Characteristics of a Good Mathematical Problem
1. Interesting - as 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 to solve - physical manipulation, observation, measurement, classification, or arranging a pattern. Something to entice students to get involved and focus their attention to bring enough information into their working memory for an initial internal representation that has a chance to lead to a successful solution.
2. Time - the amount of time required to solve the problem is appropriate for the student's developmental 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 with the mental structures available to students so they will be able to organize the information and operate on that information in a manner necessary to solve the problem.
5. Emotional value - The problem has characteristics that make it reasonable to assume students have sufficient self-efficacy and self-confidence to attempt the problem and persist long enough to solve it so they will grow to appreciate and value mathematics in their lives.
6. Communication - The problem provides students with a need or desire to communicate multiple ideas and in multiple ways.
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 it to their world to connect to other mathematical content and process knowledge to increase their feelings of empowerment by knowing.
Dr. Robert Sweetland's Notes ©