acts as an incentive, because students are not rewarded with the punchline until they complete the exercises. While students may wonder aloud who thinks of such dumb jokes, they secretly enjoy them and look forward to solving the puzzles. In addition, discovering the punchline gives a sense of closure and success. Incidentally: He found out that his girl friend was a garden hose.
OPPORTUNITIES TO WORK WITH A PARTNER. Several puzzles in this book are designed for partners. Each student does essentially the same exercises but with different numbers. Partners must work together to get the punchline. Students are encouraged to help each other, since both use the same solution processes, but not copy 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.
In an effort to make these puzzles easy
to use, we have organized them into 20 sections (10 sections in each binder) that correspond to chapters in many algebra textbooks. Each puzzle is designed for a specific topic listed in the Table of Contents and on the page itself. Many puzzles provide space for student work. Hopefully, their self-correcting feature will lighten the burden of correcting assignments. We hope you enjoy them!