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Schools have the obligation to challenge students to create in every field they ask students to learn. In some subject areas, students, their parents, and society have come to expect schools to offer the challenge of creating. In mathematics this is rarely the case.

In practice, this means that the teaching of youngsters to analyze and criticize, while important and necessary is not sufficient. Students must also be challenged to invent and create….

I assert that the essence of mathematical creativity lies in the making and exploring of mathematical conjectures.

Judah L. Schwartz
The Geometric Supposer: What Is It a Case of?, 1993