Teaching mathematics for conceptual understanding: An examination of elementary and secondary teacher candidates (Under the direction of Dr. Cyndi Edgington and Dr. Temple Walkowiak).This embedded multiple-case qualitative study aspired to learn more about how elementary (K-5) and secondary (6-12) teacher candidates (TCs) incorporated and leveraged multiple representations to facilitate the development of conceptual understanding among their students. Research highlights the non-trivial nature of teaching mathematics for conceptual understanding, especially for novice teachers. Additionally, there is a need to investigate how teaching practices learned with teacher preparation programs (TPPs) are enacted in the classroom. This study examined how these TCs demonstrated the practice of teaching mathematics for conceptual understanding within their student teaching placement classroom, as evidenced by educative teaching performance assessment (edTPA) artifacts. This study's findings suggest that TCs from both the elementary and secondary case planned for and implemented practices that can support conceptual development. The ways TCs engaged students included explicit connections between representations, as well as discourse and questioning practices. Both cases connected visual, symbolic, and contextual representations throughout planning, instruction, and assessment. The secondary case tended to enact more probing questions during instruction, whereas the elementary case planned for probing but tended to enact more gathering questions. Discourse moments were illuminated both in small group and whole group settings. While the depth with which each case demonstrated these practices that can support conceptual understanding development differed, data can be used to inform TPPs and beginning teacher support programs. [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.]