Probability and statistical inference are important ideas with a remarkably wide range of applications. However, psychological and instructional studies conducted in the last two decades have consistently documented poor understanding of these ideas among different population across different settings. The purposes of this dissertation study are to understand teachers' understandings of probability and statistical inference; and to develop theoretical frameworks for understanding teachers' understandings. To this end, our research team conducted an eight-day seminar with eight high school statistics teachers in the summer of 2001. The data we collected include videotaped sessions and interviews, teachers' written work, and researchers' field notes. My analysis of the data revealed that: 1) There was a complex mix of conceptions and understandings of probability and statistical inference, both within individual teachers and among the group of teachers, that are often situationally triggered, which are often incoherent when the teachers try to reflect on them, and which do not support their attempts to develop coherent pedagogical strategies regarding probability and statistical inference; 2) teachers' conceptions of probability and statistical inference are highly compartmentalized: They did not understand probability and statistical inference as a scheme of interconnected ideas, but rather, ideas that are isolated from one another; 3) many teachers had a conception of learning as "knowing how to solve problems", and teaching as "displaying the expertise of problem solving". These conceptions of learning did not support their engagement in reflective conversations about the ideas in probability and statistical inference. The implications of these results include: 1) Understanding statistical inference and teaching effectively entails a substantial departure from teachers' prior experience and their tacit beliefs; and 2) the goal of teachers professional development should be helping the teachers develop understandings of probability and statistical inference as a scheme of interrelated ideas by exerting a great amount of coerced effort in helping teachers develop the capacity and orientation in thinking of a distribution of sample statistics.