In this paper, we explore the role that examples play as mathematicians formulate conjectures, and we describe and exemplify one particular example-related activity that we observed in interviews with thirteen mathematicians. During our interviews, mathematicians productively used examples as they formulated conjectures, particularly by creating…

This study investigated the effects of applying mathematical modeling on revising students' preconception of the process of optimizing area enclosed by a string of a fixed length. A group of 28 high school pre-calculus students were immersed in modeling activity that included direct measurements, data collecting, and formulating algebraic…

Describes the model for decision making used in inferential statistics and real-world applications that parallel the statistical model. Discusses two activities that ask students to write about a personal decision-making experience and create a mock trial in which the class makes the decision of guilt or innocence. (MDH)