Prospective teachers, who learn mathematics by being actively involved in doing mathematics, will be more likely to teach in the same manner. The features designed to help accomplish this approach to learning are as follows:
Active Learning Each activity set uses physical materials or visual models to provide a context for understanding. The questions and activities in each activity set are sequentially developed to encourage discovery and to proceed with depth into the topic.
Cooperative Learning The activity sets can be done individually or in small groups. One activity, Logic Problems for Cooperative Groups, is designed for small group interaction.
Individual Reflections Throughout the activity sets students are encouraged to describe patterns, discuss their thinking, and write explanations of their reasoning.
Manipulative Kit and Material Cards The Manipulative Kit packaged with each Activity Book includes 9 common manipulatives on color cardstock and labeled ziplock bags in which to store them. There are 40 additional material cards in the Activity Book that contain manipulatives, models, grids, templates, game mats and other materials to be used in the activities.
Pedagogy The activity sets demonstrate ways that manipulatives and visual models can be used in classrooms to promote conceptual understanding and mathematical thinking. There are concrete or visual models for teaching the following:
| reasoning | even and odd numbers |
| numeration | factors and primes |
| whole numbers | greatest common divisor |
| fractions | least common multiple |
| integers | geometry |
| decimals | length, area and volume |
| percent | statistics and probability |
| patterns and sequences | story problems |
| algebraic expressions | metric measurement |
| indirect measurement | |
Metric System There are explorations, games and activities for learning the metric system in Chapter 10. Metric units are used in several activities after that chapter.
Just for Fun All thirty-four activity sets are followed by Just for Fun activities. These are usually related to the topics of the activity sets but extend the ideas to recreational or artistic areas.
Classroom Ideas At the end of each chapter a Suggested Classroom Activity is given for students to try with children. All of the models and manipulatives are appropriate for use with children.
Readings for More Classroom Ideas Many creative teachers have written about activities they have successfully used in their classrooms. Also, the National Council of Teachers of Mathematics has sponsored many booklets that discuss reform issues for teachers. A selected list of readings appears at the end of each chapter.
Puzzlers These brainteasers are interspersed throughout the text to add variety and provide practice in problem solving.