Theses and Dissertations Collection

Mathematicians routinely use the skill of self-generation of examples to test and verify mathematical principles, theorems, and concepts, and yet the processes through which undergraduates learn to productively generate examples is not well understood. Students in multiple first-semester calculus courses participated in a teaching experiment designed to develop the mathematical skill of example generation and productive use of these examples to learn novel mathematical concepts. Through three iterations, a hypothetical learning trajectory was tested and refined to align with the actual learning observed in students. The findings show that students participating in the teaching experiment became more self-directed, productive, and skillful example generators when learning novel mathematical concepts. The study provides evidence that the use of example generation is a plausible teaching method for introducing novel mathematical concepts in a first-semester calculus course.