A good learning environment is one where:

- students can make mistakes without fear of embarrassment or failure. 

- students are active and interacting with each other. 

- students are allowed time to discover new concepts and to practice these new concepts before they leave the classroom.

A Cooperative Learning classroom can make this possible. 

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Imagine walking into a mathematics classroom where students are working in cooperative groups  (four or five students) to determine the relationship between the circumference and diameter of a circle. They are engaged in working cooperatively as the teacher moves about the room, observing and offering suggestions when needed. The classroom is decorated with students' original geometric artwork and posters made for student presentations.

Throughout the school year, the students and teacher are focusing on developing conjectures and understanding them without feeling overwhelmed by unfamiliar geometry concepts or procedures. When the class is investigating the polygon sum conjecture for example, you see groups using a variety of tools for their investigations: 

- some are using rulers and protractors to draw and measure polygons;

- some are cutting out polygons, reassembling the pieces to examine angle sums;

- others are at the computer, using a dynamic geometry program to observe angle sums as they change the shapes and types of polygons they are exploring;

-still others are using paper folding with patty papers to demonstrate the angle sums. 

Students are discussing their conjectures, using calculators to verify conclusions, comparing and summarizing results, asking “What if . . .,” and planning how they will present their conclusions to the entire class. They are clearly comfortable working in teams and are experienced in using data to discern patterns.

By the end of class, the groups have reported their results, final clarifications have been made, and the students have begun to work on their homework assignment after returning their tools to the storage areas. This activity is typical of what you should expect in a cooperative learning classroom. Through inductive learning, students ground themselves in geometric ideas and then verify their conjectures with more formal deductive reasoning.