Mathematics classrooms where students sit passively, working in isolation to copy notes, should be a thing of the past. Instead, the classroom should be alive with collaborative problem solving activity. Current professional standards (AMATYC and MAA) suggest that an active classroom learning environment should be the norm. Too often instructors and students spend much of their time focusing on basic computational skills rather than engaging in mathematically rich problem-solving experiences. Worthwhile mathematical thinking occurs when students struggle and learn to overcome initial frustrations to make sense of powerful ideas while solving realistic problems. Developing this type of thinking requires a classroom environment where students are comfortable sharing their correct or incorrect ideas in the public forum of a classroom setting. However, such an environment does not occur naturally: it must be developed by the instructor. The ideal classroom learning environment is characterized by the following attributes.

- is positive and cooperative
- piques student interest and provides the opportunity to enjoy learning
- creates a strong personal sense of motivation and responsibility
- encourages relevant questions and discussions
- helps students learn that making mistakes is a natural and acceptable part of the learning process
- develops student confidence in making sense of mathematics
- produces an understanding that
*correctness* is determined by the logic of mathematics, not by the instructor, a “smart” student, or the back-of-the-book

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