Teachers in Saudi Arabia are attempting to advance their teaching in mathematics to address specific reforms by the Ministry of Education. Saudi teachers must improve their students' thinking through engagement in problem solving. This qualitative study investigated how teachers use knowledge of student mathematical learning and how they promote students' experiences of various mathematical processes. The research investigated the process standards of the National Council of Teachers of Mathematics (2000) that teachers should encourage students to experience during instruction. The study gathered data from 12 teachers at female-only middle schools in a city in eastern Saudi Arabia. The investigation used, in sequence, three methods: classroom observations, initial interviews, and scenario-based interviews. The observations used Instructional Quality Assessment rubrics (Boston & Wolf, 2006) and field notes. The initial interviews linked to the observations and asked teachers about their instructional philosophy and how they supported student learning processes. Delving deeper, the scenario-based interviews helped the researcher to understand how the teachers might respond to novel mathematics teaching situations. Most of the findings related to the process of problem solving. The participants overtly guided students while solving problems. Teachers perceive that discovery problem solving can be achieved through gradual hints and reminders to the students. Saudi teachers appear to understand the power of various features of problem solving such as discovery, high-level tasks, and encouraging multiple solutions. Further, the study revealed that teachers encourage students' verbal and written expression. The participants believed that their students can be taught about mathematical connections in a declarative way. The observed and indicated problem-solving approaches lack many of the necessary features cited in the literature on promoting students' mathematical processes and supporting students' understanding of mathematics. The teachers' declarative approaches for helping students form mathematical connections do not align with practices cited in research literature and reform documents, which recommend engaging students in mathematical activities that allow them to think of and experience mathematical connections. An important interpretation of the findings is that teachers in Saudi Arabia tend to avoid students' struggling while solving complex problems even if such struggle could deepen their mathematical thinking and learning. [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.]