In the introduction the author sets forth her goal for the users of her book: to show children that math can be exciting and fascinating through the hands-on exploration of some of the important ideas in mathematics. What follows is a collection of what are described as "ready-to-go" activities. The topics include two-dimensional and three-dimensional geometry, number theory, topology, and probability. Classics such as infinity, fractals, π, tessellations, Möbius bands, and the Pythagorean theorem appear, some with a new twist. For example, the classic Möbius band experiment involves twisting a band, taping it, and then experimenting with the resultant object. The activity in this book has the children solving a problem involving trekking bugs by creating a Möbius band. I found this new take refreshing and much more interesting.
Each activity begins with a statement of the "BIG idea," that is, the main objective of the activity. This is followed by a discussion of the age-appropriateness of the activity, the content areas covered, and the required process skills and prerequisite knowledge. Each activity contains a list of required materials as well as a discussion of the necessary preparation for the instructor.
With each activity, the author includes helpful suggestions for successful outcomes. These include directions for the instructor on how to get the activity started and keep it moving. In activity #16, Balloons and Dice Game, the students use a carnival game with two dice in order to explore the idea of probability. The author suggests allowing some time for experimentation and then prompting the students with a question such as "How many different rolls would have a sum of 7?" to begin focusing the students' thinking towards a solution. In activity #17, Balances and Equations, the students use a balance, balls, and coins in order to experiment with allowable operations when working with equations. The author suggests insisting that the balance stay level at all times in order to stress the allowable operations and discourage the trial-and-error method. She also gives ideas for expanding some of the exercises for older children. For example, in Balances and Equations older students can practice writing out the equations and the corresponding operations.
In some cases the author mentions potential pitfalls. For example, activity #3, Cubes in a Room, has children working in pairs. One of the students uses cubes to build a three-dimensional object that is hidden from their partner. The builder then must describe the construction accurately enough so that the other student can duplicate the structure. The exercise stresses verbal communication, spatial reasoning and precise mathematical language. The potential pitfall is that children can misunderstand the instructions and think that the object is to have their partner not guess the shape they have built. In hindsight, this is clearly an easy mistake for a child to make. After all, most games they play have a winner and a loser and do not promote cooperation.
The author includes an assessment section at the end of each activity. Criteria are given to help the instructor determine whether or not the students have reached the objectives set at the beginning. This is an important part of the process that is often overlooked, so its inclusion here is very helpful.
My only criticism is that some of the activities are not fully explained and perhaps too much research is left to the instructor. For example, activity #5, Soma Cubes, involves Piet Hein's idea that the six possible irregular shapes formed by four cubes and the one irregular shape formed by three cubes can be arranged to themselves form a cube. Creation of the six irregular shapes is left to the reader. A teacher who is uncomfortable with mathematics may be reluctant to take on this activity. A simple solution, which would avoid cluttering the activities, is to provide an appendix where things such as the six irregular shapes could be shown. This would give those hesitant instructors the reassurance they need to conduct the activity with confidence.
Overall the activities are fun, easy to set up, and allow for the hands-on experience with mathematics that the author stated as one of her goals. Three useful charts in the beginning of the book list activities by content area, process skills, and pre-requisite knowledge. This will help instructors quickly find activities appropriate to the students' age-level, skill set, and that contain the content areas of interest to the class. I would recommend this book to elementary school teachers and instructors of teacher preparatory courses in order to supplement the work already being done in the classroom.
Laurie Johnson (JohnsonLA@trinitydc.edu) is Clare Boothe Luce Assistant Professor of Mathematics at Trinity College in Washington DC. Her academic interests include undergraduate mathematics education and the history of mathematics. She also enjoys traveling and playing competitive volleyball whenever possible