The Purpose of this Book
This book is intended as a resource for middle school and high school math teachers, in part, to supplement the normal daily homework and classroom material (such as the Making Math Meaningful middle school and high school workbooks).
There may be times when things seem to get dull and the students begin to lose their spark. It is then that the teacher knows it is time to do something different. This book provides ideas for that “something different.”
What’s New in the Third Edition?
· Now includes easier puzzles for 4th and 5th graders
· Additional puzzles for grades 6 – 12
· More than 100 new puzzles in this edition
What Makes This Book Unique?
There are many math puzzle books available today. However, it can be daunting for a teacher (especially a teacher in the lower grades for whom math is not a specialty) to pick up a math puzzle book that consists of a couple hundred puzzles, and find a good one that would work well for a math class tomorrow.
This book is specifically geared toward the teacher who needs to find an excellent puzzle or game for tomorrow’s math class. We have tried to limit the number of puzzles and games to just a few excellent ones. We have categorized the puzzles according to grade level. For example, in order to find a puzzle, the teacher needs only to consider the 20 puzzles listed under that grade.
Skills and Thrills
Unfortunately, today there is an over-emphasis on the mastery of skills in mathematics curricula. Even for students who appear to be successful, their experience with math amounts to a long list of procedures to be followed in order to solve problems, many of which may seem to be quite meaningless. All too often the repetition and drill of solving endless problems from a textbook or workbook can kill the students’ natural enthusiasm for learning. Students rarely have the opportunity to experience the thrill of mathematics.
What is this thrill of mathematics? It is perhaps best experienced when students encounter a challenge – often a challenge that at first seemed formidable – and they persevere and emerge successful. A good math puzzle or game provides an excellent opportunity for such a thrill.
This is not to say that skills aren’t important; they are. But, it is equally important for students to experience meaningful math, and to have enthusiasm for learning math.
The art of teaching math is, at least partly, how to balance all of the above.
The Art of Problem Solving
There’s a difference between solving problems (e.g., doing a problem on a homework sheet) and problem solving. To some degree, real problem solving should receive a greater emphasis in the later high school years, but there should be elements of problem solving in the earlier years as well.
Usually solving a problem (e.g., as given as part of a homework assignment) amounts to following a procedure that the student has been previously shown how to do. Often, this aspect of math teaching is essential and effective. However, even a typical word problem isn’t true problem solving.
So what is true problem solving? There are shades of gray here, but true problem solving must include an experience of uncertainty. The student might say to himself, “I have never seen this before. I have no idea what to do.” Thus begins the experience of problem solving.
These kinds of problem solving experiences may occasionally be encountered through a daily homework assignment, but often the teacher needs to carefully plan these experiences. A good puzzle or game is one way to give the students a genuine problem solving experience.
Guidelines for Using This Book
This book is divided into the following sections: