- answers
- approaches to an answer
- interpretations
- extensions
- perspectives on a mathematical idea
- layers of complexity
- algorithms

Problems with multiple solutions and/or multiple approaches are often called
*open-ended problems*, although
many other problems also go by that name.

Open and open-ended problems are frequently used in Japanese classrooms to achieve deep understanding of mathematical concepts. In American classrooms, they can be used effectively with teaching methods like the SPOSA model.

Although we are developing a database of potent problems, we don't pretend that by themselves the problems will lead to deep understanding. The teacher counts. Many somewhat normal mathematics problems can be made potent by a teacher willing to accept diversity of thought. And many of these potent problems can be restricted by teachers who have only one right answer or best approach in mind.

The database, which is appearing here slowly, is organized according to the
content standards of NCTM *Principles and Standards 2000*:

data, geometry (without measurement), measurement, numbers, and variables (algebra, functions)

Ideas and suggestions are welcome. Send email to copes at edmath.org:

- What is a favorite potent problems?
- What responses, if any, have you observed students making to the problem?
- What multiple does the problem include--answers, approaches, interpretations, extensions, or intuitively-conflicting models?

*Last modified 20 October, 2005*