Characteristics of a Good Mathematical Problem

1. Interesting - either it is a topic, subject, or includes people or characters that are interesting to the students. It is fascinating enough to create curiosity and develop a need for a solution within the students. It requires some kind of action - physical manipulation to solve (observation, measurement, classification, or arranging a pattern) that will entice students to get involved.

2. Time - the amount of time that is required to solve the problem matches the student's developmental interest level.

3. Developmentally appropriate - The problem can be solved in a way that will not contradict the students developmental way of understanding, if the student isn't ready for a developmental change.

4. Understandable - Has at least one solution that can be understood by the students - A solution is possible that students have a mental structure that will be able to organize the information and operate on that information in the manner necessary to solve the problem.

5. Emotional value - The problem is such that it is reasonable to assume that the students have will maintain their self-confidence and self-efficacy sufficiently to solve it and appreciate and value mathematics in their lives.

6. Communication - The problem provides students with a need or desire to communicate, multiple ideas to communicate, and a different ways those ideas can be communicated.

7. Mathematical value - The problem requires mathematical ideas that are powerful and something the students should know at this point in their lives, will be able to apply to their world, will be able to connect to other mathematical content and process knowledge, and will feel empowered by knowing.