- students who learn mathematics constructively through the appropriate use of manipulatives, models, and diagrams, are more likely to develop a solid conceptual basis.

- a concrete approach diminishes the mathematical anxiety often accompanying a more abstract approach.

- tactile and visual approaches provide mental images which can be more easily retained than symbols and called forth, as needed, in mathematical thinking.

- prospective teachers who learn mathematics by being actively involved in doing mathematics, will be more likely to teach in the same manner.

- the best way to inform students of current mathematical reforms is to involve them in a learning environment which incorporates them.

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 groups 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 contains 9 common manipulatives on colored cardstock together with envelopes to organize them. The Activity Book also has 39 additional material cards with 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:

Metric System There are explorations, games and activities for learning the metric system in Chapter 11. Metric units are used in several activities after that chapter.

Calculators The use of calculators is encouraged throughout the book. Several activities are designed to be carried out with calculators.

Just for Fun Thirty-seven of the 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 which discuss reform issues for teachers. A selected list of readings appears at the end of each chapter.

Puzzlers Brain teasers are interspersed throughout the text to add variety and provide practice in problem solving.