This research project is an investigation of the role that examples play in helping learners become proficient in proving mathematical conjectures. Researchers at the University of Wisconsin and New York University are building a framework that characterizes the development of example use as students advance from middle school into post secondary school. Using this developmental information, the researchers are creating instructional strategies that help students think about the nature and value of proof as well as how to construct a mathematical proof.

The researchers are interviewing middle school students, high school students, undergraduate mathematics majors in college, and practicing mathematicians in order to learn how they use examples in the process of creating a proof or a deductive argument. They are using teaching experiments to test various strategies on individual students and to learn more about students' thinking about the process of proving. They are also using small group instruction to experiment with instructional strategies and move closer to a future goal of preparing materials for full class instruction.

Creating and understanding mathematical proofs has always been difficult for students, and yet it is a critical foundation for developing mathematical understanding. Students often cling to the idea that a large set of examples is sufficient for proving a conjecture true. This misconception has often discouraged instructors from using examples in teaching students to prove conjectures. However, examples can stimulate thinking that guides a student to construct a proof through valid, deductive reasoning. This project is advancing understanding of how students learn to prove and providing tested, instructional strategies that teachers can use to help students.