Teachers' questioning is a key practice that influences student learning, yet not all teachers' questioning is equally effective, and fine-grained analyses uncovering the details of teachers' questioning are scarce. My study investigated the types of questions asked by three in-service elementary school math teachers, the associated levels of cognitive demand, and the relationship between these types, cognitive demand levels, and three characteristics of the teachers known to influence questioning practices: mathematical knowledge for teaching (MKT), years of experience, and mathematical beliefs. The data was drawn from a major two-year project on teacher professional development that aimed to improve in-service teachers' knowledge and pedagogical skills in mathematics. Using a mixed-methods approach, I analyzed four videorecorded lessons, an audiorecorded semi-structured interview and four post-teaching coaching interviews, as well as data from a mathematical beliefs survey for each teacher. 16 specific criteria known to form part of MKT were analyzed, while the beliefs survey data was used to calculate a rating of the productivity of the teachers' beliefs based on guidelines from the National Council of Teachers of Mathematics (NCTM). Both within-case and cross-case analysis were carried out of the teachers' question types and levels of cognitive demand. Although the study found that the three participants asked a variety of question types, the majority of these types were asked at a low level of cognitive demand. The study found that teachers' MKT and their mathematical beliefs both appeared to be important factors influencing their questioning--an alignment of both MKT and productive beliefs was associated with greater use of question types more focused on student thinking and with higher levels of cognitive demand--whereas the influence of years of teaching experience was more indirect. This has implications for teacher training programs, as both MKT and beliefs can be directly acted upon by training programs in a way that years of experience cannot. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]