favorite0Each time a new subject is introduced, students work at exploring that subject before they begin writing proofs in that domain.
favorite3One of the authors of this paper and the text, Diane Resek, was a PhD student of Leon Henkin, and worked closely with him on mathematics education projects as well as mathematical logic.
favorite13The text and the course sought to help students learn how to cope with open-ended, unstructured questions; how to formulate conjectures; how to evaluate the reasonableness of a statement; how to make plausibility arguments; how to make constructive use of examples; etc.
favorite3That is, in order to understand a new idea, they must play with it, examine examples, look for counterexamples, ask themselves questions about it, and more.
favorite25Such courses help undergraduate mathematics majors move from learning procedures to learning to function as critical mathematicians in order to understand and work with abstract concepts.