Though the United States maintains a great presence in our global economy, our country is still lagging behind many others in terms of achievement in mathematics. Developing the ability to think creatively and communicate effectively is paramount to ensuring our students are prepared for the competitiveness of the 21st century world. Rich mathematical tasks provide students with opportunities to make sense of problems and to work productively in teams to persevere in solving them. Purposeful questioning assists teachers in encouraging students to fully articulate their thinking to others. Both rich mathematical tasks and purposeful questioning result in higher levels of student engagement in their learning through peer-to-peer discourse. This study will seek to understand teacher beliefs regarding the use of rich mathematical tasks and purposeful questioning as strategies for promoting student discourse and the frequency with which they are currently used. Supporting and encouraging teachers to provide opportunities for students to develop effective communication and problem-solving skills will have far reaching benefits for our schools and country. [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.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]